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?

Thanks in advance.

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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