Solutions

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Question

If x^2 = y^2, is true that x>0?

I. x=2y+1

II. y<= -1


 

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

Hard

Solution

Option C is the correct answer.


Option Analysis

x^2=y^2 –> |x|=|y| –> either y=x or y=−x.

Statement I is insufficient: x=2y+1 –> if y=x then we would have: x=2x+1 –> x=−1<0 (notice that in this case y=x=−1) but if y=−x then we would have: x=−2x+1 –> x=1/3>0 (notice that in this case y=−x=−1/3). Not sufficient.

Statement II is insufficient: y<= -1. Clearly insufficient.

Together I and II, Since from (2) y≤−1 then from (1) y=x=−1, so the answer to the question is NO. Sufficient.


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