Data Sufficiency

VJesus12 wrote:a, b, x and 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

The OA is C.

Why is not sufficient the statement (1)? Can any expert help me? Please.

We have ay = bx => x = (a/b)y

We have to determine whether 7 a factor of x.

(1) 35 is a factor of a.

Say a = 35n; where n = any positive integer

Thus, x = 35n/b

Say b = 35n, then the answer is No; however, if say n = n, then the answer is Yes. No unique answer. Insufficient.

(2) b when prime factorized will be of the form (5)^s

We do not have any information about a and y. Insufficient.

(1) and (2) together

x = (a/b)y = 35n/5^s = (5*7*n)/5^s

Since x is an integer, and there only 5s in the denominator, x must be a factor of 7. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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