# Problem Solving Select Many GRE Sample Questions 3

## GRE Problem Solving Select Many Sample Questions

1. Question:

Which of the following is not a rational number? Indicate all correct options.

• A. 2/5
• B. 4/7
• C. -9/10
• D. 23.52
• E. sqrt(2)

Explanation:

A, B and C are rational numbers. D is a decimal number and E is an irrational number.

2. Question:

Which of the following statements is true for the year 2000? Indicate all correct options.

• A. It is a leap year
• B. It is not a leap year
• C. The year has 365 days
• D. The year has 366 days
• E. The year has 367 days

Explanation:

2000 is divisible by 4 and hence it is a leap year.

An ordinary year has 365 days and a leap year has 366 days.

Hence, options A and D are true.

3. Question:

Which of the following is the GCD of the polynomials x^3+x^2+x+1 and x^4-1? Indicate all such statements.

• A. (x+1)(x^2+1)
• B. (1+x^2)(1+x)
• C. (1+x)(x^2-1)
• D. x(x+2)
• E. (x+1)(x^2+2)

[x^2=x*x]

Explanation:

x^3+x^2+x+1 = x^2(x+1)+(x+1)

=(x^2+1)(x+1)

x^4-1=(x^2+1)(x^2-1)

=(x^2+1)(x+1)(x-1)

GCD = (x^2+1)(x+1)

The options A and B are true.

## GRE Problem Solving Select Many Sample Questions

### Terms and Conditions

Information published in TestPrepPractice.net is provided for informational and educational purpose alone for deserving students, researchers and academicians. Though our volunteers take great amount of pain and spend significant time in validating the veracity of the information or study material presented here, we cannot be held liable for any incidental mistakes. All rights reserved. No information or study material in this web site can be reproduced or transmitted in any form, without our prior consent. However the study materials and web pages can be linked from your web site or web page for

• Research

• Education