GMAT Problem Solving Questions | GMAT Quantitative Sample Questions

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

All numbers used are real numbers.

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.

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)

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

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.

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.

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.

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.

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.

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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**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.