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

No - As square root of 16 can be 4 or -4. I think you are confusing this with square root of a negative number which is not defined. Bunuel can you please confirm if my logic is correct??

From the Official Guide:

A square root of a number n is a number that, when squared, is equal to n. Every positive number n has two square roots, one positive and the other negative, but √n denotes the positive number whose square is n. For example, √9 denotes 3.

So, √n is always greater than or equal to zero.

Cheers,
Brent

Hello, I think the answer is "C"
1) sqrt of n is between 1 and 5 hence, the value of n can be 4(which is a positive integer as stated in question) and root of 4 will be 2 which satisfies the inequality

2) sqrt. of n is between 10 and 24 hence, n is 16, which satisfies the second statement.

hence the official answet must be "C"

...
Please comment if I am wrong.

Only n = 16 satisfies the second statement so it's sufficient. Answer is B.

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

(1) \(1 < \sqrt{n} < 5\)
How many integral values lies between 1 - 5
1,2,3,4,5

1, \(\sqrt{4},\sqrt{9},\sqrt{16}\), 5
Multiple values of \(\sqrt{n}\)
Therefore not sufficient

(2) 10 < n < 24
How many integers are between 10 - 24 ? Many .. But since question stem tells us that \(\sqrt{n}\) is a positive integer, so we are looking for a perfect square
How many perfect squares are between 10 - 25
11=no, 12= no, 13= no, 14= no, 15=no, 16= yes (\(4^2\)), 17=no,18=no,19=no,20=no
SO only one perfect square

SUFFICIENT

ANSWER IS B

Hi,

1) 1<n√<5
what it means is that root n can take all the values between 1 and 5 , namely 2,3,4
therefore n can have a number of values

thus insufficient.

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

\(\sqrt{n}\) is a positive integer, this leaves 3 possible values for \(\sqrt{n}\)

Insufficient.

\(\textbf{(2) } 10 < n < 24\)

\(n\) is a perfect square. The perfect squares close to the value are: \(3^2, 4^2, 5^2.\)
\(4^2 = 16\) is the only valid value in the range.

Sufficient

P.S. "If \(\sqrt{n}\) is a positive integer" means n is a perfect square

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

i.e. \(\sqrt{n}\)= 2, 3, 4

i.e. n = 4, 9, 16
NOT SUFFICIENT

Statement 2: 10 < n < 24

The only perfect square in the given range = 16
Hence, SUFFICIENT

Answer: Option B

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

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