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If m, x, and y are positive integers, what is the value of x – y?

I. 2^x=m(2^y)

II. m is a multiple of 4

Option A:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Option B:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Option C:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Option D:

EACH statement ALONE is sufficient to answer the question asked.

Option E:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Option E is the correct answer.

Statement I is insufficient: 2^x=m(2^y) –> divide both sides by 2^y: 2^(x−y)=m. We need the value of m to get the value of x-y. Not sufficient.

Statement II is insufficient: m is a multiple of 4. Clearly insufficient.

Together I and II,

We still don’t know the value of m: if m=4, then 2^(x−y)=2^2 and in this case x−y=2 but if m=8, then 2^(x−y)=2^3 and in this case x−y=3. Not sufficient.

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