Is positive Integer x divisible by 7 a.) Sum of prime

Question

Is positive Integer x divisible by 7

a.) Sum of prime factors of x is 7
b.) Sum of distinct prime factors of x is 12

Can somebody explain how to solve this .

hgp2k · Answer

a) Consider Prime factors to be 2 and 5 (sum of these two prime factors is 7). 
The integer X could be 10 (not divisible by 7), 70 (divisible by 7)
Not Sufficient.

b) Consider the prime factors 5 and 7 (these are the only prime factors satisfying the condition).
So integer X is divisible by 7 for sure.
Sufficient.

Statement 2 alone is sufficient, but 1 alone is not.

deepakraam · Answer

Here is huv I worked it out

statement 1:
==========
Factors must contain only prime nos as 2 & 5 or 7.

10 - 1,2,5,10
49 - 1,7,49

so insuff

statement 2:
==========
distinct prime nos sum is 12 which gives 2,3,7.Since one of the factors is 7, the no must be divisible by 7.

So I wud go with option 2

IanStewart · Answer

The question doesn't really make sense. When we talk about the 'prime factors' of a number, we normally *mean* the distinct prime factors: the factors of 20 are 1, 2, 4, 5, 10 and 20, and of those, 2 and 5 are prime; 2 and 5 are the prime factors of 20 (not 2, 2, and 5).

With that interpretation, the two statements are clearly contradictory. Even if we take Statement 1 to mean "The sum of the prime factors of x, including any repeated prime factors, is 7", the statements are still contradictory; if we include repeated factors, the sum of the prime factors of x must be at least as large as the sum of the distinct prime factors of x. The statements in a genuine GMAT DS question can never contradict each other, since it needs to be logically possible for the test taker to consider both statements together. Where is the question from?

All of that said, from Statement 1, x might be 7, or x might be 10, for example, so S1 is not sufficient. From Statement 2, x might be 5*7 = 35, or 2*3*7 = 42, each of which are divisible by 7. Of course, we could also combine those primes with exponents and satisfy the condition in Statement 2, but in any case, the prime 7 needs to appear in the prime factorization.

Is positive Integer x divisible by 7 a.) Sum of prime

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