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# GMAT: Data sufficiency 32

129-131, pg. 289. Created by Sal Khan.

## Want to join the conversation?

• At , wouldn't 1) n=3 together with 2) a=2^n+1 and b+3^n+1 be sufficient? If you use both 1) and 2) together you only have to solve for a single variable, n, right? Please respond in less than a year :)
(1 vote) • The question we need to be able to answer is whether this is true:
b - a ≥ 2(3ⁿ - 2ⁿ)

One way to think of this is the following:
Is the first condition sufficient by itself? Yes is the answer.
Is the second condition sufficient `by itself`? The answer is no.
With only the information that n = 3, we DO know that 2(3ⁿ - 2ⁿ) = 2(3³ - 2³) = 2(27 - 8) = 2 (19) = 38
However, we still do not know the value of b - a, so we cannot answer whether
the quantity b - a is greater than (equal to) 38
So, that second condition does not help us, (it alone is not sufficient) and the first condition is completely sufficient. If the first one is sufficient, it does not become more sufficient by the addition of knowing the value of n

Hope that helps, and it was not a year :)