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# If X is a positive integer, is X divisible by 48? 1) X is

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If X is a positive integer, is X divisible by 48? 1) X is [#permalink]  20 Mar 2010, 11:38
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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

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?

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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?

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

Manager
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Schools: UCLA (Anderson) - Class of 2013
GMAT 1: Q V
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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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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.
Manager
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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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