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Solutions

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Question

If both x and y are nonzero numbers, what is the value of y/x?

I. x = 6

II. y^2 = x^2


 

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 E is the correct answer.


Option Analysis

Note that √x^2=|x|.

Statement I is insufficient: x = 6. Not sufficient.

Statement II is insufficient: y^2 = x^2 –> |x|=|y| –> if x and y have the same sign then xy=1 (for example x=y=6) but if x and y have the opposite signs then xy=−1 (for example x=6 and y=−6). Not sufficient.

Together I and II, We still don’t know whether x and y have the same sign or not. Not sufficient.





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