The Diagnostic Math Test Part I
This test is to identify your current math knowledge. Do not worry if you do not know all of the answers. Please answer every question.
- 1.
Round 577,312 to the nearest thousand.
- A.
577,000
- B.
577,300
- C.
578,000
- D.
580,000
Correct Answer
A. 577,000Explanation
The given number, 577,312, is rounded to the nearest thousand. To round a number to the nearest thousand, we look at the hundreds place. If the digit in the hundreds place is 5 or greater, we round up to the next thousand. In this case, the digit in the hundreds place is 3, which is less than 5. Therefore, we round down to the nearest thousand, which is 577,000.Rate this question:
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- 2.
How many millimeters are in 2 centimeters?
- A.
0.2
- B.
20
- C.
200
- D.
2,000
Correct Answer
B. 20Explanation
There are 10 millimeters in 1 centimeter, so to find out how many millimeters are in 2 centimeters, we multiply 2 by 10, which equals 20.Rate this question:
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- 3.
Find 3,000-1,532.
- A.
1,468
- B.
2,468
- C.
2,532
- D.
4,532
Correct Answer
A. 1,468Explanation
To find 3,000-1,532, we subtract the second number from the first. Subtracting 1,532 from 3,000 gives us 1,468. Therefore, the correct answer is 1,468.Rate this question:
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- 4.
Which number expression represents "5 more than 10?"
- A.
10>5
- B.
5x10
- C.
10-5
- D.
10+5
Correct Answer
D. 10+5Explanation
The number expression "10+5" represents "5 more than 10" because when you add 5 to 10, you get a sum of 15, which is 5 more than the original number 10.Rate this question:
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- 5.
Which of the following best describes the probability of spinning a 5 when you spin this spinner once?
- A.
Likely
- B.
Unlikely
- C.
Impossible
- D.
Certain
Correct Answer
C. ImpossibleExplanation
The probability of spinning a 5 when spinning the spinner once is impossible because the options provided do not include a 5.Rate this question:
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- 6.
In the circle, the segment is a:
- A.
Radius.
- B.
Center.
- C.
Chord.
- D.
Diameter.
Correct Answer
A. Radius.Explanation
A segment in a circle is a part of the circle that is enclosed by a chord. A chord is a line segment that connects two points on the circumference of the circle. In this case, the segment mentioned in the question is not a chord because it does not connect two points on the circumference. Instead, it is a radius, which is a line segment that connects the center of the circle to any point on the circumference. Therefore, the correct answer is radius.Rate this question:
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- 7.
What is the product of 6 and 9?
- A.
3
- B.
15
- C.
54
- D.
63
Correct Answer
C. 54Explanation
The product of 6 and 9 is found by multiplying the two numbers together. In this case, 6 multiplied by 9 equals 54.Rate this question:
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- 8.
Find the elapsed time from 7:30 A.M. to 9:12 A.M.
- A.
2 hours 18 minutes
- B.
1 hour 42 minutes
- C.
1 hour 32 minutes
- D.
1 hour 12 minutes
Correct Answer
B. 1 hour 42 minutesExplanation
The elapsed time from 7:30 A.M. to 9:12 A.M. is 1 hour and 42 minutes. To find the elapsed time, subtract the starting time from the ending time. In this case, subtracting 7:30 A.M. from 9:12 A.M. gives us 1 hour and 42 minutes.Rate this question:
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- 9.
Which polygon has 6 vertices?
- A.
Triangle
- B.
Quadrilateral
- C.
Pentagon
- D.
Hexagon
Correct Answer
D. HexagonExplanation
A hexagon is a polygon with six vertices. It is a closed shape with six straight sides. The term "hexa" means six, so a hexagon has six angles and six vertices. Therefore, the correct answer is hexagon.Rate this question:
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- 10.
What fraction of this set is gray?
- A.
1/5
- B.
3/8
- C.
5/8
- D.
8/5
Correct Answer
C. 5/8Explanation
The fraction 5/8 represents the proportion of the set that is gray. This means that out of the total set, 5 out of 8 parts are gray.Rate this question:
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- 11.
Use mental math to multiply 70 x 4,000.
- A.
280
- B.
2,800
- C.
28,000
- D.
280,000
Correct Answer
D. 280,000Explanation
To multiply 70 by 4,000 using mental math, we can first multiply 7 by 4 to get 28. Then, we add four zeros to the end of this result to get 280,000.Rate this question:
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- 12.
Find the product of 23 and 125.
- A.
148
- B.
625
- C.
2,765
- D.
2,875
Correct Answer
D. 2,875Explanation
To find the product of 23 and 125, multiply the two numbers together. 23 multiplied by 125 equals 2,875.Rate this question:
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- 13.
Each of 6 rows has the same number of seats. If there are a total of 42 seats, how many are in each row?
- A.
7
- B.
8
- C.
36
- D.
48
Correct Answer
A. 7Explanation
Since there are 6 rows with the same number of seats, we can divide the total number of seats (42) by the number of rows (6) to find out how many seats are in each row. 42 divided by 6 equals 7, so there are 7 seats in each row.Rate this question:
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- 14.
Order the numbers from least to greatest.214,681 213,671 213,761
- A.
214,681 213,671 213,761
- B.
213, 761 213,671 214,681
- C.
213,671 214,681 213,761
- D.
213,671 213,761 214,681
Correct Answer
D. 213,671 213,761 214,681Explanation
The numbers are ordered from least to greatest by comparing the digits from left to right. In the given answer, 213,671 is the smallest number as it has the smallest digit in the thousands place. Next, 213,761 is larger than 213,671 as it has a larger digit in the thousands place. Finally, 214,681 is the largest number as it has the largest digit in the thousands place. Therefore, the correct order is 213,671, 213,761, 214,681.Rate this question:
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- 15.
Which dotted line is a line of symmetry?
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
D. DExplanation
The dotted line D is a line of symmetry because when the image is folded along this line, the two halves will perfectly overlap each other. This means that the shape on one side of the line is a mirror image of the shape on the other side of the line. Therefore, line D is a line of symmetry.Rate this question:
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- 16.
Each member of the Spanish club raised $65 in a fundraiser. If there are 7 members in the club, how much money was raised?
- A.
$72
- B.
$425
- C.
$455
- D.
$485
Correct Answer
C. $455Explanation
There are 7 members in the Spanish club, and each member raised $65 in the fundraiser. To find the total amount of money raised, we multiply the number of members (7) by the amount raised per member ($65). 7 * $65 = $455. Therefore, the correct answer is $455.Rate this question:
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- 17.
What is 12/22 in simplest form?
- A.
6/22
- B.
24/44
- C.
6/11
- D.
11/6
Correct Answer
C. 6/11Explanation
To simplify the fraction 12/22, we can divide both the numerator and denominator by their greatest common divisor, which is 2. 12 divided by 2 is 6, and 22 divided by 2 is 11. Therefore, the simplest form of 12/22 is 6/11.Rate this question:
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- 18.
Find the missing number to complete the pattern.4, 8, 16, 32, __, 128
- A.
36
- B.
48
- C.
64
- D.
72
Correct Answer
C. 64Explanation
The pattern in the given sequence is that each number is obtained by multiplying the previous number by 2. Starting with 4, we multiply it by 2 to get 8, then multiply 8 by 2 to get 16, and so on. Therefore, to find the missing number, we need to multiply the previous number (32) by 2, which gives us 64.Rate this question:
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- 19.
Find 263 divided by 3.
- A.
86 R2
- B.
87
- C.
87 R2
- D.
88 R1
Correct Answer
C. 87 R2Explanation
The correct answer is 87 R2. This means that when 263 is divided by 3, the quotient is 87 and the remainder is 2.Rate this question:
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- 20.
Which unit would you use to measure the water used to take a shower?
- A.
Gallon
- B.
Pint
- C.
Cup
- D.
Fluid ounce
Correct Answer
A. GallonExplanation
The gallon is the most appropriate unit to measure the water used to take a shower because it is a larger unit of volume compared to the other options. Showers typically use a significant amount of water, and gallons are commonly used to measure larger quantities of liquid. Pints, cups, and fluid ounces are smaller units and would not accurately represent the amount of water used in a shower.Rate this question:
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- 21.
Which is the most reasonable estimate for 12 x 472?
- A.
5,000
- B.
8,000
- C.
50,000
- D.
80,000
Correct Answer
A. 5,000Explanation
The most reasonable estimate for 12 x 472 is 5,000 because it is the closest option to the actual product. Multiplying 12 by 472 gives us 5,664, which is closest to 5,000 compared to the other options.Rate this question:
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- 22.
Write 3 1/8 as an improper fraction.
- A.
3/8
- B.
4/8
- C.
25/8
- D.
25/3
Correct Answer
C. 25/8Explanation
To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction and add the numerator. In this case, multiplying 3 by 8 gives us 24, and adding the numerator 8 gives us 32. Therefore, 3 1/8 can be written as the improper fraction 32/8, which can be simplified to 25/8.Rate this question:
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- 23.
Which product is NOT the same as 6 x 3 x 5?
- A.
18 x 5
- B.
6 x 15
- C.
30 x 3
- D.
6 x 18
Correct Answer
D. 6 x 18Explanation
The product of 6 x 3 x 5 is equal to 90. Among the given options, the product 6 x 18 is not the same as 6 x 3 x 5.Rate this question:
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- 24.
Which number sentence is TRUE?
- A.
0.9
- B.
0.6>0.57
- C.
0.35>0.4
- D.
0.52
Correct Answer
B. 0.6>0.57Explanation
The number sentence 0.6>0.57 is true because 0.6 is greater than 0.57.Rate this question:
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- 25.
What is the value of the underlined digit?35,028
- A.
30
- B.
3,000
- C.
30,000
- D.
300,000
Correct Answer
C. 30,000Explanation
The underlined digit in the number 35,028 is 30,000. This is because the underlined digit is the digit in the ten thousands place, which is the fourth digit from the right. In the number 35,028, the digit 3 is in the ten thousands place, so the value of the underlined digit is 30,000.Rate this question:
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- 26.
Find 23,816 + 71,614.
- A.
94,426
- B.
95,403
- C.
95,430
- D.
95,490
Correct Answer
C. 95,430Explanation
The correct answer is 95,430. To find the sum of 23,816 and 71,614, we add the corresponding place values of each digit. Starting from the rightmost digit, 6+4 equals 10, so we write down 0 and carry over the 1 to the next column. In the next column, we have 1+1+1 equals 3. Then, in the next column, we have 8+6 equals 14, so we write down 4 and carry over the 1. Finally, in the leftmost column, we have 2+7+1 equals 10, so we write down 0 and carry over the 1. The sum is 95,430.Rate this question:
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- 27.
Evaluate the expression 3n, for n=7
- A.
10
- B.
28
- C.
21
- D.
37
Correct Answer
C. 21Explanation
The expression 3n means multiplying 3 by the value of n. In this case, n is given as 7. So, 3 multiplied by 7 is equal to 21.Rate this question:
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- 28.
Carol bought 5 yards of fabric. What was the total cost of the fabric?Fabric: $2.79 a yard
- A.
$139.50
- B.
$105.50
- C.
$13.95
- D.
$10.55
Correct Answer
C. $13.95Explanation
The total cost of the fabric can be calculated by multiplying the number of yards (5) by the cost per yard ($2.79). Therefore, the total cost of the fabric is $13.95.Rate this question:
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- 29.
Which is the most reasonable estimate for 315 divided by 4?
- A.
8
- B.
9
- C.
80
- D.
90
Correct Answer
C. 80Explanation
To estimate 315 divided by 4, we can round 315 to the nearest multiple of 4, which is 316. Dividing 316 by 4 gives us 79 with a remainder of 0. Since 315 is slightly less than 316, the most reasonable estimate would be slightly less than 79, which is 80. Therefore, 80 is the most reasonable estimate for 315 divided by 4.Rate this question:
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- 30.
Find the range for the following data.Shoe Sizes: 4 5 810 12 9 6 5 11
- A.
12
- B.
10
- C.
8
- D.
6
Correct Answer
C. 8Explanation
The range is the difference between the highest and lowest values in a data set. In this case, the highest shoe size is 12 and the lowest shoe size is 4. Therefore, the range is 12 - 4 = 8.Rate this question:
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- 31.
Which number is divisible by 3?
- A.
109
- B.
132
- C.
179
- D.
253
Correct Answer
B. 132Explanation
132 is divisible by 3 because the sum of its digits (1 + 3 + 2 = 6) is divisible by 3.Rate this question:
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- 32.
Find 7/8 - 5/8.
- A.
1/4
- B.
2/4
- C.
1/2
- D.
3/4
Correct Answer
A. 1/4Explanation
To find the difference between two fractions with the same denominator, we subtract their numerators and keep the denominator the same. In this case, the numerator of the first fraction is 7 and the numerator of the second fraction is 5. Subtracting 5 from 7 gives us 2. Since the denominator is 8, the result is 2/8, which can be simplified to 1/4.Rate this question:
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- 33.
Which is the most reasonable estimate for 6 x 379?
- A.
180
- B.
240
- C.
1,800
- D.
2,400
Correct Answer
D. 2,400Explanation
The most reasonable estimate for 6 x 379 is 2,400. This can be determined by rounding 379 to the nearest hundred, which is 400, and then multiplying it by 6. Since 400 is close to 379, the product of 6 x 400 is a reasonable estimate for 6 x 379. The product of 6 x 400 is 2,400.Rate this question:
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- 34.
Round 21.83 to the nearest tenth.
- A.
20
- B.
21.8
- C.
21.9
- D.
22
Correct Answer
B. 21.8Explanation
To round a number to the nearest tenth, we look at the digit in the hundredth place. In this case, the digit in the hundredth place is 8. Since 8 is greater than or equal to 5, we round up the digit in the tenths place, which is 1, to the next higher number. Therefore, 21.83 rounds to 21.8.Rate this question:
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- 35.
What is 7/10 written as a decimal?
- A.
0.07
- B.
0.17
- C.
0.7
- D.
7.10
Correct Answer
C. 0.7Explanation
The fraction 7/10 can be written as a decimal by dividing 7 by 10. When 7 is divided by 10, the quotient is 0.7. Therefore, the correct answer is 0.7.Rate this question:
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- 36.
36 ft = __ yd
- A.
3
- B.
6
- C.
9
- D.
12
Correct Answer
D. 12Explanation
To convert feet to yards, divide the number of feet by 3, since there are 3 feet in a yard. In this case, 36 feet divided by 3 equals 12 yards.Rate this question:
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- 37.
Use mental math to divide 5,400 divided by 90.
- A.
6
- B.
60
- C.
600
- D.
6,000
Correct Answer
B. 60Explanation
To divide 5,400 by 90 mentally, we can start by dividing each number by 10. 5,400 divided by 10 is 540, and 90 divided by 10 is 9. Then, we can divide 540 by 9, which gives us 60. Therefore, the answer is 60.Rate this question:
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- 38.
Who had the most votes for class representative?
- A.
Barb
- B.
Damon
- C.
Desi
- D.
Sara
Correct Answer
A. BarbExplanation
Barb had the most votes for class representative.Rate this question:
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- 39.
Find the perimeter of the rectangle.
- A.
14 m
- B.
20 m
- C.
28 m
- D.
48 m
Correct Answer
C. 28 mExplanation
The perimeter of a rectangle is calculated by adding up all the sides of the rectangle. In this case, the two sides given are 14 m and 20 m. To find the perimeter, we add these two sides together: 14 m + 20 m = 34 m. However, since the question asks for the perimeter, we need to double this value because a rectangle has two pairs of equal sides. Therefore, the perimeter of the rectangle is 2 * 34 m = 68 m. Since none of the given options match this answer, the correct answer is not available.Rate this question:
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- 40.
Find the area of the rectangle.
- A.
48 square meters
- B.
36 square meters
- C.
28 square meters
- D.
14 square meters
Correct Answer
A. 48 square metersExplanation
The area of a rectangle is calculated by multiplying its length by its width. Since the question does not provide any specific measurements for the length and width, we can assume that the length and width are both equal to 48 meters. Therefore, the area of the rectangle would be 48 meters multiplied by 48 meters, which equals 48 square meters.Rate this question:
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