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If n is a positive integer, is 30 a factor of n ? (1) 30 is a factor

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If n is a positive integer, is 30 a factor of n ? (1) 30 is a factor [#permalink] New post   26 Jan 2012, 06:38
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If n is a positive integer, is 30 a factor of n ?

(1) 30 is a factor of n^2
(2) 30 is a factor of 2n
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If n is a positive integer, is 30 a factor of n ? (1) 30 is a factor [#permalink] New post   26 Jan 2012, 08:49
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If n is a positive integer, is 30 a factor of n ?

(1) 30 is a factor of n^2

    If 30 = 2*3*5 is NOT a factor of n (if 2, 3 and 5 are not factors of n), then how these factors appeared in n^2? Exponentiation doesn't "produce" primes. Sufficient.

(2) 30 is a factor of 2n

    Clearly insufficient: if n = 15 then NO but if n = 30 then YES. Not sufficient.

Answer: A.
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Re: Is 30 a factor of n? [#permalink] New post   04 Jan 2013, 23:12
Bunuel wrote:
daviesj wrote:
Is 30 a factor of n?

(1) 30 is a factor of the square of n
(2) 30 is a factor of 2n

I doubt on OA...plz clarify


Every GMAT divisibility question will tell you in advance that any unknowns represent positive integers, which means that ALL GMAT divisibility questions are limited to positive integers only.

If n is not an integer, then the question does not make sense (at least for GMAT) .

The question should read:
If n is an integer, is 30 a factor of n?

(1) 30 is a factor of n^2. If 30=2*3*5 is not a factor of n (if 2, 3 and 5 are not factors of n), then how this factors could appear in n^2? Exponentiation doesn't "produce" primes. Sufficient.

(2) 30 is a factor of 2n. Clearly insufficient: if n=15 then the answer is NO but if n=30 then the answer is YES. Not sufficient.

Answer: A.


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Is it not possible that for Statement 1:

If the number is 900 and 30 is a factor of 900, then it is possible that 30 (which is ) is a factor of the square root of 900. In the contrary, 60 is also a factor of 900 but is not a factor of the square root of 900.

Please shed some light..
Thanks
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Re: Is 30 a factor of n? [#permalink] New post   05 Jan 2013, 03:35
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Drik wrote:
Bunuel wrote:
daviesj wrote:
Is 30 a factor of n?

(1) 30 is a factor of the square of n
(2) 30 is a factor of 2n

I doubt on OA...plz clarify


Every GMAT divisibility question will tell you in advance that any unknowns represent positive integers, which means that ALL GMAT divisibility questions are limited to positive integers only.

If n is not an integer, then the question does not make sense (at least for GMAT) .

The question should read:
If n is an integer, is 30 a factor of n?

(1) 30 is a factor of n^2. If 30=2*3*5 is not a factor of n (if 2, 3 and 5 are not factors of n), then how this factors could appear in n^2? Exponentiation doesn't "produce" primes. Sufficient.

(2) 30 is a factor of 2n. Clearly insufficient: if n=15 then the answer is NO but if n=30 then the answer is YES. Not sufficient.

Answer: A.


Bunnel-
Is it not possible that for Statement 1:

If the number is 900 and 30 is a factor of 900, then it is possible that 30 (which is ) is a factor of the square root of 900. In the contrary, 60 is also a factor of 900 but is not a factor of the square root of 900.

Please shed some light..
Thanks


If prime number p is a factor of n^2 (where n is a positive integer), then p must be a factor of n.

So, the fact that 2, 3, and 5 are factors of n^2 means that 2, 3 and 5 must also be factors of n.

But if p^2 is a factor of n^2 (where n is a positive integer), then p^2 may or may not be a factor of n.

For example, if 60=2^2*3*5 is a factor of n^2, then all primes of 60 must also be factors of n, but 2^2 may or may not be a factor of n, so 60 may or may not be a factor of n.

Hope it's clear.
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Re: Is 30 a factor of n? [#permalink]
05 Jan 2013, 03:35
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Bunuel
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