# GRE Problem Solving Select Many SAMPLE QUESTIONS-10

## GRE Problem Solving Select Many Sample Questions

1. Question:

Let A = {1, 3, 5, {6, 8}}. Which of the following is true? Indicate all correct options.

A. 1 is an element of A

B. {6, 8} is a subset of A

C. {3} is a subset of A

D. {1, 3, 5} is an element of A

E. 8 is an element of A

Correct Answer: A and C

Explanation:

1 is an element of A. Option A is true.

{6, 8}is an element of A and hence option B is false.

3 is an element of A and hence {3} is a subset of A. Option C is true.

{1, 3, 5} is a subset of A and it is not an element of A. Option D is false.

8 is not an element of A. Option E is false.

2. Question:

The area of a trapezium is 2500 sq.m. One of its parallel sides is 75m. If the distance between the two parallel sides in 40 m, which of the following is true? Indicate all correct choices.

A. The length of the other parallel side is 50 m

B. The area of the trapezium is independent of the lengths of the non-parallel sides.

C. The length of the other parallel side is 35m

D. The distance between the two parallel lines varies

E. The length of the other parallel side is 25m

Correct Answer: A and B

Explanation:

Area of a trapezium = 1/2*sum of length of parallel sides*distance between parallel sides

The area is independent of the lengths of the non-parallel sides. Option B is true.

Let the unknown length be x

2500 = 1/2*(75+x)*40

2500*2/40 = 75+x

x = 125-75=50m

Option A is true and C and E are false.

The distance between any two parallel sides is constant. Option D is false.

3. Question:

The length of the diagonal of a square is decreased by 10%. Which of the following is true? Indicate all such options.

A. The area reduces by 19%

B. The area reduces by 10%

C. The area increases by 19%

D. The length of each side of the square reduces

E. The length of each side of the square increases

Correct Answer: A and D

Explanation:

Let the length of the diagonal be 100 units initially.

Initial area = diagonal^2/2 = 100^2/2 = 10000/2

= 5000 sq.units

Initial side = sqrt(Area)

= sqrt(5000) units

Diagonal reduces by 10%. The new diagonal will be 100-10 = 90 units

The new area will be

Area = 90^2/2 = 8100/2 = 4050 sq units.

Decrease in area = (old area-new area)/ old area *100

= (5000-4050)/5000*100

= 0.19*100 = 19%

Option A is true and B and C are false.

Each side of the square shall also decrease.

Option D is true and E is false.

[90^2=90*90]