Problem Solving Select Many GRE Sample Questions 1
GRE Problem Solving Select Many Sample Questions
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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
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
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
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.
GRE Problem Solving Select Many Sample Questions
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