What is the value of the positive integer $n$?

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BTGmoderatorLU: Moderator; Posts: 2554; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Mon Nov 25, 2019 1:21 pm

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

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Source: Beat The GMAT — Problem Solving | Mon Nov 25, 2019 1:21 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

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 â‰ 1. No unique answer. Insufficient.

(1) and (2) together

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

The correct answer: C

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8154; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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 â‰ n^2

We see that if n > 1, then n â‰ 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 â‰ 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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