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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? [#permalink]

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16 Jan 2005, 16:49
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If $$\sqrt{n}$$ is a positive integer, what is the value of n?

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

(2) 10 < n < 24
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Oct 2013, 08:17, edited 2 times in total.
Edited the question and added the OA
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16 Jan 2005, 17:56
vote for B..
A is insufficient.. lot of values of N..possible.
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16 Jan 2005, 19:33
How did you get B?

1) gives you 1<n<25 and 2) gives you 10<n<24. Both statements have many possibilities
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16 Jan 2005, 21:13
ywilfred wrote:
How did you get B?

1) gives you 1<n<25 and 2) gives you 10<n<24. Both statements have many possibilities

The question stem says the sqrt(n) is a positive integer. So, n has to be a perfect square. The only perfect square that lies in the range 10<n<25 is 16.
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17 Jan 2005, 04:07
Agree with B, but isn't it a nonsence to say that sqrt(n) is positive?
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Re: If sqrt(n) is a positive integer, what is the value of n? [#permalink]

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09 Oct 2013, 04:17
SQUARE ROOT of any number is posituive in gmat and its also mentioned in the question stem , then why A is not an option.
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Re: If sqrt(n) is a positive integer, what is the value of n? [#permalink]

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09 Oct 2013, 04:26
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ruplun wrote:
SQUARE ROOT of any number is posituive in gmat and its also mentioned in the question stem , then why A is not an option.

Hi,

$$1 < \sqrt{n} < 5$$

n can have the below possible values as per the given condition:
n = 4, 9 or 16
Hence $$\sqrt{n}$$ = 2, 3 or 4

Hence Statement 1 is insufficient.

Hope it helps
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Re: If sqrt(n) is a positive integer, what is the value of n? [#permalink]

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09 Oct 2013, 04:56
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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.

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Re: If sqrt(n) is a positive integer, what is the value of n? [#permalink]

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09 Oct 2013, 06:21
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Bunuel wrote:
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.

You have the OA as A in the OP, I think you meant B
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Re: If sqrt(n) is a positive integer, what is the value of n? [#permalink]

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09 Oct 2013, 06:29
@bunuel please change the OA it shows the answer as A when the correct answer is B..
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Re: If sqrt(n) is a positive integer, what is the value of n? [#permalink]

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09 Oct 2013, 07:40
gayathri wrote:
If $$\sqrt{n}$$ is a positive integer, what is the value of n?

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

(2) 10 < n < 24

OA is incorrect, answer is B, however OA shows A.
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Re: If sqrt(n) is a positive integer, what is the value of n? [#permalink]

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09 Oct 2013, 08:17
Edited the OA. Tnank you.
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Re: If sqrt(n) is a positive integer, what is the value of n? [#permalink]

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11 Oct 2013, 07:16
Bunuel wrote:
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.

Nowhere, it is shown that \sqrt{n} is a positive whole number...It is integer. 3.5 can also be a integer
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Re: If sqrt(n) is a positive integer, what is the value of n? [#permalink]

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11 Oct 2013, 07:32
himang wrote:
Bunuel wrote:
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.

Nowhere, it is shown that \sqrt{n} is a positive whole number...It is integer. 3.5 can also be a integer

Sorry, but your post makes no sense at all. Can you please elaborate what you mean? Thank you.
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Re: If sqrt(n) is a positive integer, what is the value of n? [#permalink]

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Re: If sqrt(n) is a positive integer, what is the value of n? [#permalink]

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Re: If sqrt(n) is a positive integer, what is the value of n? [#permalink]

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09 Apr 2016, 05:59
gayathri wrote:
If $$\sqrt{n}$$ is a positive integer, what is the value of n?

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

(2) 10 < n < 24

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

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Re: If sqrt(n) is a positive integer, what is the value of n? [#permalink]

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10 Apr 2016, 07:33
lovely_baby wrote:
Agree with B, but isn't it a nonsence to say that sqrt(n) is positive?

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??
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Re: If sqrt(n) is a positive integer, what is the value of n? [#permalink]

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10 Apr 2016, 10:39
MeghaP wrote:
lovely_baby wrote:
Agree with B, but isn't it a nonsence to say that sqrt(n) is positive?

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
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Re: If sqrt(n) is a positive integer, what is the value of n? [#permalink]

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18 Jul 2016, 12:07
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.
Re: If sqrt(n) is a positive integer, what is the value of n?   [#permalink] 18 Jul 2016, 12:07

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