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What is the value of the positive integer \(n\)?

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by Jay@ManhattanReview » Mon Nov 25, 2019 11:15 pm
BTGmoderatorLU wrote:Source: Official Guide

What is the value of the positive integer \(n\)?

1) \(n^4 < 25\)
2) \(n \neq n^2\)

The OA is C
Let's take each statement one by one.

1) \(n^4 < 25\)

=> n = 1 or 2. No unique answer. Insufficient.

2) \(n \neq n^2\)

=> n ≠ 1. No unique answer. Insufficient.

(1) and (2) together

From (1), we know that n ≠ 1, thus, n = 2. Sufficient

The correct answer: C

Hope this helps!

-Jay
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by Scott@TargetTestPrep » Wed Nov 27, 2019 10:53 am
BTGmoderatorLU wrote:Source: Official Guide

What is the value of the positive integer \(n\)?

1) \(n^4 < 25\)
2) \(n \neq n^2\)

The OA is C
Statement One Alone:

n^4 < 25

We see that n can be 1 or 2. Statement one is not sufficient.

Statement Two Alone:

n ≠ n^2

We see that if n > 1, then n ≠ n^2. Since n can be an infinite number of values, statement two alone is not sufficient.

Statements One and Two Together:

From statement 1, we know that n can be 1 or 2. Statement 2 says that n ≠ n^2, and so n cannot equal 1 (since 1 = 1^2). Using statements one and two, we see that n must be 2.

Answer: C

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