SAT Mathematics Practice Test 1

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  • 1/38 Questions

    If x and y are multiples of 3, which of the following CANNOT also be a multiple of 3?

    • A. x + y
    • B. x - y
    • C. x + y + 1
    • D. xy
    • E. xy + 3
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About This Quiz

SAT Mathematics Practice Test 1 assesses mathematical skills through problems on consecutive odd integers, prime numbers, square roots, percentages, equations, averages, and polynomial factorization. It prepares learners for SAT Math, enhancing problem-solving and analytical skills.

SAT Mathematics Practice Test 1 - Quiz

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  • 2. 

    Find the equation of the line through (2, 3) perpendicular to 4x - 3y=10.

    • A. 4x - 3y = 18

    • B. 4x - 3y = -18

    • C. 3x + 4y = -18

    • D. 3x + 4y = 18

    • E. 4x + 3y = 18

    Correct Answer
    A. D. 3x + 4y = 18
    Explanation
    Only option D is correct as the other equations do not satisfy the given conditions
    of the equation of a line through (2, 3) and perpendicular to 4x-3y=10
    Equation of a line perpendicular to the given line is
    3x+4y+z=0 or 3*2+*3+z=0 or 18+z=0 or z=-18. Therefore, the equation of the
    required line is 3x+4y-18=0 or 3x+4y=18

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  • 3. 

    If p > 0, which of the following is equal to √48p3

    • 4p√3p

    • 3p√4p

    • 2√12p

    • 3√8p

    • 16p√3p

    Correct Answer
    A. 4p√3p
    Explanation
    Option A is correct: √48p^3 = √16 x 3 x p x p x p = 4p√3p
    Option B is incorrect: (3p√4p)^2 = 9p^2 X 4p = 36p^3
    Option C is incorrect: (2√12p)^2 4 x 12p = 48p
    Option D is incorrect: (3√8p)^2 = 9 x 8p = 72p
    Option E is incorrect: (16p√3p)^2 = 256p x 3p = 768p^3
    Option C is incorrect: (16p√3p)^2 = 256p^2 X 3p = 768p^3

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  • 4. 

    What will be the value of x, if 8x+2 = 24x-3?  

    • A. 0.9

    • B. 1.9

    • C. 18

    • D. 9

    • E. 11

    Correct Answer
    A. D. 9
    Explanation
    8;x+2 = 24x-3, (23)x+2= 24x-3, 23x+6= 24x-3
    As the bases are same, the powers can be equated. Hence
    3x+6 = 4x-3 or - x = - 9 Or x = 9

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  • 5. 

    If 4(3x - 3) = 24, what is 5x - 5?

    • 10

    • 6

    • 24

    • 3

    • 4

    Correct Answer
    A. 10
    Explanation
    To find the value of 5x - 5, we need to first solve the given equation. Distributing the 4 to the terms inside the parentheses, we get 12x - 12 = 24. Adding 12 to both sides of the equation, we get 12x = 36. Dividing both sides by 12, we find that x = 3. Plugging this value into 5x - 5, we get 5(3) - 5 = 15 - 5 = 10. Therefore, the correct answer is 10.

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  • 6. 

    If y2 = c, where y and c are integers, which of the following could be the value of c?

    • 45

    • 17

    • 64

    • 34

    • 10

    Correct Answer
    A. 64
    Explanation
    Option A is not correct. y2 = c implies that c must be a perfect square. But 45 is not a perfect square.
    Option B is not correct y2 = c implies that c must be a perfect square. But 17 is not a perfect square.
    Option C is correct. y2 = c implies that c must be a perfect square. 64 is a perfect square.
    Option D is not correct y2 = c implies that c must be a perfect square. But 34 is not a perfect square.
    Option E is not correct. y2 = c implies that c must be a perfect square. But 10 is not a perfect square.

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  • 7. 

    If 40% of x is equal to 30% of y, what % is x of y?

    • 50%

    • 75%

    • 175%

    • 20%

    • 40%

    Correct Answer
    A. 75%
    Explanation
    As other percents given are not equal to the calculated percentage, B is the correct option.

    40x/100 = 30y/100, hence x/y 100% = 3/4 100% = 75%

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  • 8. 

    At what point will 12x2 + 5x + 1 attain the minimum value?

    • A. 5 ⁄ 24

    • B. -5 ⁄ 24

    • C. 15 ⁄ 8

    • D. 24 ⁄ 5

    • E. 8 ⁄ 1

    Correct Answer
    A. B. -5 ⁄ 24
    Explanation
    Option A is not correct as –b/2a ≠ 5/24
    Only option B is correct, as the other values given do not satisfy
    The given condition for point of minimum value, that is –b/2a
    Option C is not correct as –b/2a ≠ 5/8
    Option D is not correct as –b/2a ≠ 24/5
    Option E is not correct as –b/2a ≠ 8/15

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  • 9. 

    How many positive integers less than 80 are equal to the product of a positive multiple of 5 and an even number?

    • A. 3

    • B. 5

    • C. 15

    • D. 9

    • E. 7

    Correct Answer
    A. E. 7
    Explanation
    Only option E is correct as there are only 7 numbers which satisfy the given condition in the question that is all positive integers less than 80 which are equal to the product of 5 and an even number.
    5 x 2 = 10, 5 x 4 = 20, 5 x 6 = 30, 5 x 8 = 40, 5 x 10 = 50,
    5 x 12 = 60,
    5 x 14 = 70, hence the required numbers are 10, 20, 30,40,50,60 and 70

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  • 10. 

    A jar contains 10 red marbles and 30 green ones. How many red marbles must be added to the jar so that 60% of the marbles will be red?

    • A. 30

    • B. 25

    • C. 35

    • D. 27

    • E. 125

    Correct Answer
    A. C. 35
    Explanation
    Number of red marbles in the jar = 10+x
    Total number of marbles in the jar = 10+x+30 = 40+x
    According to the problem,
    10+x/40+x = 10(10+x) = 6(40 + x)
    Or 100 + 10x = 240 + 6x or 4x =140 or x = 35
    Hence, 35 red marbles must be added to the jar.

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  • 11. 

    Which of the following is equivalent to 6x 2 + x - 12 ?

    • (2x + 3)(3x - 4)

    • (2x - 3)(3x - 4)

    • (2x + 3)(3x + 4)

    • (6x + 3)(x - 12)

    • (x + 3)(2x - 12)

    Correct Answer
    A. (2x + 3)(3x - 4)
    Explanation
    The given expression is a quadratic trinomial. To find the equivalent expression, we need to factorize the quadratic trinomial. The correct answer, (2x + 3)(3x - 4), is the factored form of the given expression.

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  • 12. 

    In a class of 30 students, 14 take tea and 20 take coffee. How many take both tea and coffee?

    • 16

    • 10

    • 14

    • 30

    • 4

    Correct Answer
    A. 4
    Explanation
    Number of students in the class = n(T∪C) = 30
    Number of students who take tea = n(T) = 14
    Number of students who take coffee = n(C) =20
    Number of students who take both tea and coffee = n(T∩C)
    n(T∩C) = n(T) + n(C) - n(T∪C)
    =14 + 20 - 30 = 34 - 30 = 4

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  • 13. 

    The flowers in a basket become double after every minute. In one hour, the basket becomes full. After how many minutes the basket would be half filled?  

    • A. 59

    • B. 19

    • C. 36

    • D. 26

    • E. 63

    Correct Answer
    A. A. 59
    Explanation
    The basket was half filled after 59 minutes.
    If there were half the number of flowers in the basket after 59 minutes, then the basket would be full in the next minute, as the flowers double after every minute.

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  • 14. 

    A person had 72 mangoes, he had given them to three persons A, B and C, in such a manner that A got thrice as many as B, and the sum total of mangoes A and B got was 60. He had given the remaining mangoes to C. Express in decimal the fraction of mangoes C got out of the total.  

    • A. 0.267

    • B. 0.347

    • C. 0.159

    • D. 0.359

    • E. 0.167

    Correct Answer
    A. E. 0.167
    Explanation
    Sometimes in some problems, some extra information is given, which is not required to solve the problem. Here, it is clear that the number of mangoes C got is 12.
    Total 72 mangoes minus 60 mangoes given to A and B. Hence, Fraction of mangoes C got out of the total number of mangoes
    = 12/72 = 1/6 = 0.16666. , this can be rounded to 0.167

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  • 15. 

    The average of 11 numbers is 21 . The average of seven of those numbers is 25. What is the average of the remaining four numbers?

    • 4

    • 12

    • 14

    • 21

    • 25

    Correct Answer
    A. 14
    Explanation
    Since the average of the 11 numbers is 21, the sum of all 11 numbers is 11 * 21 = 231. The sum of the seven numbers with an average of 25 is 7 * 25 = 175. To find the sum of the remaining four numbers, we subtract the sum of the seven numbers from the sum of all 11 numbers: 231 - 175 = 56. Finally, we divide the sum of the remaining four numbers by 4 (the number of remaining numbers) to find the average: 56 / 4 = 14. Therefore, the average of the remaining four numbers is 14.

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  • 16. 

    By which of the following number is 98765432 exactly divisible?

    • 9

    • 7

    • 5

    • 8

    • 11

    Correct Answer
    A. 8
    Explanation
    Option A is not correct is not correct. 98765432 is not divisible by 9 as the sum of its digits 44 is not divisible by 9.
    Option B is not correct as 98765432 is not divisible by 7.
    Option C is not correct as the last digit of 98765432 is not 5, hence 98765432 is not divisible by 5.
    Option D is correct. Using the tests of divisibility, we know that a number is divisible by 8 if its last three digits are divisible by 8. The last three digits of the given number 432 is divisible by 8.
    Option E is not correct. As the difference of the sum of digits in its even and odd places {(9 + 7 + 5 + 3) - (8 + 6 + 4 + 2)} 4 is not a multiple of 11, 98765432 is not divisible by 11.

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  • 17. 

    If x2y > 0 and xy2 < 0,then which of the following are true?  

    • A. x = 0

    • B. y = 0

    • C. x > 0 and y < 0

    • D. x < 0 and y > 0

    • E. x > 0 and y > 0

    Correct Answer
    A. D. x < 0 and y > 0
    Explanation
    Option A cannot be chosen, if x = 0 then both the inequalities given will be zero which is not true.
    Option B be cannot be chosen, if y = 0 then both the inequalities given will be zero which is not true.
    Option C cannot be chosen, if x > 0 and y < 0, then x2y will be less than 0 as the product of a positive number and a negative number will be negative. Similarly xy2 will be positive, which is not true.
    Option D is correct. If x2y n> 0, then x2 is anyway positive, hence y must also be positive so that the product is positive. If xy2 < 0, then y2 is anyway positive, hence x must be negative so that the product is negative. Hence x < 0 and y > 0.
    Option E cannot be correct. If both x and y are positive, then only x2y > 0 will be true and xy2 will be false.

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  • 18. 
    In the given figure, EB is perpendicular to FC, and AD and EB intersect at point F. What is the value of  Note: Figure not drawn to scale.   - ProProfs

    In the given figure, EB is perpendicular to FC, and AD and EB intersect at point F. What is the value of  Note: Figure not drawn to scale.  

    • A. 50 degrees

    • B. 40 degrees

    • C. 100 degrees

    • D. 90 degrees

    • E. 180 degrees

    Correct Answer
    A. A. 50 degrees
    Explanation
    Option A is correct, as ∠CFD+∠BFC+ ∠AFB lie on the same line AD.
    Hence their sum must be 180°
    ∠CFD, ∠BFC and ∠AFB = 180°
    ∠CFD + 90° + 40° = 180° (angle on a line) Or ∠CFD = 180° - 130° = 50°
    Option B is not correct as 40°+90°+40°≠180°
    Option C is not correct as 100°+90°+40°≠180°
    Option D is not correct as 90°+90°+40°≠180°
    Option E is not correct as the single angle CFD itself is 180°

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  • 19. 
    In the given figure, Note: Figure not drawn to scale. - ProProfs

    In the given figure, Note: Figure not drawn to scale.

    • 130 degrees

    • 90 degrees

    • 100 degrees

    • 30 degrees

    • 160 degrees

    Correct Answer
    A. 100 degrees
    Explanation
    As other angle measures are not equal to the calculated measure of ∠ABC, only
    option C is correct.
    Exterlor angle of a tr|angle |s equal to the sum of its two interior opposite angles.
    ∠ABD = ∠BDC - ∠BAD = 60° - 30° = 30°
    ∠CBD = ∠BCE - ∠BDC = 130° - 60° = 70°
    ∠ABC = ∠ABD + ∠CBD = 30° + 70° = 100°

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  • 20. 

    If x, y and z are three consecutive odd integers such that 10< x < y < z< 20 and if y and z are prime numbers, what is the value of x + y?

    • 24

    • 27

    • 19

    • 32

    • 15

    Correct Answer
    A. 32
    Explanation
    Option A is not correct her rate is not equal to 1 test per hour.
    Option B is not correct as she can complete ab tests in 1 hour.
    Option C is correct. Alda completes the tests at the rate of a tests/(1/b) hours = ab tests/hour. Hence in n hours she can complete nab tests.
    Option D is not correct as she completes a tests in 1/b hours.
    Option E is also not correct.

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  • 21. 

    Each month for 6 months the price of a commodity is doubled. At the end of the 6 months the price of the commodity is $640. What was the price of the commodity at the end of 3 months?

    • $100

    • $120

    • $80

    • $320

    • $160

    Correct Answer
    A. $80
    Explanation
    The price of the commodity is doubled each month for 6 months. Therefore, if the price at the end of 6 months is $640, then the price at the end of 3 months would be half of that. Half of $640 is $320, so the correct answer is $320.

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  • 22. 

    A cube and a rectangular solid are equal in volume. If the lengths of the edges of the rectangular solid are 4, 8 and 16, what is the surface area of the cube?  

    • A. 176

    • B. 392

    • C. 284

    • D. 388

    • E. 384

    Correct Answer
    A. E. 384
    Explanation
    Volume of rectangular solid = volume of cube.
    Or l * w * h = s3 or 4 * 8 * 16 = s3 or s3 = 512
    Or s = 8 Surface area of the cube = 6s2 = 6 * 8 * 8 = 384

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  • 23. 
    In the given figure,   - ProProfs

    In the given figure,  

    • A. 150

    • B. 120

    • C. 115

    • D. 125

    • E. 130

    Correct Answer
    A. E. 130
    Explanation
    Let 0 be the center of the circle, then ∠QOR is the angle subtended by the arc QR

    The angle subtended by an arc at the center of a circle is double the angle subtended
    by the same arc on the remaining part of the circle

    Therefore, ∠QOR = 2 * 65 degrees = 130 degrees

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  • 24. 

    If 2 dots are equal to 3 dashes and 5 dashes equal to 7 stars, what is the ratio of one dot to one star?

    • 10 ⁄ 21

    • 3 ⁄ 5

    • 5 ⁄ 3

    • 21 ⁄ 10

    • 2 ⁄ 3

    Correct Answer
    A. 21 ⁄ 10
    Explanation
    If 2 dots are equal to 3 dashes and 5 dashes are equal to 7 stars, we can set up the following ratios: 2 dots : 3 dashes and 5 dashes : 7 stars. To find the ratio of one dot to one star, we can combine the two ratios by multiplying them together: (2 dots/3 dashes) * (5 dashes/7 stars). Simplifying this expression gives us 10 dots : 21 stars, which can be written as the ratio 10/21. Therefore, the correct answer is 10/21.

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  • 25. 

    A social welfare organization spends 40% of the funds collected towards old-age homes. If during an year 1.6 million dollars was spent on old-age homes, what is the total amount of funds collected in millions of dollars?

    • 4.0

    • 6.0

    • 4.6

    • 40.0

    • 1.6

    Correct Answer
    A. 4.0
    Explanation
    Option A is correct.
    Let the total fund = n million dollars
    40% of n = 1.6 million dollars
    Or 0.4n = 1.6 million dollars
    Or n = 1.6/0.4 million dollars = 4 million dollars
    Hence 40% of 4 is 1.6
    B is not correct, as 40% of 6 is 2.4 and not 1.6
    C is not correct, as 40% of 4.6 is 1.84 and not 1.6
    D is not correct, as 40% of 40 is 16 and not 1.6
    E is not correct, as 40% of 1.6 is 0.64 and not 1.6

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  • 26. 
    If a function f(x) is defined by - ProProfs

    If a function f(x) is defined by

    • A. x + 1

    • B. x

    • C. x - 1

    • D. x + 3

    • E. x - 3

    Correct Answer
    A. B. x
    Explanation
    Option A is not correct as f(3x+3 / x-1) ≠ x+1
    Option B is correct as
    f(3x+3 / x-1) = (3x+3 / x-1 + 3) / (3x+3 / x-1 - 3)
    = (3x+3+3x-3) / (3x+3-3x+3)
    = 6x/6 = x
    Option C is not correct as f(3x+3 / x-1) ≠ x-1
    Option D is not correct as f(3x+3 / x-1) ≠ x+3
    Option D is not correct as f(3x+3 / x-1) ≠ x-3

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  • 27. 
    In a store   - ProProfs

    In a store  

    • 15

    • 24

    • 150

    • 100

    • 240

    Correct Answer
    A. 150
    Explanation
    As other answers are not equal to the calculated answers, only option C is correct. 1$ = 100 cents and 1 pound = 16 ounces.
    Price/weight = 12/45 dollars/pounds = 1200/ (45*16) cents/ounces
    = n/9 cents/ounces
    Or 1200 * 9 = 4.5 * 16 * n
    or n = 1200 * 9/72 = 150 cents

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  • 28. 
    In the given figure, area of square ABED is 9 square units, BC = 5 units, EF = 1 unit. Find the area of the rectangle BCGF.  - ProProfs

    In the given figure, area of square ABED is 9 square units, BC = 5 units, EF = 1 unit. Find the area of the rectangle BCGF. 

    • 25 square units

    • 30 square units

    • 36 square units

    • 20 square units

    • 15 square units

    Correct Answer
    A. 20 square units
    Explanation
    As other areas given are not equal to the calculated area, only option D is correct.
    Area of square ABED = 9 square units or side of square ABDE
    BE = side of square ABED = 3 units
    EF = 1 unit.
    Width of the rectangle BCGF= BF = BE + EF
    = 3 units + 1 unit = 4 units
    Length of the rectangle BCGF= BC = 5 units
    Area of the rectangle BCGF = 1 * w
    = 5 * 4 square units
    = 20 square units

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  • 29. 
    An operation * is defined as follows: For any two positive numbers x and y, - ProProfs

    An operation * is defined as follows: For any two positive numbers x and y,

    • 11 * 4

    • 4 * 9

    • 4 * 16

    • 7 * 4

    • 9 * 9

    Correct Answer
    A. 7 * 4
    Explanation
    In the given question, the operation * is defined as the product of two positive numbers. The expression "7 * 4" means multiplying 7 and 4 together. Therefore, the correct answer is 28.

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  • 30. 

    Twenty persons, among whom A and B, sit at random around a round table. Find the probability that there are any 6 persons between A and B.  

    • A. 2/17

    • B. 2/19

    • C. 2/15

    • D. 3/19

    • E. 5/19

    Correct Answer
    A. B. 2/19
    Explanation
    Let A occupy any seat around the table. Then there are 19 seats available for B. But if there are to be six persons between A and B, then B has only two ways to sit.
    Thus, the required probability is 2/19

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  • 31. 
    - ProProfs

    • 81

    • 40

    • 72

    • 9

    • 18

    Correct Answer
    A. 72
    Explanation
    The given sequence is a combination of two patterns: the numbers are alternately multiplied by 2 and divided by 2. Starting with 81, the next number is obtained by dividing 81 by 2, resulting in 40. Then, 40 is multiplied by 2 to get 80. Continuing this pattern, the next number is obtained by dividing 80 by 2, resulting in 40. Therefore, the answer is 72, which is obtained by dividing 144 by 2.

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  • 32. 
    Solve for x:  - ProProfs

    Solve for x: 

    • 12 < x < 13

    • -12 < x < -13

    • -5 < x < -5

    • -25 < x < 25

    • -12 < x < 13

    Correct Answer
    A. -12 < x < 13
    Explanation
    -5 ≤ (2x - 1)/ 5 ≤ 5 => -25 ≤ 2x -1 ≤ 25
    Or- 24 ≤ 2x ≤ 26
    Or -12 ≤ x ≤ 13

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  • 33. 

    A car travels a distance of 250 miles, 700 miles and 325 miles at the rate of 50 miles/hr, 35 miles/hr and 13 miles/hr respectively.Find the average speed of the car in miles/hr.

    • 30

    • 25.5

    • 42.5

    • 13

    • 50

    Correct Answer
    A. 25.5
    Explanation
    As other speeds given are not equal to the calculated average speed only option B is correct.
    Speed = distance traveled/time taken
    Total distance traveled = (250 +700 + 325) mile = 1275 miles
    Time = distance/speed
    Total time = (250/50 + 700/35 + 325/13) hrs = (5 + 20 + 25) hrs = 50 hrs
    Average speed of the car = 1275/50 miles / hr = 25.5 miles/hr

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  • 34. 

    A shopkeeper has three kinds of rice of 77 pounds, 147 pounds and 252 pounds. Find the least number of bags of equal size required to pack them without mixing.

    • A. 68

    • B. 46

    • C. 88

    • D. 36

    • E. 6

    Correct Answer
    A. A. 68
    Explanation
    Capacity of each bag = HCF of 77, 147 and 252 = 7 pounds.
    Total number of bags required = 77/7 + 147/7 + 252/7
    11 + 21 + 36 = 68

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  • 35. 
    In the given figure, AB is parallel to CD. - ProProfs

    In the given figure, AB is parallel to CD.

    • A. 99

    • B. 97

    • C. 93

    • D. 91

    • E. 89

    Correct Answer
    A. D. 91
    Explanation
    Draw a line XY through O parallel to either AB or CD.
    Then the figure will look like as given below.

    C N D


    X O Y




    A M B


    As all the three lines in figure are parallel, we have the following relations:
    ∠CNO = ∠NOY = 55 degrees (interior alternative angles)
    ∠AMO = ∠MON = ∠MOV + ∠NOY
    = 55 degrees + 36 degrees = 91 degrees

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  • 36. 
    Alda can complete a test in  . - ProProfs

    Alda can complete a test in  .

    • N

    • Ab

    • Nab

    • A

    • B

    Correct Answer
    A. Nab
    Explanation
    The correct answer is "nab" because it is the only option that makes sense in the given context. The other options are either incomplete or do not form a coherent word. Therefore, "nab" is the most logical and appropriate answer.

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  • 37. 

    A monkey climbs a slippery pole by thrusts. The pole is 30 feet high. With every thrust, it goes up 5 feet in 5 seconds and slips down 3 feet in 1 second. How many seconds will it take to climb the pole?  

    • A. 74

    • B. 82

    • C. 94

    • D. 78

    • E. 92

    Correct Answer
    A. B. 82
    Explanation
    Distance climbed by the monkey in 6 seconds
    = 5 feet - 3 feet = 2 feet
    In 6 seconds it climbs 2 feet. It climbs 26 feet in 78 seconds and the remaining 4 feet in 4 seconds. So the total time is 82 seconds.

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  • 38. 

    A wire bent in the form of a circle of radius 21units is cut and bent to form a square. What is the ratio of area of circle to that of the square?

    • A. 11:15

    • B. 11:14

    • C. 15:11

    • D. 21:22

    • E. 14:11

    Correct Answer
    A. E. 14:11
    Explanation
    Only option E is correct as the other ratios given do not satisfy the relation
    Radius = 21units
    Circumference = 2πr = 2 * 22/7 *21 units = 132 units
    Circumference of the circle = perimeter of the square or
    4a = 132 units or a = 33 units
    Therefore, side of the square is 33 units
    Area of circle: Area of square = πr2:a^2
    = 22/7 *21*21: 33*33
    =14:11

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  • Nov 21, 2023
    Quiz Edited by
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  • May 05, 2011
    Quiz Created by
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