SAT Mathematics Practice Test 4

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SAT Mathematics Practice Test 4 - Quiz


Questions and Answers
  • 1. 

    Which of the following numbers is between 3 and 4?

    • A.

      A. 12/15

    • B.

      B. 15/4

    • C.

      C. 17/4

    • D.

      D. 13/6

    • E.

      E. 11/6

    Correct Answer
    B. B. 15/4
    Explanation
    Option A is not correct as 12/5 = 2.4
    Option B is correct as 15/4 = 3.75 and 3.75 lies between 3 and 4.
    Option C is not correct as 17/4 = 4.25
    Option D is not correct as 13/6 = 2.1666...
    Option E is not correct as 11/6 = 1.83...

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  • 2. 

    A team of 24 men can complete a job in 18 days working 9 hours per day. How many hours a day would 27 men have to work in order to finish it in 12 days?

    • A.

      A. 12

    • B.

      B. 24

    • C.

      C. 27

    • D.

      D. 36

    • E.

      E. 18

    Correct Answer
    A. A. 12
    Explanation
    As other options are not equal to the calculated answers, only option A is correct.
    Men Days Hours
    24 18 9
    27 12 ?
    The number of men and the number of days vary inversely with the number of hours.

    No. of hours = 24*18*9 / 27*12 = 12 hours

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  • 3. 

    4 pens cost as much as 6 pencils; 2 pencils cost as much as 4 erasers; If the cost of 1 eraser is $1, what is the cost of four pens?

    • A.

      A. $6

    • B.

      B. $3

    • C.

      C. $1

    • D.

      D. $12

    • E.

      E. $18

    Correct Answer
    D. D. $12
    Explanation
    As other options are not equal to the calculated answer, only option D is correct.
    Cost of 4 pens = cost of 6 pencils or
    Cost of 1 pen = 6/4 cost of 1 pencil = 3/2 cost of 1 pencil
    Cost of 2 pencils = cost of 4 erasers or
    Cost of 1 pencil = 4/2 cost of 1 eraser = 2 cost of 1 eraser
    Cost of 1 eraser = $1
    Cost of 1 pencil = 2 * cost of 1 eraser = 2 * 1 = $2
    Cost of 1 pen = 3/2 cost of 1 pencil
    = 3/2 * 2 = $3
    Cost of 4 pens = 4 * 3 = $12

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  • 4. 

    The table given below shows the number of credit points scored by five students in a five week course. Which student has earned total maximum credit points in the course?

    • A.

      A. Jane

    • B.

      B. Mike

    • C.

      C. Mathew

    • D.

      D. Peter

    • E.

      E. Stephen

    Correct Answer
    A. A. Jane
    Explanation
    Option A is correct. Jane´s total credit points = 9 + 7 + 20 + 21 + 7 = 64
    Option B is not correct. Mike´s total credit points = 10 + 6 + 16 + 22 + 8 = 62
    Option C is not correct. Mathew's total credit points = 15+ 8 +22 + 5 + 11 = 61
    Option D is not correct. Peter´s total credit points = 20 + 6 + 14 + 5 + 12 = 57
    Option E is not correct. Stephen´s total credit points = 8 + 20 + 16 + 7 + 5 = 56

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  • 5. 

     If  y = 3/4 xz, what is the value of z when x = 2 and y = 27

    • A.

      A. 2

    • B.

      B. 6

    • C.

      C. 18

    • D.

      D. 27

    • E.

      E. 9

    Correct Answer
    C. C. 18
    Explanation
    Option A is not correct. If z =2, 3/4 xz = 3/4 * 2 * 2 = 3 ≠ 27
    Option B is not correct. If z = 6, 3/4 xz = 3/4 * 2 * 6 = 9 ≠ 27
    Option C is correct. If z = 18, 3/4 xz = 3/4 * 2 * 18 = 27 = y
    Option E is not correct. If z = 27, 3/4 xz = 3/4 *2 * 27 = 81/2 ≠ 27
    Option E is not correct. If z = 9, 3/4 xz = 3/4 * 2 * 9 = 27/2 ≠ 27

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  • 6. 

    If x is a positive integer, which of the following is(are) true.
    1. If x is odd, then (x+1)2is even.
    2. If x is even, then (x-1)2is odd.
    3. If x is even, then  is irrational.

    • A.

      A. I and II

    • B.

      B. I and III

    • C.

      C. II and III

    • D.

      D. Only I

    • E.

      E. Only I

    Correct Answer
    A. A. I and II
    Explanation
    Option A is correct.
    Let us take x as 5 which is odd, then (x + 1)^2 is (5 + 1)^2 which is equal to 36, which is even. Hence I is true. Let us take x as 8 which is even, then (x - 1)^2 is (8 - 1)^2 which is equal to 49, which is odd. Hence II is also true. As I and II are true option A is correct.
    Option B is not correct.
    I is true as seen above. If x is 8 which is even, then √(8-1) = √7
    is irrational, but If x is 10 which is even, then √(10-1) = √9 = 3 is rational, hence III is not true.
    Option C is not correct.
    II is true as seen above but III is not true as seen above.
    Option D is not correct.
    Only I is false, as both I and II are true.
    Option E is not correct.
    Only II is false, as both I and II are true.

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  • 7. 

    If a and b are the lengths of the legs of a right triangle whose hypotenuse is 10 units and whose area is 20 square units, what is the value of (a + b)2?

    • A.

      A. 120

    • B.

      B. 10

    • C.

      C. 20

    • D.

      D. 100

    • E.

      E. 180

    Correct Answer
    E. E. 180
    Explanation
    As other options are not equal to the calculated answer, only option E is correct. Let the sides of the right triangle be a, b and c in increasing order. Hence, c is its hypotenuse. According to Pythagora's theorem,
    a^2 + b^2 = c^2, or a^2 + b^2 = 102 or a^2 + b^2 = 100
    Area of a right triangle = 1/2 ab or 1/2 ab = 20 or ab = 40
    (a+b)^2 = a^2 + b^2 + 2ab = 100 + 2 * 40 = 180

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  • 8. 

    The average sale of soaps of 24 salesmen excluding Michael´s is 46 pieces per day, whereas Michael alone sells 96 pieces per day. What will be the average sale of soaps if Michael´s sale is also included in it?

    • A.

      A. 36

    • B.

      B. 38

    • C.

      C. 48

    • D.

      D. 42

    • E.

      E. 140

    Correct Answer
    C. C. 48
    Explanation
    Option A is not correct as average sale of 24 salesmen itself is greater than 36.
    Option B is not correct as average sale of 24 salesmen itself is greater than 38.
    Option C is correct.
    Average sale = total sale / number of salesmen or
    Total sale = Average sale * number of salesmen
    = 46 * 24 = 1104
    Michael´s sale per day = 96
    Total sale including Michael´s sale = 1104 + 96 = 1200
    Total number of salesmen including Michael =24 + 1 = 25
    Average sale of soaps including Michael´s sale = 1200/25 = 48
    Option D is not correct as average sale of 24 salesmen itself is greater than 46.
    Option E is not correct as average sale figure of 140 is too high, compared to the average sale of 24 salesmen.

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  • 9. 

    If x > 2y and , then which of the following is true?

    • A.

      A. x > 6z

    • B.

      B. x < 6z

    • C.

      C. y < 6/x

    • D.

      D. z > 6/x

    • E.

      E. x = 6z

    Correct Answer
    A. A. x > 6z
    Explanation
    Only option A is correct as other options do not satisfy the given inequalities.

    x > 2y and z < y/3 or x > 2y and 3z < y or y > 3z or x > 2* 3z or x > 6z

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  • 10. 

    Which of the following has the greatest perimeter?

    • A.

      A. A square with an area of 36 square units.

    • B.

      B. An equilateral triangle with a side of 9 units.

    • C.

      C. A rectangle with 10 units length and 40 square units area.

    • D.

      D. A right triangle whose one side is 4 units and hypotenuse 5 units.

    • E.

      E. All the given figures have the same perimeter.

    Correct Answer
    C. C. A rectangle with 10 units length and 40 square units area.
    Explanation
    Option A is not correct.
    Area of the square = 36 square units = s2 or s = 6 units.
    Perimeter of the square= 4s = 4 * 6 units = 24 units.
    Option B is not correct.
    Side of the equilateral triangle = a = 9 units.
    Perimeter of an equilateral triangle = 3a = 3 * 9 units = 27 units.
    Option C is correct.
    Length of the rectangle = 10 units.
    Area of the rectangle = 40 square units.
    Width of the rectangle = 40/10 units = 4 units.
    Perimeter of the rectangle = 2(l + w)
    = 2(10 + 4) units
    = 2 * 14 = 28 units.
    Option D is not correct.
    In a right triangle c2= a2 + b2 or 52 = 42 + b2 or b2 = 25 - 16 or b2 = 9
    Or b = 3. Perimeter of the triangle = (3 + 4 + 5) units = 12 units.
    Option E is not correct as is observed no two of the given figures have the same perimeter.

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  • 11. 

    Which of the following is the correct factorization of the quadratic expression 6z2 - 11z + 4?

    • A.

      A. (3z - 4)(2z - 1)

    • B.

      B. (3z + 4)(2z - 1)

    • C.

      C. (3z - 4)(2z + 1)

    • D.

      D. (3z + 4)(2z + 1)

    • E.

      E. (2z - 4)(3z - 1)

    Correct Answer
    A. A. (3z - 4)(2z - 1)
    Explanation
    Option A is correct: 6z^2 - 11z + 4 = 6z^2 - 8z - 3z + 4
    = 2z(3z - 4) - 1(3z -4)
    = (3z-4) (2z - 1)
    Option B is not correct as 6z^2 - 11z + 4 ≠ (3z + 4) ( 2z -1)
    Option C is not correct as 6z^2 - 11z + 4 ≠ (3z -4) (2z +1)
    Option D is not correct as 6z^2 - 11z + 4 ≠ (3z + 4) (2z +1)
    Option E is not correct as 6z^2 - 11z + 4 ≠ (2z -4) (3z -1)

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  • 12. 

    If  a - 5/6 = 1/243, then what does a equal?

    • A.

      A. 3

    • B.

      B. 81

    • C.

      C. 243

    • D.

      D. 729

    • E.

      E. 27

    Correct Answer
    D. D. 729
    Explanation
    Option A is not correct. 1/243 = 3^-5, If a = 3, then 3^-5/6 6z^2 - 11z + 4 ≠ 3^-5
    Option B is not correct. 1/243 = 3^-5. If a = 81, then (81)^-5/6 = (3^4)^-5/6 ≠ 3^-5
    Option C is not correct. 1/243 = 3^-5. If a = 243, then (243)^-5/6 = (3^5)^-5/6 ≠ 3^-5
    Option D is not correct 1/243 = 3^-5. If a = 729, then (729)^-5/6 = (^6)^-5/6 ≠ 3^-5
    Option E is not correct 1/243 = 3^-5. If a = 3, then (27)^-5/6 = (^3)^-5/6 ≠ 3^-5

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  • 13. 

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

    • A.

      A. x + y

    • B.

      B. xy

    • C.

      C. xy + 3

    • D.

      D. x - y

    • E.

      E. x + y + 1

    Correct Answer
    E. E. x + y + 1
    Explanation
    Option A is not correct. x + y is a multiple of 3. For example 6 and 15 are multiples of 3, 6 + 15 = 21 is also a multiple of 3.
    Option B is not correct. xy is a multiple of 3. For example 6 and 9 are multiples of 3 their product 6 * 9 = 54 is also a multiple of 3.
    Option C is not correct. xy + 3 is a multiple of 3. For example 3 and 6 are multiples of 3. 3 * 6 + 3 = 21 is also a multiple of 3.
    Option D is not correct. For example 12 and 9 are multiples of 3, 12 - 9 = 3 is also a multiple of 3.
    Option E is correct. For example 6 and 21 are multiples of 3, 6 + 21 + 1 = 28 is not a multiple of 3.

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  • 14. 

    In a group of 15 persons 10 are mathematicians and 8 are statisticians. How many people are both mathematicians and statisticians?

    • A.

      A. 15

    • B.

      B. 10

    • C.

      C. 3

    • D.

      D. 8

    • E.

      E. 25

    Correct Answer
    C. C. 3
    Explanation
    As the calculated answer is not equal to the other options given, only option C is correct.

    Total number of persons in the group = n(M∪S) = 15
    Number of mathematicians = n(M) = 10
    Number of statisticians = n(S) = 8
    Number of persons who know both subjects = n(M∩S)
    n(M∪S) =n(M) + n(S) - n(M∩S) or n(M∩S) = 10 + 8 + 15 + 18 - 15 = 3

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  • 15. 

    A club has 108 members. Two-thirds of them are men and the rest are women. All members are married except for 9 women members. How many married women are there in the club?

    • A.

      A. 20

    • B.

      B. 24

    • C.

      C. 27

    • D.

      D. 30

    • E.

      E. 9

    Correct Answer
    C. C. 27
    Explanation
    As the calculated answer is not equal to the other options, only option C is correct.
    Total number of members in the club = 108
    Number of male members = 2/3 * 108 = 72
    Number of women members = 108 - 72 = 36
    Number of women who are not married = 9
    Number of married women in the club = 36 - 9 = 27

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  • 16. 

    If p#q@r = (p + q + r)(p2 + q2 + r2), then find the value of 8#5@2.

    • A.

      A. 15

    • B.

      B. 80

    • C.

      C. 120

    • D.

      D. 135

    • E.

      E. 1395

    Correct Answer
    E. E. 1395
    Explanation
    Option A is not correct. 8#5@2 ≠ 15
    Option B is not correct. 8#5@2 ≠ 80
    Option C is not correct. 8#5@2 ≠ 120
    Option D is not correct. 8#5@2 ≠ 135
    Option E is correct. According to the give rule,
    Here p = 8, q = 5, and r = 2,
    hence, 8#5@2 = (8 + 5 + 2 )(8^2 + 5^2 + 2^2)
    = 15 * (64 + 25 + 4)
    = 15 * 93
    = 1395

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  • 17. 

    In the given figure, O is the centre of the circle. Note: Figure not drawn to scale.

    • A.

      A. 30 degrees

    • B.

      B. 20 degrees

    • C.

      C. 50 degrees

    • D.

      D. 100 degrees

    • E.

      E. 90 degrees

    Correct Answer
    D. D. 100 degrees
    Explanation
    As the calculated answer is not equal to the other options, only option D is correct.

    Join PO. ∠OQP = ∠OPQ = 30 degrees (Isosceles triangle property)
    ∠ORP = ∠OPR = 20 degrees (Isosceles triangle property)
    ∠QPR = ∠OPQ + ∠OPR = 30 degrees + 20 degrees = 50 degrees
    ∠QOR = 2 * ∠QPR = 2 * 50 degrees = 100 degrees (angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at any other point on the remaining circle)

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  • 18. 

    The percent increase from 8 to 14 is equal to the percent increase from 12 to what number.

    • A.

      A. 21

    • B.

      B. 28

    • C.

      C. 14

    • D.

      D. 16

    • E.

      E. 24

    Correct Answer
    A. A. 21
    Explanation
    As the calculated answer is not equal to the other options only option A is correct.This problem can be solved either using percentages or ratios.
    Using ratios makes it simpler.
    (14 - 8)/8 = (x - 12)/1 2
    Or 6/8 = (x - 12)/12
    Or (x - 12) * 8 = 6 * 12
    Or x - 12 = 72/8 or x - 12 = 9 or x = 9 + 12 or x = 21
    Therefore, the required number is 21.

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  • 19. 

    Johnson has to cover a distance of 240 miles, of which

    • A.

      A. 240

    • B.

      B. 30

    • C.

      C. 40

    • D.

      D. 50

    • E.

      E. 120

    Correct Answer
    C. C. 40
    Explanation
    As the calculated answer is not equal to the other options, only option C is correct.
    Total distance traveled = 240 miles.
    Distance traveled at a speed of 30 miles/hr =1/4 * 240 miles = 60 miles.
    Time taken to travel 60 miles = 60/30 hrs = 2 hrs (Time = distance/speed)
    Distance traveled at a speed of 40 miles/hr = 1/3 * 240 miles = 80 miles.
    Time taken to travel 80 miles = 80/40 hrs = 2 hrs.
    Distance traveled at a speed of 50 miles/hr = {240 - (60 + 80)}miles
    = 100 miles.
    Time taken to travel 100 miles = 100/50 hrs = 2 hrs.
    Total time taken to travel 240 miles = 2hrs + 2hrs + 2hrs = 6hrs
    Average speed of Johnson = total distance traveled/total time taken
    = 240 miles/6hrs
    = 40 miles/hr.

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  • 20. 

    Mrs. Alice is four times as old as her son. After 4 years the sum of their ages would be 63 years. Find her son´s present age.

    • A.

      A. 12

    • B.

      B. 11

    • C.

      C. 4

    • D.

      D. 2

    • E.

      E. 15

    Correct Answer
    B. B. 11
    Explanation
    Option A is not correct. If son is 12 years, then mother would be 48 years old, after 4 years sum of their ages = 12 + 4 + 48 + 4 = 68 63.
    Option B is correct.
    Let´s son´s present age be x years.
    Mrs. Alice´s age = 4x years
    Son's age's age after 4 years = (x + 4) years
    Mrs. Alice's age after 4 years = (4x + 4) years
    Given, x + 4 + 4x + 4 = 63
    Or 5x + 8 = 63 or 5x = 63 - 8 = 55 or 5x = 55 or x = 11
    Hence son's present age = 11 years.
    Option C is not correct. If son is 4 years, then mother would be 16 years old,after 4 years sum of their ages = 4 + 4 +16 + 4 = 28 63
    Option D is not correct. If son is 2 years, then mother would be 8 years old, which is absurd.
    Option E is not correct. If son is 15 years, then mother would be 60 years old,after 4 years sum of their ages = 15 + 4 + 60 + 4 = 83 63

    Rate this question:

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  • Mar 22, 2023
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