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

Question

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

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

(2) 10 < n < 24

Bunuel · Accepted Answer

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

\sqrt{n}=integer  means that n is a perfect square.

(1)  1 < \sqrt{n} < 5  -->  \sqrt{n}  is 2, 3, or 4. Thus n can be 4, 9, or 16. Not sufficient.

(2) 10 < n < 24. There is only one perfect square in this range, thus n=16. Sufficient.

Answer: B.

HKD1710 · Answer

if sqrtN is a POSITIVE INTEGER. so n is a perfect square.

stmt1:
1 < sqrtN < 5
as sqrtN is int so only possible value in this range are 2,3,4. hence N could be 4,9, or 16. Insuff.

stmt:2
10 < n < 24
n should be a perfect square. only 16 is such a number. suff

B is the correct answer.

bethebest · Answer

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??

BrentGMATPrepNow · Answer

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

ankitkamod02 · Answer

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.

Bunuel · Answer

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

LogicGuru1 · Answer

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

CounterSniper · Answer

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.

DAllison2016 · Answer

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

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

Insufficient .

extbf{(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

(B) statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question

GMATinsight · Answer

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

BrentGMATPrepNow · Answer

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

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

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