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If \(\sqrt{n}\) is a positive integer, what is the value of

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Source: — Data Sufficiency |

by Jay@ManhattanReview » Thu Sep 19, 2019 11:20 pm
AAPL wrote:GMAT Paper Tests

If \(\sqrt{n}\) is a positive integer, what is the value of \(n\)?

1) \( 1 < \sqrt{n} < 5 \)
2) \( 10 < n < 24 \)

OA B
Note that √n is a positive integer and n is not necessarily an integer; it is a real number.

Let's take each statement one by one.

1) \( 1 < \sqrt{n} < 5 \)

\sqrt{n} can be 2/3/4; thus, n is 4/9/25. No unique value of n. Insufficient.

2) \( 10 < n < 24 \)

=> \( √10 < √n < √24 \)

\( 3... < √n < 4... \)

The only possible value of √n = 4, thus, n = 4^2 = 16. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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