Solutions
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Question
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.
Difficulty Level
EasySolution
Option E is the correct answer.
Option Analysis
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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