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broall
If n is an integer, is \(\frac{(100-n)}{n}\) an integer?

(1) \(n > 4\)
(2) \(n^2 = 25\)

Target question: Is \(\frac{(100-n)}{n}\) an integer?
This is a good candidate for rephrasing the target question.

The GMAT loves to test the following property: \(\frac{a-b}{c}=\frac{a}{c}-\frac{b}{c}\)
So, \(\frac{100-n}{n}=\frac{100}{n}-\frac{n}{n}=\frac{100}{n}-1\)
Since \(1\) is already an integer, all we need is for \(\frac{100}{n}\) to be an integer.
In order for \(\frac{100}{n}\) to be an integer, we need \(n\) to be a divisor of \(100\)
We can now rephrase the target question as follows:
REPHRASED target question: Is n a divisor of 100?

Statement 1: \(n > 4\)
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 5. In this case, the answer to the REPHRASED target question is YES, n is a divisor of 100
Case b: n = 6. In this case, the answer to the REPHRASED target question is NO, n is not a divisor of 100
Since we can’t answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: \(n^2 = 25\)
This means that EITHER n = 5 OR n = -5
Since both possible n-values yield the same answer to the REPHRASED target question (YES, n is a divisor of 100), statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

VIDEO ON REPHRASING THE TARGET QUESTION:
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