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Is |x| = |y|?

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Source: — Data Sufficiency |

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by ErikaPrepScholar » Thu Jan 04, 2018 7:43 am
If |x| = |y|, this means that either x = y OR x = -y. If we can prove or disprove either, the statement is sufficient.

Statement 1 tells us that x - y = 6, which can be arranged to x = y + 6. If x = 3 and y = -3, |x| = |y|, but if x = 7 and y = 1, |x| does not equal |y|. Insufficient.

Statement 2 tells us that x + y = 0, which we can rearrange to x = -y. Sufficient.
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by [email protected] » Thu Jan 04, 2018 11:08 am
Hi M7MBA,

We're asked if |X| = |Y|. This is a YES/NO question. We can answer it by TESTing VALUES.

1) X - Y = 6

IF...
X=6 and Y=0, then the answer to the question is NO.
X=3 and Y= -3, then the answer to the question is YES.
Fact 1 is INSUFFICIENT.

2) X + Y = 0

Given the equation in Fact 2, X and Y are either both 0 OR they are 'opposites' (such as +1 and -1)

IF...
X=0 and Y=0, then the answer to the question is YES.
X=1 and Y= -1, then the answer to the question is YES.
X and Y are opposites, then the answer to the question is YES.
Fact 2 is SUFFICIENT.

Final Answer: B

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