Problem Solving Select Many GRE Sample Questions 7
GRE Problem Solving Select Many Sample Questions
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1. Question:In how many ways can the letters of the word SOCIETY be arranged such that the vowels come together? Indicate all correct options.
- A. 5!
- B. 7!
- C. 4!*3!
- D. 5!3!
- E. 720
Explanation:
There are 7 letters in the word out of which 3 are vowels.
The vowels can be considered as one letter as they are to appear together.
Then, we are to arrange (7-3+1) = 5 letters
This can be done in 5! ways.
The 3 vowels can be arranged among themselves in 3! ways.
Total number of words = 5!3!
= 5*4*3*2*3*2
= 720 ways
Options D and E are true.
2. Question:
The ratio of the circumference of two circles is 2:3. Which of the following is true? Indicate all correct options.
- A. The ratio of their radii is 4:9
- B. The ratio of their radii is 2:3
- C. The ratio of their radii is sqrt(2):sqrt(3)
- D. The ratio of their area is 4:9
- E. The ratio of their area is 2:3
Explanation:
Let the radii of the circles be x and y
Circumference of a circle = 2pi*r, where r is the radius
Ratio of circumference is 2:3
2pi*x/2pi*y=2/3
x:y = 2:3
Hence ratio of their radii is 2:3
Area of a circle = pi*r^2, where r is the radius
Ratio of area = pi*x^2/(pi*y^2)
= x^2/y^2 = (x/y)^2
= (2/3)^2 = 4/9
Ratio of area = 4:9
Options B and D are true.
[pi=22/7]
3. Question:
Which of the following lies between 0.001 and 0.1? Indicate all correct choices.
- A. 0.0001
- B. 0.1^2
- C. 0.01^2
- D. 0.01^3
- E. 2* (0.1^3)
[0.1^2=0.1*0.1]
Correct Answer: B and EExplanation:
Consider the numbers 0.001 and 0.1
0.0001 < 0.001
0.1^2 = 0.01, 0.001<0.01<0.1
0.01^2 = 0.0001 < 0.001
0.01^3 = 0.000001 < 0.001
2*0.1^3 = 2*0.001 = 0.002, 0.001<0.002<0.1
Options B and E are true
GRE Problem Solving Select Many Sample Questions
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