Problem Solving Select Many GRE Sample Questions 8

GRE Problem Solving Select Many Sample Questions

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1. Question:

The length of a stick is 2x cm. Which of the following is true? Indicate all correct options.

  • A. It is the longest stick that can fit into a cuboid of side x cm
  • B. It is the longest stick that can fit into a sphere of radius 2x cm
  • C. It is the longest stick that can fit into a hemi-sphere of radius x cm
  • D. It is the longest stick that can fit into a cylinder of height 5x cm.
  • E. It is the longest stick that can fit into a cuboid of side 2x/sqrt(3) cm
Correct Answer: C and E

Explanation:

The longest stick that can fit into a cuboid of side x cm = length of

the doagonal of the cuboid

Diagonal of the cuboid = sqrt(3)*side

= sqrt(3)*x

Option A is false.


The longest stick that can fit into a sphere of radius 2x cm = diameter of the sphere

Diameter of the sphere = 2*2x = 4x cm

Option B is false.


The longest stick that can fit into a hemi-sphere of radius x = diameter of the hemisphere

Diameter of the hemi-sphere = 2*x = 2x cm

Option C is true.


We cannot determine the length of the longest stick that can fit into a cylinder of height 5x cm since we do not know

the radius of the cylinder.

Option D is false.


The longest stick that can fit into a cuboid of side 2x/sqrt(3) cm = diagonal of the cuboid

Diagonal of the cuboid = sqrt(3)*side

= sqrt(3)*2x/sqrt(3) = 2x

Option E is true.




2. Question:

The diagonal of a square is doubled to form another square. Which of the following is true? Indicate all correct choices.

  • A. The side of the square remains the same
  • B. The side of the square doubles
  • C. The area of the square becomes four fold
  • D. The area of the square becomes three times
  • E. The area of the square becomes double.
Correct Answer: B and C

Explanation:

Let the side of the square be x cm

The diagonal will be sqrt(2)*x cm

Area of the square = side^2

= x^2 = diagonal^2/2


Diagonal doubles itself, and hence it becomes 2x*sqrt(2)

Side of the square becomes = diagonal/ sqrt(2)

= 2x*sqrt(2)/sqrt(2)

= 2x

Hence, side of the square doubles.


Area of the square becomes (2x)^2

= 4x^2

Area of square becomes four times.

Options B and C are true.

[x^2=x*x]




3. Question:

The shorter diagonal of a rhombus is 80% of the length of the longer diagonal. Which of the following is true? Indicate all such statements.

  • A. The longer diagonal is 125% of the shorter diagonal.
  • B. The longer diagonal is 100% of the shorter diagonal.
  • C. The area of the rhombus is 0.4 times the square of the longer diagonal
  • D. The area of the rhombus is 2/5 times the square of the longer diagonal
  • E. The area of the rhombus cannot be defined in terms of the lengths of its diagonals.
Correct Answer: A, C and D

Explanation:

Let the length of the longer diagonal be x cm

The length of the shorter diagonal will be 80% of x

= 0.80x cm

Required Percentage= x/0.80x*100

= 125%

Option A is true.


Area of rhombus = 1/2 product of diagonals

= 1/2 *0.80x*x = 2/5x^2

= 0.4x^2

= 0.4 times the square of the longer side

Option C and D are true.

Clearly, option E is false.

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