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# Is the integer x divisible by 36 ?

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Is the integer x divisible by 36 ? [#permalink]  08 Sep 2007, 14:16
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Question Stats:

81% (01:36) correct 19% (00:37) wrong based on 48 sessions
Is the integer x divisible by 36 ?

(1) x is divisible by 12.
(2) x is divisible by 9.

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-the-integer-x-divisible-by-167497.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Nov 2014, 03:20, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Is the integer x divisible by 36 ? [#permalink]  08 Sep 2007, 14:22
gowani wrote:
a question from the retired GMAT papers...I tried to search for this but wasn't able to find the explanation

Is the integer x divisible by 36?

(1) x is divisible by 12.
(2) x is divisible by 9.

C.

36 = 2*2*3*3

(1) x is only divisible by 2*2*3, missing a 3 INSUFFICIENT
(2) x is only divisible by 3*3, missing 2*2 INSUFFICIENT

Together, here is the tricky part,
you know that x has a factor of 2*2*3 and 3*3. Therefore, at bare minimum, x must be divisible by 2*2*3*3
SUFFICIENT
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Re: Is the integer x divisible by 36 ? [#permalink]  01 Nov 2014, 12:33
bkk145 wrote:
gowani wrote:
a question from the retired GMAT papers...I tried to search for this but wasn't able to find the explanation

Is the integer x divisible by 36?

(1) x is divisible by 12.
(2) x is divisible by 9.

C.

36 = 2*2*3*3

(1) x is only divisible by 2*2*3, missing a 3 INSUFFICIENT
(2) x is only divisible by 3*3, missing 2*2 INSUFFICIENT

Together, here is the tricky part,
you know that x has a factor of 2*2*3 and 3*3. Therefore, at bare minimum, x must be divisible by 2*2*3*3
SUFFICIENT

Hi -- question here.

Since 12 has factors of 2, 2, and 3 and 9 has factors of 3, and 3. Does this mean, that when combined, their PF's are 2, 2, 3, 3, 3 (Three 3's?) or are we only supposed to pick the max number of 3's?
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Re: Is the integer x divisible by 36 ? [#permalink]  02 Nov 2014, 03:32
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Expert's post
russ9 wrote:
bkk145 wrote:
gowani wrote:
a question from the retired GMAT papers...I tried to search for this but wasn't able to find the explanation

Is the integer x divisible by 36?

(1) x is divisible by 12.
(2) x is divisible by 9.

C.

36 = 2*2*3*3

(1) x is only divisible by 2*2*3, missing a 3 INSUFFICIENT
(2) x is only divisible by 3*3, missing 2*2 INSUFFICIENT

Together, here is the tricky part,
you know that x has a factor of 2*2*3 and 3*3. Therefore, at bare minimum, x must be divisible by 2*2*3*3
SUFFICIENT

Hi -- question here.

Since 12 has factors of 2, 2, and 3 and 9 has factors of 3, and 3. Does this mean, that when combined, their PF's are 2, 2, 3, 3, 3 (Three 3's?) or are we only supposed to pick the max number of 3's?

Tot find the least common multiple of two positive integers:
1. Make prime factorization;
2. Multiply all the primes keeping their powers (pick the highest power of the common primes).

$$12 = 2^2*3$$.
$$9 = 3^2$$.

$$LCM = 2^2*3^2$$.

Is the integer x divisible by 36 ?

(1) x is divisible by 12. If x=12, then the answer is NO but if x=36, then the answer is YES. Not sufficient.

(2) x is divisible by 9. If x=9, then the answer is NO but if x=36, then the answer is YES. Not sufficient.

(1)+(2) From above it follows that x must be divisible by the least common multiple of 12 and 9, which is 36. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-the-integer-x-divisible-by-167497.html
_________________
Re: Is the integer x divisible by 36 ?   [#permalink] 02 Nov 2014, 03:32
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