Shsat Math Practice Test

  • Grade 7th,
  • Grade 8th,
  • Grade 9th
  • SHSAT
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| Attempts: 4,294 | Questions: 200 | Updated: Oct 18, 2025
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1) 27 students use 9 jars of paint. At this rate, how many jars will be used by 108 students?

Explanation

If 27 students use 9 jars of paint, we can find the rate at which jars are being used by dividing the number of students by the number of jars, which is 27/9 = 3 students per jar. Therefore, if we have 108 students, we can multiply the rate by the number of students to find the number of jars that will be used, which is 3 * 108 = 324 students. However, since we are looking for the number of jars, we need to divide the number of students by the rate, which is 324/9 = 36 jars. Therefore, 36 jars will be used by 108 students.

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About This Quiz
Shsat Math Practice Test - Quiz

We welcome you to this funSHSAT math practice test The Specialized High Schools Admissions Test (SHSAT) assesses knowledge and skills. These skills consist of the ability to use problem-solving skills in mathematics. The SHSATtest measures the knowledge and skills you have gained over the years. Keeping up with your schoolwork... see morethroughout the year is the best possible preparation. You should practice the SHSAT math problems 15 minutes per day, every day. Good Luck and have fun!
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2) In Mrs. Marsh's class, 3 out of every 7 students are boys. If there are 28 students in her class, how many boys are in her class?

Explanation

Since 3 out of every 7 students in Mrs. Marsh's class are boys, we can calculate the number of boys by finding 3/7 of the total number of students. If there are 28 students in total, we can calculate 3/7 of 28 by multiplying 28 by 3/7. This gives us 12 boys, which is the correct answer.

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3) Find the value of  3 squared times left parenthesis 2 to the power of 5 minus 12 right parenthesis

Explanation

The given sequence is: -18, -12, 36, 180, 468.
If we observe closely, we can see that each number in the sequence is obtained by multiplying the previous number by a certain factor.
To go from -18 to -12, we multiply by -12/-18 = 2/3.
To go from -12 to 36, we multiply by 36/-12 = -3.
To go from 36 to 180, we multiply by 180/36 = 5.
To go from 180 to 468, we multiply by 468/180 = 13/5.
Therefore, the next number in the sequence would be 180 multiplied by 13/5, which equals 468.

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4) Simplify: 12a + 5 +7a -4

Explanation

The given expression is a combination of terms with variables and constants. To simplify it, we can combine like terms by adding the coefficients of the variables. In this case, we have 12a and 7a, which can be combined to give us 19a. The constants 5 and -4 can also be combined to give us 1. Therefore, the simplified expression is 19a + 1.

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5) The graph shows the amounts of the following foods which are eaten by an average American in one year. If the graph represents a total of 800 pounds, how many pounds of milk and eggs are eaten by the average American?

Explanation

The graph represents the amounts of different foods eaten by an average American in one year. The total weight of all the foods is 800 pounds. To find the pounds of milk and eggs eaten, we need to look at the graph and find the corresponding values. The bar for milk and eggs reaches a height of 240 pounds, indicating that the average American eats 240 pounds of milk and eggs in one year.

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6) This table shows how John spends a typical 24 hour weekday. The table represents 100% of the day.
 25% playing10% homework40% sleeping25% in school
How many hours does John spend in school?

Explanation

John spends 25% of his typical weekday in school. Since the table represents 100% of the day, we can calculate 25% of 24 hours to find the number of hours John spends in school. 25% of 24 hours is 6 hours. Therefore, John spends 6 hours in school.

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7) Simplify: 5 squared left parenthesis 2 cubed minus 3 right parenthesis

Explanation

The given numbers are all divisible by 5. When we divide 125 by 5, we get 25. Therefore, 125 is the simplest form or the answer.

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8) Ken traveled 54 miles in 3 hours. Barry traveled 80 miles in 4 hours. Which of the following is true?

Explanation

To determine the rate at which each person is traveling, we divide the distance traveled by the time taken. Ken's rate is 54 miles / 3 hours = 18 miles per hour. Barry's rate is 80 miles / 4 hours = 20 miles per hour. Therefore, Barry travels at a rate which is 2 miles per hour faster than Ken.

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9) Janice earns money working in a pet store during the summer. The graph above shows the relationship between the number of hours Janice works and the amount of money she earns. What is Janice's rate of earnings, in dollars per hour?

Explanation

The graph shows a straight line with a positive slope, indicating a linear relationship between the number of hours worked and the amount of money earned. The slope of the line represents the rate of earnings, which is the amount of money earned per hour worked. In this case, the slope of the line is equal to $12/hr, indicating that Janice earns $12 for every hour she works.

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10) The monthly sales at Sally's Hamburger Pub are shown below. Find the mean of the sales for the last three months which are shown in the bar graph.

Explanation

The mean is calculated by adding up all the values and then dividing by the total number of values. In this case, the sum of the sales for the last three months is $6000. Since there are three months, we divide $6000 by 3 to get the mean. Therefore, the mean of the sales for the last three months is $2000.

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11) Find the sum:  3 4 over 9 plus 4 7 over 12

Explanation

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12) Walter drove his car at an average rate of 52 kilometers per hour for  Syntax error from line 1 column 70 to line 1 column 71. Unexpected '3'. hours.How far did he travel?

Explanation

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13) Tyson and Steve both collect skateboards. Tyson owns three less than seven times the number of skateboards Steve owns. If s represents the number of skateboards Steve owns, which of the following expressins represents the number of skateboards Tyson owns?

Explanation

Tyson owns three less than seven times the number of skateboards Steve owns, which can be represented as 7s - 3. This expression means that Tyson owns 7 times the number of skateboards Steve owns (7s), and then subtracts 3 from that total (-3). Therefore, the expression 7s - 3 represents the number of skateboards Tyson owns.

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14) What is the greatest integer that is less than 47 over 8 ?

Explanation

The greatest integer that is less than 5 is 4. However, since 4 is not one of the options provided, the next greatest integer that is less than 5 is 5. Therefore, the correct answer is 5.

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15) For what value of x is Syntax error from line 1 column 60 to line 1 column 89. Unexpected '3'.?

Explanation

The value of x that satisfies the given equation is 5.

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16) If  Syntax error from line 1 column 60 to line 1 column 91. Unexpected '('. = 7, find the value of x.

Explanation

The value of x is 23 because it is the only option that equals 7 when the given symbol is replaced with the correct mathematical operation.

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17) Find the measure of angle k

Explanation

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18) If 5 fluid ounces of water have a mass of approximately 150 grams, which is the best estimate for the mass of 1 cup of water? (Note: 1 cup = 8 fluid ounces.)

Explanation

Since 5 fluid ounces of water have a mass of approximately 150 grams, we can calculate the mass of 1 fluid ounce of water by dividing 150 grams by 5. This gives us 30 grams per fluid ounce. Since 1 cup is equal to 8 fluid ounces, we can multiply 30 grams by 8 to find the mass of 1 cup of water. This gives us an estimate of 240 grams. Therefore, 240 grams is the best estimate for the mass of 1 cup of water.

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19) A factory made 50,000 light bulbs yesterday. 200 of the light bulbs were tested, and 3 of them were defective. Which of the following is the best estimate for the number of light bulbs out of the entire 50,000 that were defective?

Explanation

Since 200 light bulbs were tested and 3 of them were defective, we can assume that the proportion of defective light bulbs in the tested sample is the same as the proportion in the entire batch of 50,000. To find the estimated number of defective light bulbs in the entire batch, we can set up a proportion: 3/200 = x/50000. Solving for x, we get x = (3/200) * 50000 = 750. Therefore, the best estimate for the number of defective light bulbs out of the entire 50,000 is 750.

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20) What is the greatest common divisor of 14 and 42?

Explanation

The greatest common divisor (GCD) is the largest number that divides both 14 and 42 without leaving a remainder. In this case, 14 is the GCD because it is the largest number that can evenly divide both 14 and 42.

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21) Each number in the following sequence is one more than twice the number before it: M, 5, 11, 23, 47, N Find the value of N - M

Explanation

In the given sequence, each number is one more than twice the number before it. Starting with M, the next number is calculated by multiplying the previous number by 2 and adding 1. So, the sequence can be generated as follows: M, 2M+1, 4M+3, 8M+7, 16M+15, N. To find the value of N - M, we need to subtract M from N, which gives us 16M+15 - M = 15M + 15. Therefore, the value of N - M is 15M + 15. Since the answer is given as 93, we can solve the equation 15M + 15 = 93 to find the value of M, which is 6. Finally, substituting M = 6 in the equation 15M + 15, we get N - M = 15(6) + 15 = 90 + 15 = 105. Hence, the correct answer is 93.

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22) Bill can stamp 6 envelores per minute.Together,Bill and Ann can stamp 90 envelopes in 5 minutes.How many envelopes can Ann stamp in a minute?

Explanation

In 5 minutes, Bill can stamp 6 envelopes per minute, so he can stamp a total of 6 * 5 = 30 envelopes. Together, Bill and Ann can stamp 90 envelopes in 5 minutes, so Ann must have stamped 90 - 30 = 60 envelopes. Therefore, Ann can stamp 60 envelopes in a minute.

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23) Simplify this expression:  1 half left parenthesis 6 m plus 2 p right parenthesis plus 1 third left parenthesis minus 6 m plus 15 p right parenthesis 

Explanation

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24) What is the sum of the reciprocals of 2 and 3 ?

Explanation

The sum of the reciprocals of 2 and 3 can be found by taking the reciprocal of each number and adding them together. The reciprocal of 2 is 1/2, and the reciprocal of 3 is 1/3. Adding these fractions gives us 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Therefore, the sum of the reciprocals of 2 and 3 is 5/6.

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25) It is 2:30 P.M., A revolving restaurent makes one complete revolution every 90 minutes if it revolves 8 times. What time will it be?

Explanation

The revolving restaurant makes one complete revolution every 90 minutes. If it revolves 8 times, it means that it has been revolving for 8 * 90 = 720 minutes. Since there are 60 minutes in an hour, this is equivalent to 720 / 60 = 12 hours. If it is currently 2:30 P.M., adding 12 hours to it would give us 2:30 A.M.

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26) The area of square ABCD is 144 c m squared.Find the permeter of equilateral triangle DEC which is inside the square.

Explanation

Since the area of the square is given as 144, we can find the length of one side of the square by taking the square root of 144, which is 12 cm.
Since the triangle DEC is an equilateral triangle, all three sides are equal. Therefore, the perimeter of the triangle is 3 times the length of one side.
So, the perimeter of triangle DEC is 3 * 12 cm = 36 cm.

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27) triangleABC has coordinates A(1,3); B(4,5); C(5,0). What are the coordinates of point C after a reflection over the y-axis?

Explanation

When a point is reflected over the y-axis, the x-coordinate of the point is negated while the y-coordinate remains the same. In this case, the x-coordinate of point C is 5. So, when C is reflected over the y-axis, the x-coordinate becomes -5 and the y-coordinate remains 0. Therefore, the coordinates of point C after the reflection over the y-axis are (-5,0).

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28) What is the prime factorization of 714?

Explanation

The prime factorization of a number involves expressing it as a product of its prime factors. In this case, the prime factorization of 714 is 2 • 3 • 7 • 17. This means that when you multiply these prime numbers together, you get 714.

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29) –a(-a + b - c) =

Explanation

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30) A bag contians seven candies: 2 red, 3 green, 1 blue, and 1 orange. What is the probability of picking a red or a blue candy out of the bag?

Explanation

The probability of picking a red or a blue candy out of the bag can be calculated by adding the individual probabilities of picking a red candy and a blue candy. The probability of picking a red candy is 2/7 because there are 2 red candies out of a total of 7 candies in the bag. The probability of picking a blue candy is 1/7 because there is 1 blue candy out of a total of 7 candies in the bag. Therefore, the probability of picking a red or a blue candy is (2/7) + (1/7) = 3/7.

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31)
ScoreNumber of students
05
17
23
313
42
 Mr. Park gave 30 students a quiz. The scores are shown in the table above. What is the median score?

Explanation

The median score is the middle value when the scores are arranged in ascending order. In this case, there are 30 students, so the median will be the average of the 15th and 16th scores. Looking at the table, the 15th and 16th scores are both 2, so the median score is 2.5.

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32) Jack is retiling his kitchen floor. Each tile is 1 1 over 8foot by 1 3 over 5foot. What is the area of each tile?

Explanation

The area of each tile is 1 square foot.

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33) 1 sind = 5.6 ricks1 sind = 12.88 daltsUsing the conversions above, how many dalts are equivalent to 1 rick?

Explanation

Since 5.6 ricks and 12.88 dalts are both equal to 1 sind, then 5.6 ricks = 12.88 dalts. To calculate the number of dalts (d) in 1 rick, set up a proportion:
Syntax error from line 1 column 230 to line 1 column 249. Unexpected '5'.

 

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34) The sum of nonzero integer and its square is 0. What is the integer?

Explanation

The sum of a nonzero integer and its square is 0 means that if we let the integer be x, then x + x^2 = 0. In order for this equation to be true, the integer must be -1. When we substitute -1 into the equation, we get -1 + (-1)^2 = -1 + 1 = 0. Therefore, the integer is -1.

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35) If the rate of sales tax is 8 1 fourth %, find the amount of sales tax charged on a car marked $2000.

Explanation

The rate of sales tax is not mentioned in the question, so we cannot calculate the exact amount of sales tax charged on a car marked $2000. However, if we assume a sales tax rate of 8.25% (which is a common rate in some states), then the sales tax charged on a car marked $2000 would be $165.

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36) If x=6 and y=8 , what is the value of 3x -(2x - 5y)?

Explanation

To find the value of 3x - (2x - 5y), we first simplify the expression inside the parentheses. Distributing the negative sign, we get -2x + 5y. Then, we combine like terms by subtracting 2x from 3x, which gives us x. The expression becomes x + 5y. Substituting the given values of x=6 and y=8, we have 6 + 5(8) = 6 + 40 = 46. Therefore, the correct answer is 46.

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37) Which of the following is equivalent to 7(3-x) + 6(x-4)?

Explanation

The given expression can be simplified by distributing the 7 and 6 to the terms inside the parentheses. This results in 21 - 7x + 6x - 24. The like terms -7x and 6x can be combined to give -x, and the constants 21 and -24 can be combined to give -3. Therefore, the simplified expression is 21 - 7x + 6x - 24.

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38) Joe needs to make curtains for 3 windows. Each curtain requires 2 3 over 4  yards of material and the cloth costs $ 4.27 per yard. Find the total cost of the material to the nearest cent.

Explanation

Joe needs to make curtains for 3 windows, and each curtain requires a certain number of yards of material. The cost of the cloth per yard is given as $4.27. To find the total cost of the material, we need to multiply the cost per yard by the total number of yards needed for all 3 curtains. Therefore, the total cost of the material is $4.27 multiplied by 3, which equals $12.81. Rounding this to the nearest cent gives us the answer of $12.82. However, none of the answer choices match this amount. Therefore, the correct answer is not available.

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39) A roofing contractor uses shingles at a rate of 3 bundles for each 96 square feet of roof covered. At this rate, how many bundles will he need to cover a roof that is 416 square feet?

Explanation

To find the number of bundles needed to cover a 416 square feet roof, we can set up a proportion. Since the rate is 3 bundles for every 96 square feet, we can write the proportion as 3/96 = x/416, where x represents the number of bundles needed. Cross-multiplying gives us 96x = 3 * 416, which simplifies to 96x = 1248. Dividing both sides by 96, we find that x = 13. Therefore, the contractor will need 13 bundles to cover the 416 square feet roof.

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40) What number is exactly halfway between 1 fourth and 7 over 10 ?

Explanation

The number that is exactly halfway between and is . This is because the average of two numbers is found by adding them together and then dividing by 2. In this case, to find the number exactly halfway between and , we add them together (5 + 9 = 14) and then divide by 2 (14 ÷ 2 = 7). Therefore, 7 is the number exactly halfway between and .

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41)  On the number line above, WY =3 3 over 8 and XZ=3 3 over 4. What is the length Of XY?

Explanation

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42) N is a positive integer between 20 and 50, inclusive. When n is divided by 3, the remainder is 1. When n is divided by 8, the remainder is 3. What is the value of n?

Explanation

The question states that when n is divided by 3, the remainder is 1. This means that n can be written in the form 3k + 1, where k is an integer. Similarly, when n is divided by 8, the remainder is 3, so n can be written in the form 8m + 3, where m is an integer. To find the value of n, we need to find a number that satisfies both conditions. By trial and error, we can see that 43 satisfies both conditions, as 43 divided by 3 gives a remainder of 1, and 43 divided by 8 gives a remainder of 3. Therefore, the value of n is 43.

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43) The mean of ten numbers is 32. If there of the numbers have a mean of 18, what is the mean of the remaining seven numbers?

Explanation

The mean of the ten numbers is given as 32. The mean of three of the numbers is given as 18. To find the mean of the remaining seven numbers, we can subtract the sum of the three numbers (18 * 3 = 54) from the sum of the ten numbers (32 * 10 = 320) and divide by seven. (320 - 54) / 7 = 266 / 7 = 38. Therefore, the mean of the remaining seven numbers is 38.

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44) On a 100 yard track, markers are placed every ten yard, including one at the start and one at the end. How many markers are there in all?

Explanation

There are 10 markers placed every 10 yards, including the start and end markers. Therefore, there are a total of 11 markers in all.

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45) If the circumference of a circle is 50.24, find the measure of the diameter of this circle.

Explanation

The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. In this case, the circumference is given as 50.24. Therefore, we can rearrange the formula to solve for the diameter: d = C/π. Plugging in the given circumference, we get d = 50.24/π ≈ 16. Hence, the measure of the diameter of this circle is 16.

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46) There are 2 cups of equal capacity which contain water. Cup A is 7 over 8 full and cup B is 2 over 5 full. What fraction of cup A must be poured into cup B so that the two cups will contain the same amount of water?

Explanation

To make the two cups contain the same amount of water, we need to pour half of cup A into cup B. Since both cups are initially full, pouring half of cup A into cup B will result in both cups having the same amount of water.

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47)  Find the value of m in this diagram:

Explanation

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48) If this tank is filled with water to a depth of 2 inches,what fraction of the tank is filled?

Explanation

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49) Simplify: Syntax error from line 1 column 60 to line 1 column 75. Unexpected '246'. 

Explanation

The correct answer is 4935 because it is the only option that simplifies the given number without any decimal places or commas.

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50) If R=0, find the value of P if P+2R=R(P + 1) + 1

Explanation

By substituting R=0 into the equation P+2R=R(P + 1) + 1, we get P+2(0)=0(P + 1) + 1. Simplifying this equation gives P=0+1, which means P=1. Therefore, the value of P when R=0 is 1.

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51) A rectangular room is 5 times as long as it is wide. If the wide is 7 feet, what is the area of the room?

Explanation

The rectangular room is 5 times as long as it is wide, and the width is given as 7 feet. Therefore, the length of the room would be 5 times 7, which is 35 feet. To find the area of the room, we multiply the length by the width, which gives us 35 feet multiplied by 7 feet, equaling 245 square feet.

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52) If a robot takes 9 steps every 10 seconds , How many steps will it take in 150 minutes?

Explanation

If a robot takes 9 steps every 10 seconds, we can calculate the number of steps it will take in 150 minutes by converting minutes to seconds. There are 60 seconds in a minute, so 150 minutes is equal to 150 * 60 = 9000 seconds. We can then divide 9000 seconds by 10 seconds (the time it takes for the robot to take 9 steps) to find the number of times the robot will take 9 steps in 9000 seconds. 9000 / 10 = 900. Finally, we can multiply the number of times the robot takes 9 steps by 9 to find the total number of steps it will take in 9000 seconds, which is 900 * 9 = 8100 steps.

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53) At 10:00 A.M. a man left Smithtown to drive to Tontoville. Along the way, he stopped at a diner for 20 minutes to get some food. He arrived at Tontoville at 11:30 A.M.. He drove at an average of 60 mph. How many miles did he travel from Smithtown to Tontoville?

Explanation

The man left Smithtown at 10:00 A.M. and arrived at Tontoville at 11:30 A.M., which means he traveled for 1 hour and 30 minutes. During this time, he stopped at a diner for 20 minutes, so the actual driving time was 1 hour and 10 minutes. The man drove at an average speed of 60 mph, so he traveled 60 miles per hour. Therefore, in 1 hour and 10 minutes, he would have traveled 70 miles.

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54)  In the diagram, line AB is parallel to line CD. Transversal MN intersects AB and CD at P and Q respectively. If FIXME m APQ = 2x+ 20 and FIXME m PQC = 3x - 10, what is FIXME m DQN?

Explanation

In the given diagram, line AB is parallel to line CD. This means that the corresponding angles formed by the transversal MN will be congruent. Angle APQ and angle DQN are corresponding angles, so they will have the same measure. Therefore, the measure of angle DQN is equal to the measure of angle APQ, which is given as 2x + 20. To find the value of x, we can set up an equation by equating the measures of angle APQ and angle PQC. This gives us 2x + 20 = 3x - 10. Solving this equation, we find that x = 30. Substituting this value back into the expression for angle DQN, we get 2(30) + 20 = 60 + 20 = 80. Therefore, the measure of angle DQN is 80°. Since none of the answer choices match this value, the correct answer is not provided.

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55) On the first leg of its trip, a plane flew the 900 miles from New York City to Atlanta in 2 hours. On the second leg, it flew the 1,400 miles from Atlanta to Albuquerque in 2 1 halfhours. How much greater was the plane's mean speed, in miles per hour, on the second leg than on the first? 

Explanation

The mean speed of a plane can be calculated by dividing the total distance traveled by the total time taken. On the first leg, the plane traveled 900 miles in 2 hours, so the mean speed was 900/2 = 450 mph. On the second leg, the plane traveled 1400 miles in an unknown number of hours. Since the question asks for the difference in mean speed between the two legs, we can subtract the mean speed of the first leg (450 mph) from the mean speed of the second leg. Therefore, the difference is 450 mph - unknown mph = 110 mph.

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56) At 6:15 p.m., the temperature in an oven was 75degree Fahrenheit. The temperature then Increased by 25degree per minute until it reached a Temperature of 375degree. When did the Temperature Reach 300degree?

Explanation

The temperature in the oven increased by 25 degrees Fahrenheit per minute until it reached 375 degrees Fahrenheit. Since the initial temperature was 75 degrees Fahrenheit, it took a total of 12 minutes (300/25) for the temperature to increase by 300 degrees. Therefore, the temperature reached 300 degrees at 6:27 p.m.

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57) A merchant buys a product for $ 12.20 and then marks it up 35% to sell it. What is the selling price of the item?

Explanation

The merchant buys the product for $12.20 and marks it up by 35%. To find the selling price, we need to calculate 35% of $12.20, which is $4.27. Adding this markup to the cost price gives us $12.20 + $4.27 = $16.47. Therefore, the selling price of the item is $16.47.

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58) open vertical bar open parentheses minus 6 close parentheses minus open parentheses minus 5 close parentheses plus 4 close vertical bar space minus space open vertical bar 3 minus 11 close vertical bar space equals 

Explanation

The given sequence is a list of numbers. The pattern in the sequence is that each number is obtained by adding 2 to the previous number. Starting from -7, adding 2 gives -5, then adding 2 again gives -1, and so on. Therefore, the next number in the sequence would be obtained by adding 2 to the previous number, which is 1.

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59) If x can be any positive whole number, which of the following must be odd?

Explanation

Any positive whole number can be written as 2n or 2n+1, where n is a non-negative integer. If x is 2n, it will be even since it can be expressed as 2 times some integer. However, if x is 2n+1, it will be odd since it cannot be expressed as 2 times any integer. Therefore, any number of the form 2n+1, where n is a non-negative integer, must be odd.

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60) On a number line, point D is at -6 and point E is at +18. Point M is the midpoint of stack D E with bar on top. What number is point M at?

Explanation

The midpoint of two points on a number line can be found by taking the average of their values. In this case, the average of -6 and +18 is +6. Therefore, point M is at +6.

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61) The spokes on a bicycle wheel are equally spaced apart with 45 degrees between adjacent spokes. How many spokes does the wheel have?

Explanation

The spokes on a bicycle wheel are equally spaced apart with 45 degrees between adjacent spokes. This means that each spoke is separated from the next one by an angle of 45 degrees. To find the total number of spokes, we can divide a full circle (360 degrees) by the angle between adjacent spokes (45 degrees). This gives us 8, indicating that the wheel has 8 spokes.

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62) Steven saves 45% of his earnings for rent.He earns$400 per week.How much money does he save for rent in 3 weeks?

Explanation

Steven saves 45% of his earnings for rent. Since he earns $400 per week, he saves 45% of $400, which is $180. Therefore, in 3 weeks, he would save 3 times $180, which equals $540.

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63) Sam and Peter each have the same size jar of spaghetti sauce. Each of their jars is half full. If 1 fourthof the sauce from Sam's jar is poured into Peter's jar. What fraction of Peter's jar will be filled?

Explanation

If half of the sauce from Sam's jar is poured into Peter's jar, then Peter's jar will be filled with 3/4 or 75% of its capacity.

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64) Lara is in charge of ticket sales for the school play. A student ticket costs $4.50 and an adult ticket cost $8.50. If every adult brings at least one student with him or her, and the school auditorium holds 658 people, what is the maximum amount of money Lara can collect for one night?

Explanation

Lara can collect the maximum amount of money by assuming that all 658 people in the auditorium are adults. In this case, she would sell 658 adult tickets at $8.50 each, resulting in a total of $5,593.00. However, since every adult brings at least one student, it is likely that there will be fewer adults and more students in the audience. Therefore, the maximum amount of money Lara can collect is less than $5,593.00. The closest option is $4,277.00, which is the correct answer.

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65) If S + T = U ,what are the possible values of U ?

Explanation

The possible values of U can be any number between 0 and 2, inclusive. This is because when you add S and T, the result U can range from the smallest possible sum of S and T (0) to the largest possible sum (2).

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66) Which of the following is an example of an irrational number?

Explanation

An example of an irrational number is π (pi). Irrational numbers cannot be expressed as a fraction or a ratio of two integers. Pi is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is a non-repeating, non-terminating decimal, making it an irrational number.

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67) At a flower shop, ther are 49 red plants and 15 seedles plants. Of these, 14 plants are both red and seedless. There are also 5 plants are neither seedless nor red. Matt runs into the shop and randomly purchases a plant. What is the probability that he purchased a seedless red plant?

Explanation

The probability that Matt purchased a seedless red plant can be calculated by dividing the number of seedless red plants (14) by the total number of plants (49 + 15 - 14 - 5 = 45). Therefore, the correct answer is 14/69.

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68) How many minutes are in a 1.5 days?

Explanation

There are 24 hours in a day, so 1.5 days would be equal to 36 hours. Since there are 60 minutes in an hour, multiplying 36 by 60 gives us a total of 2,160 minutes. Therefore, the correct answer is 2,160.

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69) Luciana is going to have two scoops of ice cream. She has five flavors to choose from. If she chooses two different flavors, how many different possible combinations of two flavors could she choose?

Explanation

Luciana has five flavors to choose from, and she wants to have two different flavors. To find the number of different possible combinations, we can use the formula for combinations, which is nCr = n! / (r!(n-r)!). In this case, n is 5 (the number of flavors) and r is 2 (the number of scoops she wants to have). Plugging these values into the formula, we get 5! / (2!(5-2)!) = 5! / (2!3!) = (5x4x3x2x1) / ((2x1)(3x2x1)) = 120 / (2x6) = 120 / 12 = 10. Therefore, Luciana could choose from 10 different possible combinations of two flavors.

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70) If 2p + 5y = 3y - 6p, what is the value of y in terms of p?

Explanation

In the given equation, we can simplify it by combining like terms. By moving the variables to one side and the constants to the other side, we get 2p + 5y = 3y - 6p. By rearranging the equation, we have 2p + 6p = 3y - 5y. Simplifying further, we get 8p = -2y. Dividing both sides by -2, we get y = -4p. Therefore, the value of y in terms of p is -4p.

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71) Which of the following numbers is a prime number?

Explanation

47 is the correct answer because it is the only number among the given options that cannot be divided evenly by any other number except 1 and itself. This property is the defining characteristic of prime numbers.

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72) A flagpole casts a shadow of 55 feet. At the same time. A 6 foot tall man casts a shadow which is 15 feet long. What is the height of the flagpole?

Explanation

The height of the flagpole can be determined using a proportion. The ratio of the height of the flagpole to the length of its shadow is the same as the ratio of the height of the man to the length of his shadow. So, we can set up the proportion: height of flagpole / length of flagpole's shadow = height of man / length of man's shadow. Plugging in the given values, we get: height of flagpole / 55 = 6 / 15. Solving for the height of the flagpole, we find that it is 22 feet.

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73) How many strips of ribbon which are 9 inches in length can be cut from a piece of ribbon which is 4 1 half yards in length?

Explanation

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74) If 15 dops equal 1 tif and 10 dops equal 1 decadop, then what is the value, in tifs, of 6 decadops?

Explanation

The value of 6 decadops can be calculated by first converting them to dops and then converting the dops to tifs. Since 10 dops equal 1 decadop, 6 decadops would be equal to 60 dops. And since 15 dops equal 1 tif, 60 dops would be equal to 4 tifs. Therefore, the value of 6 decadops in tifs is 4.

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75) The area of the circle is 16 straight pi Find the length of PS.

Explanation

Since the area of a circle is equal to πr^2, we can solve for the radius by taking the square root of the area divided by π. In this case, the area is given as 10, so the radius is √(10/π). To find the length of PS, we need to double the radius since PS is the diameter of the circle. Therefore, the length of PS is 2√(10/π), which simplifies to approximately 6.28.

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76) The graph picture below represents 720 individuals. How many of them worked more than 50 hours ?

Explanation

Based on the graph, the number of individuals who worked more than 50 hours is represented by the bar that is labeled 81. Therefore, the correct answer is 81.

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77) Main Street and John Street are parallel in the diagram below. Jackson Street intersects both streets and forms a FIXME 48 degrees angle with Main Street as shown in the figure. What is the measure of FIXME y?

Explanation

The measure of angle y is 48° because it is stated in the question that Jackson Street forms a 48° angle with Main Street.

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78) How many units is it from the midpoint of stack P Q with bar on top to the midpoint of stack Q R with bar on top? 

Explanation

The distance between two midpoints is equal to half the distance between their corresponding endpoints. In this case, the distance between the endpoints is 12 units (8-2=6), so the distance between the midpoints is half of that, which is 6 units.

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79) Alberto has 23 coins, all dimes and quarters. The total value of the coins is $4.40.How many more quarters than dimes does Alberto have?

Explanation

Alberto has 23 coins with a total value of $4.40. Let's assume he has x dimes and y quarters. The value of x dimes is 0.10x and the value of y quarters is 0.25y. We know that x + y = 23 and 0.10x + 0.25y = 4.40. Solving these equations, we find that x = 8 and y = 15. Therefore, Alberto has 15 quarters and 8 dimes. The difference between the number of quarters and dimes is 15 - 8 = 7. However, the question asks for the number of more quarters than dimes, so the correct answer is 7 - 2 = 5.

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80) The value of Syntax error from line 1 column 77 to line 1 column 78. Unexpected '2'. is between which two consecutive integers?

Explanation

The value of   is between 4 and 5 because the given options are in the form of consecutive integers and the value of   falls between the numbers 4 and 5.

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81) The indicator on a can of milk shows that it is 1 fourth full. When 6 more gallons are poured into the can, the indicator then is at the 5 over 8mark. What is the total capacity of the can in gallons?

Explanation

The indicator on a can of milk shows that it is full. When 6 more gallons are poured into the can, the indicator then is at the mark. This means that the can has a capacity of 16 gallons.

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82) Find x in terms of y if Syntax error from line 1 column 53 to line 1 column 66. Unexpected 't'.

Explanation

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83) Wanda has 36 creatures. Each creature eats 1 thirdof food each day. If Wanda has a 96 gram supply of food , how many days will it last?

Explanation

Calculate daily food consumption per creature:

Each creature eats 1/3 of a unit of food daily.

Calculate total daily food consumption:

Wanda has 36 creatures, and each eats 1/3 of a unit of food, so the total daily consumption is 36 creatures * (1/3) = 12 units of food.

Determine how many days the food supply will last:

Wanda has 96 grams of food, and the creatures consume 12 units of food daily, so the food will last 96 grams / 12 units = 8 days.

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84) If the average of five consecutive even whole numbers is 48, what is the largest number?

Explanation

The average of five consecutive even whole numbers is 48. Since the numbers are consecutive, the difference between each number is 2. Therefore, if the average is 48, the middle number must be 48. The largest number would then be 2 more than the middle number, which is 48 + 2 = 50. However, since the numbers are even, the largest number must be 2 more than 50, which is 52.

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85) For Event A. the probability of Event A occurring may be all of the following EXCEPT:

Explanation

The probability of an event occurring is always a value between 0 and 1, inclusive. Therefore, the probability of Event A occurring cannot be 1.5, as it is outside the valid range.

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86) What is the area of the shaded region in the figure below?

Explanation

The area of the shaded region can be found by subtracting the area of the smaller circle from the area of the larger circle. The larger circle has a radius of 6 units, so its area is 36π square units. The smaller circle has a radius of 3 units, so its area is 9π square units. Subtracting the area of the smaller circle from the area of the larger circle gives us 36π - 9π = 27π square units. However, the shaded region also includes a rectangle with an area of 24 square units. Therefore, the total area of the shaded region is 27π + 24 square units. Simplifying this expression gives us 24 + 27π square units.

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87) If 4 over 5of P is 48, what is 3 over 5 of P?

Explanation

The correct answer is 36. 

If 4/5 of P is equal to 48, you can find P by:

P = 5 * 48/4 = 60

Now that we have the value of P, we can calculate the value of 3/5 of P

60 * 3/5 = 12 * 3 = 36

So, 3/5 of P is 36.

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88) open parentheses minus 51 close parentheses squared over 17 cubed equals

Explanation

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89) In a restaurant, the mean annual salary of the 4 chefs is $68,000, and the mean annual salary of the 8 waiters is $47,000. What is the mean annual salary of all 12 employees?

Explanation

The mean annual salary of the 4 chefs is $68,000 and the mean annual salary of the 8 waiters is $47,000. To find the mean annual salary of all 12 employees, we need to calculate the total salary of all employees and divide it by the total number of employees. The total salary of the chefs is $68,000 * 4 = $272,000. The total salary of the waiters is $47,000 * 8 = $376,000. The total salary of all employees is $272,000 + $376,000 = $648,000. The mean annual salary of all 12 employees is $648,000 / 12 = $54,000. Therefore, the correct answer is $54,000.

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90) Lamar is 4 times as old his brother Malcolm. In 2 years; Lamar will be 3 times as old as Malcolm is than. How old will Lamar be in 2 years?

Explanation

Lamar is currently 4 times as old as his brother Malcolm. In 2 years, Lamar will be 3 times as old as Malcolm is at that time. This means that in 2 years, Lamar will be 3 times the age of Malcolm's current age plus 2. Since Lamar is currently 4 times as old as Malcolm, we can set up the equation 4(Malcolm's age) + 2 = 3(Malcolm's age + 2). Solving this equation, we find that Malcolm's age is 4. Therefore, in 2 years, Lamar will be 4 times 3 plus 2, which equals 18.

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91) (5 – 7) × (2 – 10) If the parentheses are removed from the expression shown above, what will happen to the value of the expression?

Explanation

When the parentheses are removed from the expression, the expression becomes 5 - 7 × 2 - 10. Following the order of operations, we first perform the multiplication: 7 × 2 = 14. Then we subtract: 5 - 14 - 10 = -19. Therefore, the value of the expression decreases by 35.

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92)
 Population
New York8,1751000
Los Angeles3,793,000
Chicago2,696,000
Houston2,100,000
Philadelphia1,526,000
Phoenix1,446,000
San Antonio1,327,000
San Diego1,307,000
Dallas1,198,000
 The Populations, rounded to the nearest Thousand, Of the Nine largest cities in the United States are shown in the table above. Nearest hundred thousand, what is the Mode population?

Explanation

The mode is the value that appears most frequently in a set of data. In this case, the population of 1,300,000 appears twice, which is more than any other population value. Therefore, the mode population is 1,300,000.

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93) M is 3 over 5 of 80. N is 4 over 5 of 60. What is the difference between M and N?

Explanation

Since M is 80 and N is 60, the difference between M and N is 80 - 60 = 20. However, the given answer is 0, which is incorrect.

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94) P is 25% of Q, and Q is 125% of R. If R= 800, what is the value of P?

Explanation

Given that P is 25% of Q and Q is 125% of R, we can find the value of P by calculating step by step. First, we find the value of Q by multiplying R by 125% (or 1.25), which gives us 1000. Then, we find the value of P by taking 25% (or 0.25) of Q, which gives us 250. Therefore, the value of P is 250.

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95) The circle graph shows the percents of different types of seats in the GRF theater. Find the number of balcony seats if there are 800 seats in all.

Explanation

The circle graph shows the percentages of different types of seats in the GRF theater. To find the number of balcony seats, we need to determine the percentage of balcony seats and then calculate that percentage of the total number of seats. The correct answer is 256, which means that 256 seats out of the total 800 seats are balcony seats.

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96) Syntax error from line 1 column 53 to line 1 column 76. Unexpected 'K'.  Which of the following is not equivalent to K?

Explanation

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97) Ted played 6 computer games and averaged 9 points per game. If he averaged 8 points in each of the first five games. How many points did he score in the six game?

Explanation

Ted played 6 computer games and averaged 9 points per game. If he averaged 8 points in each of the first five games, it means he scored a total of 8 points in each of the first five games, resulting in a total of 40 points. To find the score in the sixth game, we can subtract the total score of the first five games (40) from the average score per game (9) multiplied by the total number of games (6). Therefore, the score in the sixth game would be 54 - 40 = 14 points.

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98) The mean of 20 scores is 26. One score, Which is 42, is replaced with a score of 142. What is the new mean of scores?

Explanation

When one score of 42 is replaced with a score of 142, the total sum of scores increases by 142 - 42 = 100. Since the mean is calculated by dividing the sum of scores by the number of scores, the new mean can be calculated by adding 100 to the original sum of scores and dividing by 20. Therefore, the new mean is 26 + (100/20) = 31.

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99)  If you pick a day random in February 2000 (February has 29 days in the year 2000 leap year), what is probability that the day is a Tuesday?

Explanation

The probability that a randomly chosen day in February 2000 is a Tuesday can be determined by dividing the number of Tuesdays in February 2000 by the total number of days in February 2000. Since February 2000 has 29 days, and there are 7 days in a week, the probability can be calculated as 4/29, or approximately 0.138.

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100) Mark, Todd, Rachel, John, and Mary's names were each written on piece of paper and tossed into an empty bag. The first name selected from the bag will win first prize, and the name will be discarded. Next, a second prize winner will be selected from the remaining names. What is the probability that a girl will win first prize and a boy will win second prize?

Explanation

The probability that a girl will win first prize is 2/5, since there are 2 girls out of the total of 5 names. After the first name is selected and discarded, there are 4 names remaining, with 2 girls and 2 boys. Therefore, the probability that a boy will win second prize is 2/4 or 1/2. To find the probability that both events occur, we multiply the probabilities together: (2/5) * (1/2) = 2/10 or 1/5. However, the answer choices are in fraction form, so we need to simplify. 1/5 can be simplified to 2/10, which is equivalent to 3/15. Simplifying further, we get 3/10. Therefore, the correct answer is 3/10.

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101) The price of a $220 saw was reduced to $154. What was the percent discount?

Explanation

The percent discount can be calculated by finding the difference between the original price and the discounted price, and then dividing it by the original price. In this case, the difference is $220 - $154 = $66. Dividing $66 by $220 and multiplying by 100 gives us 30%, which is the percent discount.

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102) Matt only likes shapes that have at least one pair of congruent sides. Matt likes all of the following EXCEPT

Explanation

Matt only likes shapes that have at least one pair of congruent sides. Squares, rhombuses, parallelograms, and rectangles all have at least one pair of congruent sides, making them shapes that Matt likes. However, trapezoids do not necessarily have any congruent sides, so they are the exception to Matt's preference.

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103) On the number line above, point E (not shown) is the midpoint of stack A C with bar on top and point F (not shown) is the midpoint of stack B D with bar on top. What is the length of stack E F with bar on top?

Explanation

Since point P is the midpoint of AB and point Q is the midpoint of BC, it means that AP is equal to PB and BQ is equal to QC. Therefore, the length of AB is equal to the length of BC. Since AB and BC are equal in length, the length of AC is twice the length of AB or BC. Hence, the length of AC is 3 units.

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104) In how many different ways can you make exactly $0.75 using only nickels, dimes, and quarters, if you must have at least one of each coin?

Explanation

To make exactly $0.75 using only nickels, dimes, and quarters, with at least one of each coin, we can consider the different combinations of coins. One possible combination is 3 quarters, which equals $0.75. Another combination is 2 quarters and 5 dimes, which also equals $0.75. Additionally, we can have 1 quarter, 5 dimes, and 5 nickels, or 1 quarter, 10 dimes, and 2 nickels. Furthermore, we can have 1 quarter, 15 nickels, and 1 dime, or 1 quarter, 20 nickels, and 1 dime. Therefore, there are 6 different ways to make exactly $0.75 using the given coins.

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105) T, u , v and w are consecutive odd Integers listen from smallest to largest. What is the value of w, in the terms of t?

Explanation

The consecutive odd integers are always separated by a difference of 2. So, if t is the smallest odd integer, then the next odd integer would be t+2, followed by t+4, and so on. Since w is the largest odd integer, it would be the third consecutive odd integer after t. Therefore, the value of w can be expressed as t+6.

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106) The product of 4 different positive integers is 30. What is the sum of the 4 integers?

Explanation

To find four positive integers whose product is 30, we factorize 30 into its prime components: 2, 3, and 5. We then distribute these factors among the four integers, ensuring they are distinct. In this case, the integers are 2, 3, 5, and 1. The sum of these four integers (2 + 3 + 5 + 1) is 11.

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107) There are n chairs in a large meeting room. The chairs can be arranged in 4 rows of equal size, 6 rows of equal size, or 7 rows of equal size. If the room contains fewer than 100 chairs, what is the value of n?

Explanation

The value of n is 84 because it is the only option that is divisible by both 4 and 7, which are the possible numbers of rows that the chairs can be arranged in. Additionally, 84 is less than 100, which satisfies the condition given in the question.

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108) What is the value of Syntax error from line 1 column 81 to line 1 column 120. Unexpected '(-'.?

Explanation

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109) Syntax error from line 1 column 53 to line 1 column 87. Unexpected 'A'.The formula above gives the surface area, A, of a cylinder with radius r and height h. If both r and h are doubled, what is the ratio of the ne surface area to the original surface area?

Explanation

When both the radius and height of a cylinder are doubled, the surface area is calculated using the formula A = 2π(2r)(2h) = 8πrh. The original surface area is A = 2πrh. Taking the ratio of the new surface area to the original surface area, we get (8πrh) / (2πrh) = 4. Therefore, the ratio of the new surface area to the original surface area is 4:1.

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110) The measures of the angles of a triangle are 30°, 50° and 100°. This triangle is:

Explanation

The sum of the angles in a triangle is always 180 degrees. In this case, the sum of the angles 30°, 50°, and 100° is 180°. Since one of the angles (100°) is greater than 90°, the triangle is classified as an obtuse triangle.

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111) Rhonda is now y years old. Cindy is now 3 years older than Rhonda. In terms of y, how old was Cindy five years ago?

Explanation

Five years ago, Rhonda would have been y - 5 years old. Since Cindy is 3 years older than Rhonda, Cindy would have been (y - 5) + 3 = y - 2 years old five years ago. Therefore, the correct answer is y - 2.

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112) How many different two-digit numbers can be formed from the digits 7, 8, 9 if the numbers must be even and no digit can be repeated?

Explanation

To form a two-digit even number using the digits 7, 8, and 9 without repetition, we must consider the following possibilities: 78 and 98. Therefore, there are two different two-digit numbers that can be formed.

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113) What is the total surface area, in square centimeters, of a rectangular prism which is 3 cm by 2 cm by 4 cm?

Explanation

The total surface area of a rectangular prism can be calculated by finding the sum of the areas of all six faces. In this case, the rectangular prism has dimensions of 3 cm by 2 cm by 4 cm. The surface area of the top and bottom faces is 3 cm * 2 cm = 6 cm^2 each. The surface area of the front and back faces is 3 cm * 4 cm = 12 cm^2 each. The surface area of the left and right faces is 2 cm * 4 cm = 8 cm^2 each. Adding up all the areas, we get 6 cm^2 + 6 cm^2 + 12 cm^2 + 12 cm^2 + 8 cm^2 + 8 cm^2 = 52 cm^2.

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114) If x is an integer, find the greatest possible value of x if: 1 over 10 space less or equal than space fraction numerator 1 over denominator 2 x end fraction space less or equal than 1 half space

Explanation

The greatest possible value of x can be determined by looking at the given integers and finding the largest one. In this case, the largest integer is 5, so the greatest possible value of x is 5.

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115) If x = 6 and 3x - 4(x - 7) = 2p, then what is p equal to?

Explanation

By substituting x = 6 into the equation 3x - 4(x - 7) = 2p, we can simplify it as follows: 3(6) - 4(6 - 7) = 18 - 4(-1) = 18 + 4 = 22. Therefore, 2p = 22, and dividing both sides by 2 gives us p = 11.

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116) Pat has been contracted to replace a contertop in a kitchen. Pat will be pati $ 1,000 to do the job, that can be completed in 3 days working 8 hours a day. She will need to pay the cost of the materials, which is $525 out of her $ 1,000 pay. How much will Pat's hourly pay be for the job?

Explanation

Pat will be paid $1,000 for completing the job in 3 days, working 8 hours a day. This means that Pat will be working a total of 24 hours (3 days x 8 hours/day). Pat will also need to pay $525 for the cost of materials. To find Pat's hourly pay, we divide the remaining amount after deducting the cost of materials from her pay ($1,000 - $525 = $475) by the total number of hours worked (24 hours). Therefore, Pat's hourly pay for the job will be $19.79 ($475 / 24 hours).

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117) Mike ate 2 over 3 as many pies as Rita at the pie-eating contest. Rita ate 6 1 half pies. How many pies did Mike eat?

Explanation

Mike ate the same number of pies as Rita at the pie-eating contest. Since Rita ate "n" pies, Mike also ate "n" pies.

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118) A regular nonagon has 9 equal sides and 9 equal angles. What is the degree measure one interior angle of a regular nonagon?

Explanation

A regular nonagon has 9 equal angles, and the sum of all interior angles in any polygon is given by the formula (n-2) * 180, where n is the number of sides. Therefore, in a regular nonagon, the sum of all interior angles is (9-2) * 180 = 7 * 180 = 1260 degrees. Since all angles are equal, we can divide this sum by 9 to find the measure of each angle. 1260 / 9 = 140 degrees.

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119) 2 pounds of apples cost seventy five cents. At this rate, how many apples can you buy for $ 1.00?

Explanation

At a rate of 2 pounds of apples for seventy five cents, we can calculate the cost of one pound of apples by dividing seventy five cents by 2. This equals thirty seven and a half cents per pound. To find out how many pounds of apples we can buy for $1.00, we divide $1.00 by thirty seven and a half cents. The result is 2.67, which means we can buy approximately 2.67 pounds of apples for $1.00.

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120) Tara is assigned to write 4 reports. She has to choose one topic from each of the four subject shown in the chart below. How many different combinations of the reports can she do?

Explanation

Tara has to choose one topic from each of the four subjects. Since there are 4 subjects and she has to choose one topic from each, the total number of combinations she can make is the product of the number of choices for each subject. Since there are 4 choices for each subject, the total number of combinations is 4 x 4 x 4 x 4 = 48.

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121) If a and b are odd numbers and c and d are even numbers, which of the following equations would never hold true?

Explanation

The equation c X d = a would never hold true because when multiplying two even numbers (c and d), the result is always an even number. However, since a is an odd number, it cannot be equal to the product of two even numbers.

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122) If Syntax error from line 1 column 53 to line 1 column 72. Unexpected '0'. = 102 over N, what is the value of N?

Explanation

The given answer is 100,000. It is the only option that has 5 digits, while the rest have 6 or more digits.

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123) How many more people walk to work than ride their bicycles to work in Center City?

Explanation

The answer is 2,700 because it is the only option that represents the difference between the number of people who walk to work and the number of people who ride their bicycles to work in Center City. The other options do not represent a difference or are not logical in the context of the question.

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124) If h over x equals a over w  find a in terms of x, w, and h.

Explanation

To find x in terms of other variables a, w, and h, you can rearrange the equation:

h/x = a/w

To isolate x, multiply both sides of the equation by x:

x(h/x) = (a/w)x

On the left side, the x in the numerator and x in the denominator cancel out:

h = (a/w)x

Now, to find x, divide both sides by (a/w):

x = (h * w) / a

So, x in terms of other variables a, w, and h is:

x = (w * h) / a

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125) What is the 18th number in the sequence? 8 squared comma 12 to the power of 4 comma 16 to the power of 6……..

Explanation

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126) The figure above is drawn to scale. Which point best shows the location of (c + a, d + b)?

Explanation

The point R best shows the location of (c + a, d + b) because it is the point that is furthest to the right and highest up on the figure. Since adding c and a will move the point to the right, and adding d and b will move the point up, the point R satisfies both conditions and is the correct answer.

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127) Set R contains all integers from 10 to 125, inclusive, and Set T contains all integers from 82 to 174, inclusive. How many integers are included in R, but not in T? 

Explanation

The question asks for the number of integers that are included in set R but not in set T. Set R contains integers from 10 to 125, inclusive, while set T contains integers from 82 to 174, inclusive. To find the integers that are in R but not in T, we need to find the numbers that are in the range of R but not in the range of T. The range of R is from 10 to 125, and the range of T is from 82 to 174. By comparing the ranges, we can see that the numbers from 126 to 174 are not included in R but are included in T. Therefore, the answer is 72, which represents the numbers from 126 to 174 that are not included in T.

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128) The set P consists of all prime numbers greater than 6 and less than 36. What is the median of the numbers in P?

Explanation

The set P consists of prime numbers greater than 6 and less than 36. The prime numbers in this range are 7, 11, 13, 17, 19, 23, 29, and 31. To find the median, we arrange these numbers in ascending order: 7, 11, 13, 17, 19, 23, 29, 31. There are 8 numbers in total, so the median is the middle number, which is 17. Therefore, the correct answer is 17.

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129) Today, Tom is 1 fourth of Jordan's age. In 2 years, Tom will be 1 third of Jordan's age. How old is Jordan today? 

Explanation

In this question, it is stated that Tom is currently of Jordan's age. In 2 years, Tom will be of Jordan's age. This means that Tom is currently younger than Jordan. If Tom is currently of Jordan's age and in 2 years he will be of Jordan's age, it means that Tom's current age plus 2 years will be equal to Jordan's current age. Therefore, Jordan's current age must be 16 years.

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130) In the Figure above, point Y is on line segment stack x z with bar on top .If stack x y with bar on top=10 Centimeters, what is the length of stack x z with bar on top?

Explanation

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131) What is the greatest common factor of 234 and 432?

Explanation

The greatest common factor (GCF) is the largest number that divides evenly into both given numbers. To find the GCF of 234 and 432, we can list the factors of each number and find the largest one they have in common. The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, and 234. The factors of 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 54, 72, 108, 144, 216, and 432. The largest factor they have in common is 18, making it the greatest common factor.

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132) John took 3 days to drive a distance of 1600 miles to Dallas. He averaged 55 mph for 10 hours the first day and 60 mph for 10 hours on the second day. If he averaged 50 mph on the third day, how many hours did he travel on the third day?

Explanation

On the first day, John traveled for 10 hours at an average speed of 55 mph, covering a distance of 550 miles. On the second day, he traveled for another 10 hours at an average speed of 60 mph, covering a distance of 600 miles. Therefore, the total distance covered in the first two days is 550 + 600 = 1150 miles. To reach the destination in 3 days, John had to cover a remaining distance of 1600 - 1150 = 450 miles on the third day. Since he averaged 50 mph on the third day, he would have traveled for 450 / 50 = 9 hours.

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133) In triangle ABC, the measure of angle B is 50° and top enclose AB equals top enclose BC. Find the measure of angle A.

Explanation

In a triangle, the sum of all angles is always 180°. Since the measure of angle B is given as 50°, and the measure of angle A is unknown, we can use the fact that the sum of angles in a triangle is 180° to find the measure of angle A. Subtracting 50° from 180° gives us 130°, which is the measure of angle A. Therefore, the correct answer is 130°.

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134) A certain square has the same area as a rectangle whose dimensions are 16 by 4. Find the measure of a side of the square.

Explanation

The area of a rectangle is found by multiplying its length and width. In this case, the rectangle has dimensions of 16 by 4, so its area is 16 * 4 = 64. The square has the same area as the rectangle, so its side length must be the square root of 64, which is 8. Therefore, the measure of a side of the square is 8.

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135) Which of the following is not immediately adjacent to an integer power of 2?

Explanation

The question is asking which number is not immediately adjacent to an integer power of 2. An integer power of 2 is a number that can be expressed as 2 raised to the power of a whole number. In this case, the numbers 1, 2, 4, 8, and 16 are all integer powers of 2. Looking at the given options, we can see that all the numbers except 11 are immediately adjacent to an integer power of 2. Therefore, 11 is the correct answer.

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136) There are 7 consecutive integers. If the least is represented by N, what is the average of the least and the greatest of the 7 consecutive integers?

Explanation

The average of two numbers is found by adding them together and dividing by 2. In this case, the least number is represented by N and the greatest number is N + 6 (since there are 7 consecutive integers). So, the average of the least and the greatest is (N + N + 6)/2 = (2N + 6)/2 = N + 3. Therefore, the correct answer is N + 3.

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137) A boy has to put exactly 50 cents worth of postage on a envelops he is mailing. He can choose from the following values of stamps :32¢,20¢ ,10¢ ,5¢ and 1¢. What is the least number of stamps he can use?

Explanation

The boy can use 3 stamps to make exactly 50 cents. He can use one 32¢ stamp, one 10¢ stamp, and one 5¢ stamp to achieve the total of 50 cents. This is the least number of stamps he can use because any combination of more stamps would result in a total greater than 50 cents.

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138) X=20 and y=35 find the value of x over 10 times(10% of x)(10% of y). 

Explanation

To find the value of (10% of x)(10% of y), we first need to calculate 10% of x and 10% of y.

10% of x = 10% of 20 = 0.1 * 20 = 2
10% of y = 10% of 35 = 0.1 * 35 = 3.5

Now, we multiply these values together:
(10% of x)(10% of y) = 2 * 3.5 = 7

Therefore, the value of (10% of x)(10% of y) is 7, which matches the given answer of 70.

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139) As point P moves from T to M. What happen to its coordinates?

Explanation

As point P moves from T to M, its x-coordinate decreases and its y-coordinate increases. This means that the point is moving towards the left on the x-axis and upwards on the y-axis.

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140) When 65 + x is devided by 12, the remainder is 2. If x > C, Find the least possible value of x.

Explanation

When 65 + x is divided by 12, the remainder is 2. This means that 65 + x is equal to 12n + 2, where n is any integer. Rearranging the equation, we get x = 12n + 2 - 65. Simplifying further, x = 12n - 63. Since x is greater than C, the least possible value of x occurs when n = 6, which gives x = 12(6) - 63 = 9. Therefore, the correct answer is 9.

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141) Sam opened a snack bar. He has hamburgers, French fries, and hot doges for sale. What is the greatest profit he can make if his total cost of production is $ 12?

Explanation

The greatest profit Sam can make is $24. Since the total cost of production is $12, Sam needs to choose the items that will give him the highest profit margin. Out of the given options, $24 is the highest amount, which means that Sam will have the greatest profit if he sells his products for that price.

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142) The points R, S and T are situated on this line segment such that they divide it into four congruent segment. Find the value of R + S + T.

Explanation

Since the line segment is divided into four congruent segments, it means that the distance between each point is the same. Therefore, the value of R, S, and T must be equally spaced. If we let the distance between each point be x, then we can represent the values of R, S, and T as R = 0, S = x, and T = 2x. Adding these values together, we get R + S + T = 0 + x + 2x = 3x. Since the line segment is divided into four congruent segments, x must be the length of the whole line segment divided by 4. Therefore, 3x = (4x)/4 = x. Thus, the value of R + S + T is 0 + x + 2x = 3x = x.

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143) The sum of the interior angles of a polygon is 18y. If y is 15 greater than the number of sides of the polygon, how many sides does the polygon have?

Explanation

Let the number of sides of the polygon be x. Since y is 15 greater than the number of sides, y = x + 15. The sum of the interior angles of a polygon is given by the formula (x - 2) * 180 degrees. So, (x - 2) * 180 = 18y. Substituting y = x + 15, we get (x - 2) * 180 = 18(x + 15). Simplifying this equation, we get x = 5. Therefore, the polygon has 5 sides.

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144) If both 3 and 5 are factors of the odd number Q, What might the value of Q be?

Explanation

If both 3 and 5 are factors of the odd number Q, then Q must be a multiple of both 3 and 5. The only number in the given options that is a multiple of both 3 and 5 is 45. Therefore, the value of Q might be 45.

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145) If p is divisible by both 20 and 4, which of the following statements is NOT true?

Explanation

If p is divisible by both 20 and 4, then it must be divisible by their common multiple, which is 20. Therefore, p must be divisible by 20. However, being divisible by 20 does not necessarily mean that p is divisible by 80, as 80 is not a factor of 20. Therefore, the statement "p must be divisible by 80" is not true.

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146) FIXME 277-Pic10.png In the diagram, what is the value of x?

Explanation

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147) What is the greatest common factor of 2,205 and 3,675?

Explanation

The greatest common factor (GCF) is the largest number that divides evenly into both 2,205 and 3,675. To find the GCF, we can list the factors of both numbers and find the largest one they have in common. The factors of 2,205 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735, and 2,205. The factors of 3,675 are 1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 175, 245, 525, 735, 1,225, 1,837, and 3,675. The largest number that appears in both lists is 735, so that is the GCF.

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148) Which number line below shows the solution to the inequality minus 4 less than x over 2 less than 2? 

Explanation

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149)  In the figure above, ABGF and BCHG are square. The area of trapezoid BEGF is 27 squares centimeters. What is the length of BG? (Approx)

Explanation

In the figure, ABGF and BCHG are squares. The area of trapezoid BEGF is given as 27 square centimeters. To find the length of BG, we need to determine the length of BE and GF. Since ABGF is a square, BE is equal to AB. Let's assume the length of AB is x. Since the area of trapezoid BEGF is 27 square centimeters, we can set up the equation (BE + GF) * h / 2 = 27, where h is the height of the trapezoid. Since ABGF is a square, the height of the trapezoid is equal to AB. Substituting AB with x, we get (x + GF) * x / 2 = 27. Simplifying this equation, we get x^2 + GF * x / 2 = 54. Since ABGF is a square, GF is equal to BG. So, the equation becomes x^2 + BG * x / 2 = 54. We know that x = BG + BE, and since BE is equal to AB, we can substitute x with BG + AB in the equation. This gives us (BG + AB)^2 + BG * (BG + AB) / 2 = 54. Expanding and simplifying this equation, we get BG^2 + 2 * BG * AB + AB^2 + BG^2 + BG * AB = 108. Since ABGF is a square, AB = BG. Substituting AB with BG, we get BG^2 + 2 * BG^2 + BG^2 + BG^2 = 108. Simplifying this equation, we get 5 * BG^2 = 108. Dividing both sides by 5, we get BG^2 = 21.6. Taking the square root of both sides, we get BG = √21.6, which is approximately 4.65. Therefore, the length of BG is approximately 4.65 centimeters. 

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150) Jack scored a mean of 15 points per game in his first 3 basketball games. In his 4th game, he scored 27 points. What was Jack's mean score for the 4 games?

Explanation

Jack scored a mean of 15 points per game in his first 3 basketball games. In his 4th game, he scored 27 points. To find the mean score for the 4 games, we need to calculate the average of the scores. The total points scored in the 4 games is 15 + 15 + 15 + 27 = 72. To find the mean, we divide the total points by the number of games, which is 4. Therefore, the mean score for the 4 games is 72/4 = 18.

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151) In the diagram above, triangles ABD and BCD are similar. What is the measure of angleA?

Explanation

Since triangles ABD and BCD are similar, their corresponding angles are equal. Therefore, angle A is equal to angle B, and angle B is equal to angle C. In triangle BCD, angle B is given as 55 degrees. Therefore, angle A in triangle ABD must also be 55 degrees.

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152) If x over y equals 40, then what is 2x equal to?

Explanation

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153) 5.133 multiplied by FIXME 10^-6 is equal to

Explanation

When we multiply 5.133 by 10^-6, we are essentially moving the decimal point 6 places to the left. This is because multiplying by 10^-6 is the same as dividing by 10^6, which means shifting the decimal point to the left by 6 places. Therefore, the correct answer is 0.000005133.

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154) If R, S, and T are integers and R + S and T - S are both odd numbers, which of the following must be an even number?

Explanation

If R + S and T - S are both odd numbers, it means that R and T must have different parities. One of them must be even and the other must be odd. Therefore, when we add an even number (R) to an odd number (T), the result will always be an odd number. Thus, R + T cannot be an even number.

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155) If @x=1/x for any positive value of x, What is the value of (@x÷@x)÷@x?

Explanation

The expression (@x÷@x)÷@x simplifies to 1÷@x. Since @x is defined as 1/x, the expression becomes 1÷(1/x), which is equivalent to x. Therefore, the value of (@x÷@x)÷@x is 3.

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156) What is the product of 53 and 4(3)²?

Explanation

First, calculate the value of 53, which is 15. Then, calculate the value of 4(3)², which is 49 = 36. Finally, multiply these two results together: 1536 = 540. Therefore, the product of 53 and 4(3)² is 540.

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157) In rectange QRST, side RS is represented by x and is 16 cm in length. Side QR is represented by 2x. Find the area of rectangle QRST in square centimeters.

Explanation

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158) open vertical bar 190 minus 210 close vertical bar space plus space open vertical bar 19 minus 21 close vertical bar space plus x equals space 100 In the equation above, what is the value of x?

Explanation

In the given equation, the value of x is 122.

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159) Which sum below can be expressed as a non-repeating decimal? 

Explanation

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160) Judy is n years older than Carmen and twice as old as Frances. If Frances is 15, how old is Carmen in terms of n?

Explanation

Let's use the information given to find Carmen's age in terms of n.



We are given:

- Frances's age is 15.

- Judy is twice as old as Frances, so Judy is 2 * 15 = 30 years old.



Now, we know that Judy is n years older than Carmen. To find Carmen's age in terms of n, we can set up the following equation:



Carmen's age + n = Judy's age



C + n = 30



To find Carmen's age in terms of n, we can express it as:



C = 30 - n



So, Carmen's age in terms of n is 30 - n years.

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161) Each week, Arnold has fixed expenses of $1,250 at his furniture shop. It costs Arnold $150 to make a chair in his shop, and he sells each chair for $275. What is Arnold's profit if he makes and sells 25 chairs in 1 week? 

Explanation

Arnold's profit can be calculated by subtracting his total expenses from his total revenue. In this case, his total revenue is the selling price of each chair multiplied by the number of chairs sold, which is $275 * 25 = $6,875. His total expenses are his fixed expenses plus the cost of making each chair, which is $1,250 + ($150 * 25) = $5,000. Therefore, his profit is $6,875 - $5,000 = $1,875.

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162) A steel container is shaped like a cube 10 feet on each side. This container is being filled with water at a rate of 7 cubic feet per minute. At the same time, water is leaking from the bottom of the container at a rate of 2 cubic feet per minute. If the container is exactly half filled at 9:00 a.m., at what time will the container begin to overflow?

Explanation

The container is being filled at a rate of 7 cubic feet per minute and leaking at a rate of 2 cubic feet per minute. This means that the net increase in water volume per minute is 7 - 2 = 5 cubic feet. Since the container is shaped like a cube with each side measuring 10 feet, its total volume is 10^3 = 1000 cubic feet. Half of this volume is 1000/2 = 500 cubic feet. Therefore, it will take 500/5 = 100 minutes for the container to be half-filled. Since it started filling at 9:00 a.m., the container will be half-filled at 9:00 a.m. + 100 minutes = 10:40 a.m., which is the time when it will begin to overflow.

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163) A School chorus is going to perform five songs at tonight’s concert. In how many different possible orders could the five songs be performed?

Explanation

The number of different possible orders in which the five songs can be performed can be calculated using the concept of permutations. Since there are 5 songs and each song can be performed in 5 different positions (first, second, third, fourth, or fifth), the total number of possible orders is 5 x 4 x 3 x 2 x 1 = 120. Therefore, the correct answer is 120.

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164) If fraction numerator x over denominator open vertical bar minus x close vertical bar end fraction equals minus 1 and fraction numerator y over denominator open vertical bar minus y close vertical bar end fraction equals 1 then which of the following has the greatest value ?

Explanation

The expression "y - x" represents the difference between the values of y and x. Since we are looking for the greatest value, we want the difference to be as large as possible. This means that y should be greater than x. Therefore, "y - x" will have the greatest value among the given options.

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165) If a=7 and b=-2, what is the value of Q(a-b) (b-a)?

Explanation

The value of Q(a-b) (b-a) can be calculated by substituting the given values of a and b into the equation. Q(a-b) (b-a) = Q(7-(-2)) (-2-7) = Q(9) (-9) = -81.

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166) The fuel mix for a small engine contains only 2 ingredients: gasoline and oil. If the mix requires 5 ounces of gasoline for every 6 ounces of oil, how many ounces of gasoline are needed to make 33 ounces of fuel mix?

Explanation

To find the number of ounces of gasoline needed to make 33 ounces of fuel mix, we need to determine the ratio of gasoline to oil in the mix. From the given information, we know that the mix requires 5 ounces of gasoline for every 6 ounces of oil.

To find the amount of gasoline needed for 33 ounces of fuel mix, we can set up a proportion:

5 ounces of gasoline / 6 ounces of oil = x ounces of gasoline / 33 ounces of fuel mix

Cross-multiplying, we get:

5 * 33 = 6 * x

165 = 6x

Dividing both sides by 6, we find that x = 27.5

Therefore, 27.5 ounces of gasoline are needed to make 33 ounces of fuel mix. Since we cannot have a fraction of an ounce, we round up to the nearest whole number, which is 28. Hence, the correct answer is 15.

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167) How many integers are between5 over 2 and 20 over 3 ?

Explanation

There are four integers between 3 and 15, namely 4, 5, 10, and 15.

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168) To paint a room, Suzanne uses blue and white paint in the ratio of blue:white = 8:3. What was the total number of gallons of paint used if she used 6 gallons of blue paint? 

Explanation

Suzanne uses blue and white paint in the ratio of 8:3. If she used 6 gallons of blue paint, we can find the amount of white paint used by setting up a proportion. The ratio of blue to white is 8:3, so the ratio of blue to total paint is 8:(8+3) = 8:11. We can set up the proportion 8/11 = 6/x, where x is the total amount of paint used. Solving for x, we find that x = 11/8 * 6 = 8. Therefore, the total number of gallons of paint used is 8 gallons.

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169) A water tank is 1 third full; then, 21 gallons of water are added to the tank, making it 4 over 5 full. How many gallons of water could the tank hold if it were completely full? 

Explanation

The question states that the water tank is already full, and then 21 gallons of water are added to the tank, making it full again. This means that the tank can hold 21 gallons of water. Therefore, if the tank were completely full, it could hold 21 gallons plus the additional 21 gallons that were added, resulting in a total capacity of 42 gallons. Since none of the answer choices match 42 gallons, the closest option is 45 gallons.

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170) If 1 1 half  cups of cereal are used with 4 1 half cups of water, the amount of water needed with 3 over 4 of a cup of cereal is :

Explanation

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171) The number of gallons of paint needed to cover the exterior of a house with one coat of paint is estimated by the formula FIXME [10n(l+w) - 9n] / 350, where n is the number of stories, l is the length of the house in feet, and w is the width of the house in feet. Approximately how many gallon cans of paint should somebody buy in order to paint one coat the exterior of a 30 X 50-foot 2-story house?

Explanation

The formula given estimates the number of gallons of paint needed to cover the exterior of a house. In this case, the house is a 2-story house with dimensions of 30 X 50 feet. Plugging in the values into the formula, we get (10*2*(30+50) - 9*2) / 350 = 130 / 350 = 0.371 gallons. Since we can only buy whole gallon cans of paint, we need to round up to the nearest whole number, which is 1. Therefore, somebody should buy 1 gallon can of paint to paint one coat on the exterior of this house.

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172) How many subsets does set A have if set A = {1, 2}?

Explanation

Set A = {1, 2} has 4 subsets. The subsets are: {}, {1}, {2}, {1, 2}. The empty set is always a subset of any set, and the set itself is also a subset. Additionally, each element can be either included or excluded from a subset, resulting in 2^2 = 4 possible combinations.

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173) If  f left parenthesis x right parenthesis equals 3 over x then what is F (F(6) +f left parenthesis f left parenthesis 6 right parenthesis plus f left parenthesis 4 right parenthesis right parenthesis?

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174) On a particular vehicle, the front tire makes three revolutions for every one revolution the back tire makes. How many times larger is the radius of the back tire than the radius of the front tire? 

Explanation

The front tire makes three revolutions for every one revolution of the back tire. Since the number of revolutions is directly proportional to the circumference of the tire, it means that the circumference of the front tire is three times larger than the circumference of the back tire. The circumference of a tire is directly proportional to its radius, so the radius of the front tire is also three times larger than the radius of the back tire. Therefore, the radius of the back tire is one-third the size of the radius of the front tire.

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175) X, y and m are positive integers. If x < 2y and m > y+1, which of the following must be greater than x?

Explanation

Since x < 2y, we know that 2y is greater than x. Additionally, since m > y+1, we can conclude that m-1 is greater than y+1. Therefore, m-1 must also be greater than x. Now, considering the answer choices, we can see that 2m-2 is greater than m-1 and therefore greater than x. Thus, the correct answer is 2m-2.

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176) If m = 3x + 2, then what is 5m - 3 in terms of x?

Explanation

If m = 3x + 2, then to find 5m - 3 in terms of x, we substitute the value of m into the expression. So, 5m - 3 becomes 5(3x + 2) - 3. Simplifying this expression gives us 15x + 10 - 3, which further simplifies to 15x + 7. Therefore, the correct answer is 15x - 7.

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177) Jack and Roberto were assigned to guard a tower. Each was to watch for 5 hours, then rest 5 hours while the other watched. If Roberto began his first watch at 6:00 p.m., at what time will he begin his third watch? 

Explanation

Since Jack and Roberto take turns guarding the tower for 5 hours each, and then rest for 5 hours while the other watches, it means that each cycle of guarding and resting takes 10 hours. If Roberto begins his first watch at 6:00 p.m., he will finish his first cycle of guarding and resting at 4:00 a.m. Since each cycle takes 10 hours, Roberto will begin his third watch 20 hours after he began his first watch, which would be at 2:00 p.m.

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178) Ryan must read 150 pages for school tomorrow. It took him 30 minutes to read the first 20 of the assigned pages. At this rate, how much additional time will it take him to finish the reading?  

Explanation

Ryan took 30 minutes to read the first 20 pages. Therefore, he took 30/20 = 1.5 minutes per page. To read the remaining 130 pages, he will take an additional 130 * 1.5 = 195 minutes.

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179) At a certain location on the ocean coast, low tide occurred at 5:00AM on the first day of June .If the time between consecutive low tides is 12 hours and 25 minutes, what was the first day on which low tide occurred between 8:00PM and midnight?

Explanation

Low tide occurs every 12 hours and 25 minutes. To find the first day on which low tide occurred between 8:00 PM and midnight, we need to count the number of times low tide occurs within this time frame. From 5:00 AM on the first day of June to 8:00 PM on the same day, there are 15 hours and 3 low tides. From midnight to 8:00 PM on the second day of June, there are 20 hours and 4 low tides. Therefore, the first day on which low tide occurred between 8:00 PM and midnight is June 5th.

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180) A pitcher contained 32 ounces of orange juice and 12 ounces of grapefruit juice. More grapefruit juice was added to the pitcher until grapefruit juice represented 1 third of the pitcher's contents. How many ounces of grapefruit juice were added?

Explanation

The pitcher initially contained a total of 32 + 12 = 44 ounces of juice. Let's assume x ounces of grapefruit juice were added. The grapefruit juice now represents x + 12 ounces out of the total 44 + x ounces. We are given that this represents 1/3 of the pitcher's contents. So, we can set up the equation (x + 12) / (44 + x) = 1/3. Solving this equation gives us x = 4 ounces. Therefore, 4 ounces of grapefruit juice were added.

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181) There are 1,000 cubic centimeters in 1 liter and 1,000 cubic millimeters in 1 milliliter. How many cubic millimeters are there in 1,000 cubic centimeters? 

Explanation

There are 1,000 cubic centimeters in 1 liter, and there are 1,000 cubic millimeters in 1 milliliter. Therefore, to find how many cubic millimeters are there in 1,000 cubic centimeters, we need to multiply 1,000 by 1,000. This gives us 1,000,000 cubic millimeters.

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182) DISTRIBUTION OF EYE AND HAIR COLOR FOR 64 CHILDREN
Hair color / Eye colorBrownBlueTotal
Blond111829
Black152035
The table above shows the distribution of eye color and hair color for 64 children. How many of these children have blond hair or brown eyes, but not both?

Explanation

The table shows the distribution of eye color and hair color for 64 children. To find the number of children who have blond hair or brown eyes, but not both, we need to subtract the number of children who have both blond hair and brown eyes from the total number of children who have either blond hair or brown eyes. From the table, we can see that there are 18 children with blond hair and brown eyes. Therefore, the number of children who have blond hair or brown eyes, but not both, is 44 (64 - 18).

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183) On a scale drawing, a distance of 1 foot is represented by a segment 0.25 inch in length. How long must a segment on the scale drawing be to represent a 36-inch distance?

Explanation

In the given scale drawing, 1 foot is represented by a segment 0.25 inch in length. To find out how long a segment on the scale drawing must be to represent a 36-inch distance, we can set up a proportion. Since 1 foot is equal to 12 inches, we can write the proportion as 1 foot/12 inches = x/36 inches. Solving for x, we find that x = 3 feet. Therefore, the segment on the scale drawing must be 0.75 inch in length to represent a 36-inch distance.

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184) Ang has x dollars in his savings account, and Julia has y dollars in her savings account. Ang gives Julia 1 third of the money in his savings account, which Julia deposits into her savings account. Julia then spends 1 fourth of the total in her savings account. Express the amount of money Julia spent in terms of x and y. 

Explanation

Julia receives of Ang's savings account, which is of x dollars. After depositing this amount into her savings account, Julia now has y + dollars. Julia then spends of this total amount, which is of (y + ) dollars. Therefore, the amount of money Julia spent can be expressed as of (y + ) dollars.

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185) If Syntax error from line 1 column 119 to line 1 column 139. Unexpected '='., what is the sum of h and k?

Explanation

To solve the equation 4^h*5^k=40000, let's express 40000 in terms of its prime factorization:

40000=2^5*5^4

h=5 k=4​

Therefore, h+k=5+4=9.

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186) ABCD is a rectangle. The measure of angle BFA is 60 degrees and the measure of angle FAE is 40 degrees. Find the measure, in degrees, of angle AED.

Explanation

Angle BFA and angle FAE are both angles in a triangle that share side AF. Since the sum of the angles in a triangle is 180 degrees, the third angle in this triangle, angle AFE, can be found by subtracting the measures of angle BFA and angle FAE from 180 degrees. Angle AFE = 180° - 60° - 40° = 80°.

Since angle AFE and angle AED are corresponding angles in a rectangle, they are congruent. Therefore, the measure of angle AED is also 80 degrees.

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187) |x - 3| =3.6 . What is the least possible value of x?

Explanation

To find the least possible value of x, we need to consider the two cases when the absolute value of x - 3 is equal to 3.6. In the first case, if x - 3 is positive, then x - 3 = 3.6, which gives x = 6.6. In the second case, if x - 3 is negative, then -(x - 3) = 3.6, which simplifies to -x + 3 = 3.6. Solving this equation gives x = -0.6. Since -0.6 is smaller than 6.6, it is the least possible value of x.

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188) Completely simplify: fraction numerator 10 x to the power of 2 space end exponent plus 5 x over denominator x y end fraction times fraction numerator y squared over denominator 5 y end fraction (x is not equal to 0 and y is not equal to 0)

Explanation

The given expression is a simplified version of the expression (x is not equal to 0 and y is not equal to 0). It combines the terms 2x and 1 to form 2x + 1.

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189) When graphed on the coordinate plane, what is the range of the function shown below when -10 < x < 10?f left parenthesis x right parenthesis open curly brackets table row cell minus x space i f space minus 10 less than x less than 0 end cell row cell x squared space i f space 0 less or equal than x less than 10 end cell end table close curly brackets

Explanation

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190) In the graph, what is the overall ratio of males to females for the three rooms?

Explanation

The overall ratio of males to females for the three rooms is 7:8. This means that for every 7 males, there are 8 females in the three rooms.

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191) If q is a prime number that is less than 10, what is the largest possible valued of (2q) + 1?

Explanation

If q is a prime number less than 10, the largest possible value of (2q) + 1 can be found by substituting the largest possible value of q, which is 7, into the expression. Therefore, (2q) + 1 = (2*7) + 1 = 15.

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192) Considering "If you are the president of the United States, then you must be over 35," which of the following it true?

Explanation

The correct answer is "It is sufficient to know that you are over 35 for the statement 'you are the president of the United States' to be considered true." This means that if someone is over 35 years old, they can be considered as a potential candidate for the presidency of the United States. However, it does not guarantee that they will become the president, as there are other requirements and processes involved in becoming the president.

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193) The radius of cylinder is 2x and the hieght of the cylinder is 8x + 2. What is the volume of the cylinder in terms of x?

Explanation

The volume of a cylinder is calculated by multiplying the area of the base (which is the area of a circle with radius r) by the height. In this case, the radius is given as 2x and the height is given as 8x + 2. Therefore, the volume would be (pi * (2x)^2 * (8x + 2)), which simplifies to (16x^3 + 4x^2) * pi.

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194) If the circumference of a circle measures 10 feet, what is its area in square feet?

Explanation

The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius. In this question, the circumference of the circle is given as 10 feet. The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. By rearranging this formula, we can find the radius as C/2π. Substituting the given circumference of 10 feet, we get the radius as 10/2π. Now, substituting this radius into the formula for the area, we get A = π(10/2π)^2 = 25/π square feet.

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195) There are 45 eighth graders and 20 seventh graders in a school club. The president of this club wants 40% of the club's members to be seventh graders. How many more seventh graders must join the club in order to meet the president's wishes? (Assume that the number of eighth graders remains the same.)

Explanation

In order for 40% of the club's members to be seventh graders, there must be a total of 65 members in the club (45 eighth graders + 20 seventh graders). Since there are already 20 seventh graders, the club needs 45 - 20 = 25 more members to reach a total of 65. However, since only seventh graders are needed to meet the president's wishes, the club still needs 25 - 15 = 10 more seventh graders to join.

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196) Of the 40 candies in a bowl, 1 fifth contains nuts and 1 fourth contain caramel. If 6 of the candies contain both nuts and caramel, what percent of the candies contain neither nuts nor caramel?

Explanation

Out of the 40 candies, 6 candies contain both nuts and caramel. Therefore, the remaining candies that do not contain nuts or caramel can be calculated by subtracting the candies with nuts and caramel from the total number of candies: 40 - 6 = 34. To find the percentage of candies that do not contain nuts or caramel, divide the number of candies without nuts or caramel by the total number of candies and multiply by 100: (34/40) * 100 = 85%. However, the question asks for the percentage of candies that contain neither nuts nor caramel, so subtracting this percentage from 100 gives us: 100 - 85 = 15%. Therefore, the correct answer is 15%, which is not listed as an option. Hence, the correct answer cannot be determined from the given options.

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197) There are 6 people and 6 chairs. In how many different ways can the 6 people sit in the 6 chairs?

Explanation

There are 6 people and 6 chairs, so each person can choose from 6 available chairs. The first person has 6 choices, the second person has 5 choices (since one chair is already occupied), the third person has 4 choices, and so on. Therefore, the total number of different ways the 6 people can sit in the 6 chairs is 6 x 5 x 4 x 3 x 2 x 1 = 720.

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198) Sheila has twice as many marbles as Jenna. If Sheila gives Jenna 5 marbles. She will still have 10 more marbles than Jenna. How many marbles does sheila have?

Explanation

If Sheila has twice as many marbles as Jenna, and after giving Jenna 5 marbles she will still have 10 more marbles than Jenna, we can set up the equation 2x - 5 = x + 10, where x represents the number of marbles Jenna has. Solving this equation, we find that x = 15. Since Sheila has twice as many marbles as Jenna, she must have 2 * 15 = 30 marbles. Therefore, the answer is 30.

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199) In the figure above, stack J K L with bar on top, stack M K N with bar on top, stack N P Q with bar on top, and stack L P R with bar on top are straight line segments. What is the value of x?

Explanation

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200) How many positive two-digit numbers are evenly divisible by 4?

Explanation

To find the number of positive two-digit numbers that are evenly divisible by 4, we need to determine the range of two-digit numbers divisible by 4. The smallest two-digit number divisible by 4 is 12, and the largest is 96. We can find the count of numbers in this range by subtracting the first number (12) from the last number (96) and dividing the result by 4 (since every fourth number in this range is divisible by 4). (96-12)/4 = 84/4 = 21. However, we need to include the number 96 as well, so the total count is 21 + 1 = 22. Therefore, the correct answer is 22.

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