Solutions
Get detailed explanations to advanced GMAT questions.
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
HardSolution
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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