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Is 30 a factor of n?

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Is 30 a factor of n? [#permalink]

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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]

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New post 04 Jan 2013, 07:43
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.

Answer is C
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Re: Is 30 a factor of n? [#permalink]

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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) .

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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Re: Is 30 a factor of n? [#permalink]

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New post 04 Jan 2013, 07:51
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) .

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.

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]

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New post 04 Jan 2013, 08:01
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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) .

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.

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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Re: Is 30 a factor of n? [#permalink]

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New post 04 Jan 2013, 08:59
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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Re: Is 30 a factor of n? [#permalink]

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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.


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
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Re: Is 30 a factor of n? [#permalink]

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New post 05 Jan 2013, 03:35
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]

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New post 23 Mar 2016, 11:02
what is the correct answer? Bunuel says A but the answer is C?
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Re: Is 30 a factor of n? [#permalink]

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Re: Is 30 a factor of n? [#permalink]

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New post 23 Mar 2016, 11:39
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.


Hello Bunuel,
Is there a reference for your statement
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.

somewhere in GMAT official guide. I am little confused here, because almost in every DS question we are told to not assume a number as +ve or as integer unless otherwise advised.

In my opinion, given in this question we must not assume that "n" is positive integer.
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Re: Is 30 a factor of n? [#permalink]

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New post 23 Mar 2016, 11:43
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sameerspice 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.


Hello Bunuel,
Is there a reference for your statement
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.

somewhere in GMAT official guide. I am little confused here, because almost in every DS question we are told to not assume a number as +ve or as integer unless otherwise advised.

In my opinion, given in this question we must not assume that "n" is positive integer.


I'm not saying that one should assume this. I'm saying that in its current form the question is NOT GMAT like because every GMAT divisibility question will tell you in advance that any unknowns represent positive integers. So, if it were proper GMAT question we would be given that n is an integer.
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Is 30 a factor of n? [#permalink]

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New post 23 Mar 2016, 12:06
Quote:
I'm not saying that one should assume this. I'm saying that in its current form the question is NOT GMAT like because every GMAT divisibility question will tell you in advance that any unknowns represent positive integers. So, if it were proper GMAT question we would be given that n is an integer.



Thank Bunuel, this makes lot of sense and explain the question OA to me now.
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Re: Is 30 a factor of n? [#permalink]

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New post 23 Mar 2016, 12:59
Bunuel, if we see a divisibility question and integer details are not mentioned, should we assume that it is an integer because GMAT does mention usually? (probably asking the same question the other user asked - just wanted to confirm)
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Re: Is 30 a factor of n? [#permalink]

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New post 23 Mar 2016, 13:12
dina98 wrote:
Bunuel, if we see a divisibility question and integer details are not mentioned, should we assume that it is an integer because GMAT does mention usually? (probably asking the same question the other user asked - just wanted to confirm)


Proper GMAT question will always mention that variables in divisibility questions are positive integers.
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Re: Is 30 a factor of n?   [#permalink] 23 Mar 2016, 13:12
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