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a, b, x & y are positive integers. If ay=bx, is 7 a fact

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a, b, x & y are positive integers. If ay=bx, is 7 a fact

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a, b, x & y are positive integers. If ay=bx, is 7 a factor of x?

(1) 35 is a factor of a
(2) b when prime factorized will be of the form (5)^s

OA is C

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Hi vinni.k,

We're told that A, B, X and Y are positive INTEGERS and that (A)(Y) = (B)(X). We're asked if 7 a factor of X. This is a YES/NO questions. While this prompt might look 'scary', it's built around a Prime Factorization 'shortcut' that you can use to avoid doing lots of math.

1) 35 is a factor of A.

Fact 1 tells us that A must be a multiple of 35. Thus (A)(Y) will have at least one 5 and at least one 7 among its prime factors. By extension (B)(X) must ALSO have at least one 5 and at least one 7 among its prime factors.
IF.... there's just one 7 and it's "in" the B, then the answer to the question is NO.
there's just one 7 and it's "in" the X, then the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) B when prime-factorized will be of the form (5)^S.

Fact 2 tells us that the ONLY prime factors that COULD be in B are 5s, but this tells us nothing about the value of X.
Fact 2 is INSUFFICIENT

Combined, we know...
35 is a factor of A.
The ONLY prime factors that COULD be in B are 5s

(A)(Y) will have at least one 5 and at least one 7 among its prime factors and (B)(X) must ALSO have at least one 5 and at least one 7 among its prime factors. We know that there can NOT be any 7s 'in' B though, so that one 7 MUST be "in" X. Thus, X will ALWAYS be a multiple of 7 and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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Rich,

Thank you for the explanation. It is a very good explanation and easily understandable.

Regards
Vinni

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ay = bx
Question ; Is 7 a factor of x?
Statement 1 ; 35 is a factor of a
That is, a must be a multiple of 35.
That is, it must have at least a 5 and 7 among it's prime factors to mate 35, here we have only 7 and it's in the right hand side with x.
Hence, Statement 1 is INSUFFICIENT.

$$Statement 2;\ b,\ when\ prime\ factorized\ will\ be\ of\ the\ form\ of\ \left(5\right)^5$$
$$That\ is,\ the\ only\ prime\ factors\ that\ could\ be\ in\ b\ are\ \left(5\right)^5.$$
This does not give enough information about the value of x.
Hence, Statement 2 is INSUFFICIENT.

Combining statement 1 and 2 together, ay will have at least one 5 and one 7 among it's prime factors and bx must also have at least one 5 and one 7 among it's prime factors, there cannot be any 7 in b. So therefore, 7 must be in x and x will always be multiple of 7, hence both statement combined together is SUFFICIENT.
Option C is CORRECT.

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