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03 Aug 2018, 05:26
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
75% (01:13) correct
25%
(01:21)
wrong
based on 3354
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If \(y ≠ 0\), is \(|x| = 1\) ?
(1) \(x = \frac{y}{|y|}\)
(2) \(|x| = -x\)
(DS05986)
(1) \(x = \frac{y}{|y|}\)
(2) \(|x| = -x\)
(DS05986)
03 Aug 2018, 05:44
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Bunuel
Question stem, is \(|x| = 1\) ?
St1:- \(x = \frac{y}{|y|}\)
When y>0, \(x = \frac{y}{y}\) (where y is non-negative and non-zero)
Or, x=1; so |x|=1
when y<0, \(x = \frac{y}{-y}\)
Or, x=-1; so |x|=1
Sufficient.
St2:- \(|x| = -x\)
Or, \(|x|+x=0\)
Or, \(x\leq0\)
Insufficient.
Ans. (A)
15 Mar 2022, 15:15
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Bunuel
Target question: Is |x| = 1?
Statement 1: \(x = \frac{y}{|y|}\)
First recognize that |y| must positive.
With this in mind let's consider two possible cases: y is positive and y is negative.
Case a: If y is negative, then x = \(\frac{y}{|y|}\) = (negative y)/(positive y) = -1, in which case |x| = |-1| = 1. So, the answer to the target question is YES, |x| = 1
Case b: If y is positive, then x = \(\frac{y}{|y|}\) = (positive y)/(positive y) = 1, in which case |x| = |1| = 1. So, the answer to the target question is YES, |x| = 1
Since both possible cases yield the same answer to the target question, statement 1 is SUFFICIENT
Statement 2: |x| = -x
There are infinitely many values of x that satisfy the equation |x| = -x
Here are two:
Case a: x = -1 (notice that |x| = -x becomes |-1| = -(-1), which simplifies to be |-1| = 1 (which is true). In this case, the answer to the target question is YES, |x| = 1
Case b: x = -2 (notice that |x| = -x becomes |-2| = -(-2), which simplifies to be |-2| = 2 (which is true). In this case, the answer to the target question is NO, |x| does not equal 1
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
