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.