Jeff Miller

GMAT OFFICIAL GUIDE DS – If x is an integer…

If x is an integer…

Solution:

We need to determine whether 9^x + 9^-x = b.

Statement One Alone:

3^x + 3^-x = √(b+2)

We first square both sides of the equation in statement one, obtaining:

(3^x + 3^-x)^2 = [√(b+2)]^2

(3^x + 3^-x)(3^x + 3^-x)  = b+2

(3^x)(3^x) + (3^x)(3^-x) + (3^-x)(3^x) + (3^-x)(3^-x) = b + 2

3^(2x) + 3^0 + 3^0 + 3^(-2x) = b + 2

9^x + 1 + 1 + 9^-x = b + 2

9^x + 9^-x = b

Statement one is sufficient to answer to the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

x> 0

Only knowing that x is greater than zero is not enough information to answer the question.

Answer: A

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