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
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.
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.
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.
GRE Problem Solving Select Many Sample Questions
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