SAT Mathematics Practice Test 4
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. 15/4Explanation
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...Rate this question:
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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. 12Explanation
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 hoursRate this question:
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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. $12Explanation
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 = $12Rate this question:
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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. JaneExplanation
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 = 56Rate this question:
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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. 18Explanation
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 ≠ 27Rate this question:
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- 6.
If x is a positive integer, which of the following is(are) true.
- If x is odd, then (x+1)2is even.
- If x is even, then (x-1)2is odd.
- 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 IIExplanation
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.Rate this question:
- 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. 180Explanation
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 = 180Rate this question:
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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. 48Explanation
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.Rate this question:
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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 > 6zExplanation
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 > 6zRate this question:
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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.Rate this question:
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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)Rate this question:
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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. 729Explanation
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^-5Rate this question:
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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 + 1Explanation
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.Rate this question:
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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. 3Explanation
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 = 3Rate this question:
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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. 27Explanation
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 = 27Rate this question:
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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. 1395Explanation
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
= 1395Rate this question:
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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 degreesExplanation
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)Rate this question:
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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. 21Explanation
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.Rate this question:
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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. 40Explanation
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.Rate this question:
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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. 11Explanation
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 63Rate this question:
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