# Problem Solving Select Many GRE Sample Questions 7

## GRE Problem Solving Select Many Sample Questions

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]

Explanation:

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