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

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

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10 Jan 2009, 12:03
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Is n an integer ?

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

Last edited by GmatEnemy on 11 Jan 2009, 11:20, edited 1 time in total.

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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

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Manager
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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.

_________________

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tusharvk

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Location: Melbourne
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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.
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kris

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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.

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Manager
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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

Kudos [?]: 14 [0], given: 0

Manager
Joined: 28 Jul 2004
Posts: 135

Kudos [?]: 76 [0], given: 2

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

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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
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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.

_________________

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tusharvk

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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.
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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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