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# Is 30 a factor of n?

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Is 30 a factor of n? [#permalink]  04 Jan 2013, 06:33
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Difficulty:

85% (hard)

Question Stats:

21% (01:44) correct 79% (00:58) wrong based on 66 sessions
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
[Reveal] Spoiler: OA

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Re: Is 30 a factor of n? [#permalink]  04 Jan 2013, 06:43
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

1) If n is $$\sqrt{30}$$, Answer is no. If n is 30, answer is yes. Insufficient.

2)If n = 15, answer is no. If n = 30, answer is yes. Insufficient.

1 & 2 together. 2n has to be an even number to be divisible by 30. Hence, n has to be an integer. $$n^2$$ is divisible by 30. So $$n^2$$ should have at least one 2, one 3 and one 5. Since $$n^2$$ is the square of an integer, this further implies that n^2 has to have at least two 2s, two 3s and two 5s. Hence n has at least one 2, one 3 and one 5. Hence divisible.

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Re: Is 30 a factor of n? [#permalink]  04 Jan 2013, 06:45
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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) .

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.

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Re: Is 30 a factor of n? [#permalink]  04 Jan 2013, 06:51
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) .

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.

Hi Bunuel,

Just curious.. Why would the question not make sense if "n" were not an integer?
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Re: Is 30 a factor of n? [#permalink]  04 Jan 2013, 07:01
1
KUDOS
Expert's post
MacFauz 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) .

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.

Hi Bunuel,

Just curious.. Why would the question not make sense if "n" were not an integer?

It does not make sense for GMAT since only integers can have factors.
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Current Student
Status: Never ever give up on yourself.Period.
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Kudos [?]: 219 [0], given: 35

Re: Is 30 a factor of n? [#permalink]  04 Jan 2013, 07:59
Thanks Bunuel,

I used the same logic as you did.
that's why I didn't get C as answer...Thanks for the clarification..+1 Kudos
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Kudos [?]: 9 [0], given: 5

Re: Is 30 a factor of n? [#permalink]  04 Jan 2013, 22:12
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) .

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.

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.

Thanks
Math Expert
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Kudos [?]: 62562 [0], given: 9457

Re: Is 30 a factor of n? [#permalink]  05 Jan 2013, 02:35
Expert's post
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) .

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.

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.

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]  11 Nov 2014, 02:55
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