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# If x is a positive integer, is x divisible by 48?

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If x is a positive integer, is x divisible by 48? [#permalink]

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20 Mar 2010, 12:38
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If x is a positive integer, is x divisible by 48?

(1) x is divisible by 8
(2) x is divisible by 6

[Reveal] Spoiler:
Since prime factorization of 8 is 2x2x2 and 6 is 2x3, total of 2x2x2x2x3=48. So my answer was C.
I can see that numbers such as 24, 72 would tell me the answer is E but why wouldn't my logic above work?

[Reveal] Spoiler: OA

Last edited by Bunuel on 16 Aug 2015, 10:36, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: If x is a positive integer, is x divisible by 48? [#permalink]

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20 Mar 2010, 14:38
changhiskhan wrote:
If X is a positive integer, is X divisible by 48?

1) X is divisible by 8
2) X is divisible by 6

Since prime factorization of 8 is 2x2x2 and 6 is 2x3, total of 2x2x2x2x3=48. So my answer was C.
I can see that numbers such as 24, 72 would tell me the answer is E but why wouldn't my logic above work?

X is divisible by 8 so it is divisible by 2*2*2
X is also divisible by 6 so it is divisible by 2*3
take the least common factor of 8 and 6 to determine the highest factor we can deduce from both the stmts
= 2*2*2*3 = 24
Hence from both the stmts we can say that X is divisible by 24 for sure but we cannot say about 48.
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My debrief: done-and-dusted-730-q49-v40

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Re: If x is a positive integer, is x divisible by 48? [#permalink]

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20 Mar 2010, 21:35
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changhiskhan wrote:
If X is a positive integer, is X divisible by 48?

1) X is divisible by 8
2) X is divisible by 6

Since prime factorization of 8 is 2x2x2 and 6 is 2x3, total of 2x2x2x2x3=48. So my answer was C.
I can see that numbers such as 24, 72 would tell me the answer is E but why wouldn't my logic above work?

48 = 2*2*2*2*3

1)
8 = 2*2*2
Now, we know that X has 3 2s among its prime factors.
This doesn't tell us whether X has 1 more 2 and 1 more 3 among its prime factors.

Eliminate A and D

2)
6 = 2*3
Now, we know that X has 2 and 3 among its prime factors.
This doesn't tell us whether X has 3 more 2s among its prime factors.

Eliminate B

Let's combine the information:
What we know for certain -

Prime factor of X = 2*2*2*3

There are only 3 2s because the 2 from fact 2) is actually a duplicate.

X can potentially have more 2s thus the answer is E.
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Re: If x is a positive integer, is x divisible by 48? [#permalink]

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05 Apr 2010, 09:10
I understand the explanation, but I thought that if a number "N" is divisible by two factors, then N will also be divisible by the product of those two factors.

In other words
6 * 8 = 48
and N is divisible by both 6 and 8
then N would also be divisible by the product of 6 and 8, 48.
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Re: If x is a positive integer, is x divisible by 48? [#permalink]

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05 Apr 2010, 14:32
You will be clear with the explanation from sidhu4u.
Take N=24, it is divisible by 8 and also by 6. But is not divisible by 48.
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Re: If x is a positive integer, is x divisible by 48? [#permalink]

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31 Jul 2015, 05:11
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x is a positive integer, is x divisible by 48?   [#permalink] 31 Jul 2015, 05:11
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