Data Sufficiency

If x is an integer, is 9^x + 9^-x = b?

1) 3^x + 3^-x = sq.root(b+2)
2) x > 0

To compare equations or integrate data from different equations, make them look as similar to each other as possible. This is particularly helpful in DS. In this case, to evaluate (1), we should isolate variable b since b is isolated in the original question.

The full solution below is taken from the GMATFix App.



-Patrick

BlueDragon2010 wrote:If x is an integer, is 9^x + 9^-x = b?

1) 3^x + 3^-x = sq.root(b+2)
2) x > 0

Memorize the following quadratic indentities:
(a+b)² = a² + 2ab + b²
(a-b)² = a² - 2ab + b²
(a+b)(a-b) = a² - b².

Statement 1: 3^x + 3^-x = √(b+2)
Squaring both sides, we get:
(3^x + 3^-x)² = b+2

The identity in red can serve to rephrase the lefthand side:
(a+b)² = a² + 2ab + b²
(3^x + 3^-x)² = (3^x)² + 2(3^x)(3^-x) + (3^-x)².

Simplifying further, we get:
(3^x)² + 2(3^x)(3^-x) + (3^-x)²

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

= 9^x + 2 + 9^(-x).

Since the lefthand side can be rephrased as 9^x + 2 + 9^(-x), we get:
9^x + 2 + 9^(-x) = b+2
9^x + 9^(-x) = b.
SUFFICIENT.

Statement 2: x > 0
No information about b.
INSUFFICIENT.

The correct answer is A.