# Problem Solving Select Many GRE Sample Questions 1

## GRE Problem Solving Select Many Sample Questions

1. Question:

Which of the following is true about an equilateral triangle with each side 6 cm long? Indicate all such choices.

• A. The area of the triangle is 9 sq.cm
• B. The area of the triangle is 9*sqrt(3) sq.cm.
• C. The altitude of the triangle is 9 cm
• D. The altitude of the triangle is 3*sqrt(3) cm
• E. Each angle of the triangle is 60 degrees
Correct Answer: B, D and E

Explanation:

For an equilateral triangle with side a cm, we have

area = sqrt(3)*a^2/4 and altitude = sqrt(3)*a/2

Area of a triangle with side 6 cm = sqrt(3)*6^2/4

= sqrt(3)*3*3

= 9*sqrt(3) sq.cm.

Altitude of triangle = sqrt(3)*6/2

= 3*sqrt(3)

Options A and C are wrong and options B and D are true.

Each angle in an equilateral triangle is 60 degrees. Option E is true.

[6^2=6*6]

2. Question:

The diagonal of a cube is 8*sqrt(3) cm. Which of the following is true? Indicate all correct options.

• A. The surface area of the cube is 384 sq.cm
• B. The surface area of the cube is 216 sq.cm
• C. The surface area of the cube is 1152 sq.cm
• D. The volume of the cube is 512 cc
• E. The volume of the cube is 1536*sqrt(3) cc
Correct Answer: A and D

Explanation:

The surface area of a cube with diagonal d is given by 2*d^2

Surface area = 2*[8*sqrt(3)]^2

= 2*8*8*3

= 384 sq.cm.

Option A is true and B and C are false.

The volume of a cube with diagonal d is given by (d/sqrt(3))^3

Volume = [8*sqrt(3)/sqrt(3)]^3

= 8^3

= 512 cc

Option D is true and E is false.

3. Question:

What are the next two numbers in the series 53, 48, 50, 50, 47? Indicate all correct choices.

• A. 51
• B. 52
• C. 53
• D. 44
• E. 45
Correct Answer: B and D

Explanation:

The even places in the series form an AP with common difference 2

The odd places in the series form an AP with common difference -3

The next place is even. The number will be 50+2=52

The next place is odd. The number will be 47-3=44

The options B and D are true and other options are false.