GMAT Problem Solving Test Paper | GMAT Quantitative Section Test Paper

GMAT Problem Solving Test Paper | GMAT Quantitative Section Test Paper

1. Of the following, which is greater than ½ ?
A. 2/5
B. 4/7
C. 4/9
D. 5/11
E. 6/13

2. If an object travels at five feet per second, how many feet does it travel in one hour?
A. 30
B. 300
C. 720
D. 1800
E. 18000

3. What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?
A. 90
B. 95
C. 100
D. 105
E. 110

4. A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
A. 48
B. 32
C. 24
D. 18
E. 12

5. In a class of 78 students 41 are taking French, 22 are taking German and 9 students are taking both French and German. How many students are not enrolled in either course?
A. 6
B. 15
C. 24
D. 33
E. 54

6. A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)
A. 17
B. 28
C. 35
D. 39
E. 50

7. ( √2 – √3 )² =
A. 5 – 2√6
B. 5 – √6
C. 1 – 2√6
D. 1 – √2
E. 1

8. 2³⁰ + 2³⁰ + 2³⁰ + 2³⁰ =
B. 8³⁰
C. 2³²
D. 2³⁰
E. 2²⁶


9. Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?
A. 10
B. 8
C. 6
D. 4
E. 2


10. In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?
A. 18
B. 13.5
C. 9
D. 4.5
E. 3

11. Which of the following could be a value of x, in the diagram above?
A. 10
B. 20
C. 40
D. 50
E. any of the above

12. Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes per hour, or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?
A. 10
B. 15
C. 20
D. 25
E. 30

13. Jo’s collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
A. 5 : 1
B. 10 : 5
C. 15 : 2
D. 20 : 2
E. 25 : 2

14. A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?
A. 2.5π
B. 3π
C. 5π
D. 4π
E. 10π

15. Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
A. 4
B. 7
C. 8
D. 12
E. it cannot be determined from the information given.

16. A circular logo is enlarged to fit the lid of a jar. The new diameter is 50 per cent larger than the original. By what percentage has the area of the logo increased?
A. 50
B. 80
C. 100
D. 125
E. 250

17. ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilateral EBFD ?
A. 2.25
B. 3
C. 4
D. 4.5
E. 6

11. Which of the following could be a value of x, in the diagram above?
A. 10
B. 20
C. 40
D. 50
E. any of the above

12. Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes per hour, or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?
A. 10
B. 15
C. 20
D. 25
E. 30

13. Jo’s collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
A. 5 : 1
B. 10 : 5
C. 15 : 2
D. 20 : 2
E. 25 : 2

14. A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?
A. 2.5π
B. 3π
C. 5π
D. 4π
E. 10π

15. Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
A. 4
B. 7
C. 8
D. 12
E. it cannot be determined from the information given.

16. A circular logo is enlarged to fit the lid of a jar. The new diameter is 50 per cent larger than the original. By what percentage has the area of the logo increased?

A. 50
B. 80
C. 100
D. 125
E. 250

17. ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilateral EBFD ?

A. 2.25
B. 3
C. 4
D. 4.5
E. 6

18. If n ≠ 0, which of the following must be greater than n?

I 2n
II n²
III 2 – n

A. I only
B. II only
C. I and II only
D. II and III only
E. None

19. After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce?
A. 20
B. 15
C. 8
D. 5
E. 3.2

20. n and p are integers greater than 1 5n is the square of a number 75np is the cube of a number. The smallest value for n + p is
A. 14
B. 18
C. 20
D. 30
E. 50

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GMAT Problem Solving Questions | GMAT Quantitative Sample Questions

GMAT Problem Solving Questions | GMAT Quantitative Sample Questions

Directions
Solve the problem and indicate the best of the answer choices given.

Numbers
All numbers used are real numbers.

Figures
A figure accompanying a problem solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible EXCEPT when it is stated in a specific problem that the figure is not drawn to scale. Straight lines may sometimes appear jagged. All figures lie in a plane unless otherwise indicated.

Question
If u > t, r > q, s > t, and t > r, which of the following must be true?
I. u > s
II. s > q
III. u > r
* (A) I only
* (B) II only
* (C) III only
* (D) I and II
* (E) II and III
Answer (E)

Linear Equation Word Problems
The question given below is a Math problem in Algebra and requires framing a couple of linear equations and solving the equations.

Question 1
A poultry farm has only chickens and pigs. When the manager of the poultry counted the heads of the stock in the farm, the number totaled up to 200. However, when the number of legs was counted, the number totaled up to 540. How many chickens were there in the farm?
1. 70
2. 120
3. 60
4. 130
5. 80
The correct choice is (D) and the correct answer is 130.
Explanatory Answer
Let there by ‘x’ chickens and ‘y’ pigs.
Therefore, x + y = 200 — (1)
Each chicken has 2 legs and each pig has 4 legs
Therefore, 2x + 4y = 540 — (2)
Solving equations (1) and (2), we get x = 130 and y = 70.
There were 130 chickens and 70 pigs in the farm.

Question 2
Three years back, a father was 24 years older than his son. At present the father is 5 times as old as the son. How old will the son be three years from now?
1. 12 years
2. 6 years
3. 3 years
4. 9 years
5. 27 years
The correct choice is (D) and the correct answer is 9 years.
Explanatory Answer
Let the age of the son 3 years back be x years
Therefore, the age of the father 3 years back was x + 24
At present the age of the son is x + 3 and the father is 5 times as old as the son.
i.e., x + 24 + 3 = 5(x + 3)
i.e., x + 27 = 5x + 15
or 4x = 12 or x = 3.
Therefore, the son was 3 years old 3 years back and he will be 9 years old three years from now.

Question 3
For what values of ‘k’ will the pair of equations 3x + 4y = 12 and kx + 12y = 30 not have a unique solution?
1. 12
2. 9
3. 3
4. 7.5
5. 2.5
The correct choice is (B) and the correct answer is 9.

Question 4
The basic one-way air fare for a child aged between 3 and 10 years costs half the regular fare for an adult plus a reservation charge that is the same on the child’s ticket as on the adult’s ticket. One reserved ticket for an adult costs $216 and the cost of a reserved ticket for an adult and a child (aged between 3 and 10) costs $327. What is the basic fare for the journey for an adult?
1. $111
2. $52.5
3. $210
4. $58.5
5. $6
The correct choice is (C) and the correct answer is $210.

Read full here

GMAT Problem Solving Questions | GMAT Quantitative Sample Questions

GMAT Problem Solving Questions | GMAT Quantitative Sample Questions

Directions
Solve the problem and indicate the best of the answer choices given.

Numbers
All numbers used are real numbers.

Figures
A figure accompanying a problem solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible EXCEPT when it is stated in a specific problem that the figure is not drawn to scale. Straight lines may sometimes appear jagged. All figures lie in a plane unless otherwise indicated.

Question
If u & t, r & q, s & t, and t & r, which of the following must be true?
I. u & s
II. s & q
III. u & r
* (A) I only
* (B) II only
* (C) III only
* (D) I and II
* (E) II and III
Answer (E)

Linear Equation Word Problems
The question given below is a Math problem in Algebra and requires framing a couple of linear equations and solving the equations.
Question 1
A poultry farm has only chickens and pigs. When the manager of the poultry counted the heads of the stock in the farm, the number totaled up to 200. However, when the number of legs was counted, the number totaled up to 540. How many chickens were there in the farm?
1. 70
2. 120
3. 60
4. 130
5. 80

The correct choice is (D) and the correct answer is 130.
Explanatory Answer
Let there by ‘x’ chickens and ‘y’ pigs.
Therefore, x + y = 200 — (1) Each chicken has 2 legs and each pig has 4 legs
Therefore, 2x + 4y = 540 — (2) Solving equations (1) and (2), we get x = 130 and y = 70. There were 130 chickens and 70 pigs in the farm.

Question 2
Three years back, a father was 24 years older than his son. At present the father is 5 times as old as the son. How old will the son be three years from now?
1. 12 years
2. 6 years
3. 3 years
4. 9 years
5. 27 years
The correct choice is (D) and the correct answer is 9 years.
Explanatory Answer
Let the age of the son 3 years back be x years Therefore, the age of the father 3 years back was x + 24 At present the age of the son is x + 3 and the father is 5 times as old as the son.
i.e., x + 24 + 3 = 5(x + 3)
i.e., x + 27 = 5x + 15
or 4x = 12 or x = 3.
Therefore, the son was 3 years old 3 years back and he will be 9 years old three years from now.

Question 3
For what values of ‘k’ will the pair of equations 3x + 4y = 12 and kx + 12y = 30 not have a unique solution?
1. 12
2. 9
3. 3
4. 7.5
5. 2.5
The correct choice is (B) and the correct answer is 9.

Question 4
The basic one-way air fare for a child aged between 3 and 10 years costs half the regular fare for an adult plus a reservation charge that is the same on the child’s ticket as on the adult’s ticket. One reserved ticket for an adult costs $216 and the cost of a reserved ticket for an adult and a child (aged between 3 and 10) costs $327. What is the basic fare for the journey for an adult?
1. $111
2. $52.5
3. $210
4. $58.5
5. $6
The correct choice is (C) and the correct answer is $210.

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