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# Is n an integer ? 1. n^2 is an integer. 2. Sqrt (n) is

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Joined: 19 Nov 2008
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Is n an integer ? 1. n^2 is an integer. 2. Sqrt (n) is an [#permalink]

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Updated on: 11 Jan 2009, 11:20
Is n an integer ?

1. n^2 is an integer.
2. Sqrt (n) is an integer

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Originally posted by GmatEnemy on 10 Jan 2009, 12:03.
Last edited by GmatEnemy on 11 Jan 2009, 11:20, edited 1 time in total.
Senior Manager
Joined: 02 Nov 2008
Posts: 254

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10 Jan 2009, 12:34
GmatEnemy wrote:
Is n an integer ?

1. n^2 is an integer.
2. Sqrt (n) is an integer

I dont understand what the hell is the trap in this problem ?
Its soo simple but i am shocked with the answer.

(1.4)^2 = 2
2 ^2 = 4

So A is insufficient

N will always be an integer if it's Sqrt is an integer

So the correct answer is B
Manager
Joined: 04 Jan 2009
Posts: 229

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10 Jan 2009, 14:18
if n^2 is integer, it means nothing because if n^2 is negative, n is non-integer.
Now if sqrt(n) is integer, n is (not only) integer(, but non-negative. So they should have asked if n is non-negative integer. But the) answer to the question is B. because 2 is sufficient and 1 is not.
GmatEnemy wrote:
Is n an integer ?

1. n^2 is an integer.
2. Sqrt (n) is an integer

I dont understand what the hell is the trap in this problem ?
Its soo simple but i am shocked with the answer.

_________________

-----------------------
tusharvk

Manager
Joined: 28 Jul 2004
Posts: 135
Location: Melbourne
Schools: Yale SOM, Tuck, Ross, IESE, HEC, Johnson, Booth

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10 Jan 2009, 14:23
tusharvk wrote:
if n^2 is integer, it means nothing because if n^2 is negative, n is non-integer.
Now if sqrt(n) is integer, n is (not only) integer(, but non-negative. So they should have asked if n is non-negative integer. But the) answer to the question is B. because 2 is sufficient and 1 is not.
GmatEnemy wrote:
Is n an integer ?

1. n^2 is an integer.
2. Sqrt (n) is an integer

I dont understand what the hell is the trap in this problem ?
Its soo simple but i am shocked with the answer.

Tushar, how can n^2 be negative? I did not get that part. Also, negative numbers too are integers.
_________________

kris

Senior Manager
Joined: 02 Nov 2008
Posts: 254

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10 Jan 2009, 14:40
tusharvk wrote:
if n^2 is integer, it means nothing because if n^2 is negative, n is non-integer.
Now if sqrt(n) is integer, n is (not only) integer(, but non-negative. So they should have asked if n is non-negative integer. But the) answer to the question is B. because 2 is sufficient and 1 is not.
GmatEnemy wrote:
Is n an integer ?

1. n^2 is an integer.
2. Sqrt (n) is an integer

I dont understand what the hell is the trap in this problem ?
Its soo simple but i am shocked with the answer.

n^2 can never be negative. the lowest possible value of n^2 is 0.
also an integer can be negative.
Manager
Joined: 04 Jan 2009
Posts: 229

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10 Jan 2009, 15:01
For an integer (positive or negative) n, n^2 is always positive. But 1 gives only that n^2 is integer and not non-negative integer; so if n^2 is negative, n is not integer. Thus, 1 is not enough.
Next 2=>sqrt(n)=a=>a^2=n; Thus, n is non-negative i.e. 0 or positive. Thus, 2 is sufficient.
krishan wrote:
tusharvk wrote:
if n^2 is integer, it means nothing because if n^2 is negative, n is non-integer.
Now if sqrt(n) is integer, n is (not only) integer(, but non-negative. So they should have asked if n is non-negative integer. But the) answer to the question is B. because 2 is sufficient and 1 is not.
GmatEnemy wrote:
Is n an integer ?

1. n^2 is an integer.
2. Sqrt (n) is an integer

I dont understand what the hell is the trap in this problem ?
Its soo simple but i am shocked with the answer.

Tushar, how can n^2 be negative? I did not get that part. Also, negative numbers too are integers.

_________________

-----------------------
tusharvk

Manager
Joined: 28 Jul 2004
Posts: 135
Location: Melbourne
Schools: Yale SOM, Tuck, Ross, IESE, HEC, Johnson, Booth

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10 Jan 2009, 15:16
oh !!! got it .

if n = sqrt(-2) , n^2 = -2.

A does not say whether n is a positive or negative, hence, (A) is not sufficient.
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kris

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1345

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12 Jan 2009, 02:42
krishan wrote:
oh !!! got it .

if n = sqrt(-2) , n^2 = -2.

A does not say whether n is a positive or negative, hence, (A) is not sufficient.

No, all numbers on the GMAT are real numbers. You can never take square roots of negatives on the GMAT. If you see $$n^2$$ on the GMAT, it is always de facto true that $$n^2 \geq 0$$; it is never relevant to a GMAT problem to consider the possibility that $$n^2$$ is negative.
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Manager
Joined: 04 Jan 2009
Posts: 229

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12 Jan 2009, 06:33
if N^2 is always non-negative for GMAT, does that change the answer.
Your point is well taken; I do not think it will change the answer.
n^2=2 is integer; but n is non-integer.
sqrt(n) is integer=>n which is square of integer is integer and also n is non-negative.

IanStewart wrote:
krishan wrote:
oh !!! got it .

if n = sqrt(-2) , n^2 = -2.

A does not say whether n is a positive or negative, hence, (A) is not sufficient.

No, all numbers on the GMAT are real numbers. You can never take square roots of negatives on the GMAT. If you see $$n^2$$ on the GMAT, it is always de facto true that $$n^2 \geq 0$$; it is never relevant to a GMAT problem to consider the possibility that $$n^2$$ is negative.

_________________

-----------------------
tusharvk

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1345

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12 Jan 2009, 12:06
tusharvk wrote:
if N^2 is always non-negative for GMAT, does that change the answer.
Your point is well taken; I do not think it will change the answer.
n^2=2 is integer; but n is non-integer.
sqrt(n) is integer=>n which is square of integer is integer and also n is non-negative.

The original answer is correct, but not because n^2 might be negative. The original answer is correct because n^2 might be equal to a positive integer which is not a perfect square.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Re: N integer   [#permalink] 12 Jan 2009, 12:06
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# Is n an integer ? 1. n^2 is an integer. 2. Sqrt (n) is

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