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divisible by 7

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Source: — Data Sufficiency |
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by sk818020 » Fri May 14, 2010 10:17 am
If x is divisible by 7, then 7 will be one of its prime factors. Is 7 a prime factor of x?

(1) does not help us because the prime factors could be,

2+2+2+2+2+2=12
3+3+3+3=12
5+7=12
.... there are many different combinations you could come up with.

Thus, (1) is insufficient.

(2) tells us that if you add the distinct prime factors up of x, you'll get 12. Thus the distinct prime factors must be;

We need to figure out the prime numbers before 12 and see what combinations we can come up with that will sum to 12.

Primes before 12 are 2, 3, 5, 7, 11. The only combinations that equal 12 are,

2+3+7=12, or
5+7=12

This tells us that that there is at least one 7 in the prime factorization of x. (2) is sufficient.

The answer is B.
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