Solutions

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Question

Is x > y?

I. x = 4y^2

II. x > 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

Statement I is insufficient: x = 4y^2. If x=y=0 then the answer is NO but if x=4 and y=1 then the answer is YES. Not sufficient.

Statement II is insufficient: x > 1. Not sufficient.

Together I and II, x=4y^2 –> y=√x/2 (or y=−√x/2=negative). Now, since x>1 then x>√x, so x>(√x/2=y). Sufficient.





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