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

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

(2) \( 10 < n < 24 \)

Target question: What is the value of n?

Given: √n = a positive integer
This tells us that n is a PERFECT SQUARE
So, some possible values of n are: 1, 4, 9, 16, 25, 36, 49, ...etc

Statement 1: 1 < √n < 5
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 4, in which case 1 < √4 < 5. In this case, the answer to the target question is n = 4
Case b: n = 9, in which case 1 < √9 < 5. In this case, the answer to the target question is n = 9
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 10 < n < 24
We already know that some possible values of n are: 1, 4, 9, 16, 25, 36, 49, ...etc
Among those possible values, 16 is the ONLY value that satisfies the condition that 10 < n < 24
So, the answer to the target question is n = 16
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent