If x and k are both integers, x > k, and x^{−k} = 625

[hazelnut01]

If x and k are both integers, x > k, and x^{−k} = 625, what is x?

(1) |k| is a prime number
(2) x + k > 20 

Source : Manhattan
OA=A

[[email protected]]

Hi ziyuenlau,

In certain DS questions, the prompt significantly limits the possible answers (before you even consider the information in the two Facts). By determining those limited options right from the start, you'll find that the rest of the work needed to answer the question can be done rather quickly.

Here, we're told that X and K are both INTEGERS, that X > K and that X^{-K} = 625. We're asked for the value of X.

To start, there are not that many ways to raise an INTEGER to an INTEGER power and get 625; considering that X must be GREATER than K, it's even more limited - there are only 3 ways to do it:

X = 625, K = -1
X = 25, K = -2
X = 5, K = -4

1) |K| is a prime number

Given the above three options, there's only one option that 'fits' Fact 1: X = 25, K = -2
Fact 1 is SUFFICIENT

2) X + K > 20

With Fact 2, there are two options (X = 25, K= -2 and X = 625, K = -1)
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich