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26 Feb 2012, 00:30
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C
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Difficulty:
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Question Stats:
65% (01:55) correct
35%
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If x is not equal to y, does x/(y-x) = 1?
(1) |x| = x - y
(2) x^3 < 0
(1) |x| = x - y
(2) x^3 < 0
26 Feb 2012, 00:42
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If x is not equal to y, does x/(y-x) = 1?
(1) |x| = x - y
If \(x<0\), then we'd get \(-x=x-y\) and finally, \(2x=y\). In this case, the answer is YES.
However, if \(x\geq{0}\), then we'd get \(x=x-y\) and finally \(y=0\). Since \(x\neq{y}\) (given), then \(2x\neq{y}\). In this case, the answer is NO. (If \(y=0\), then for \(2x=y\) to hold true, \(x\) must also be 0. However, we are told that \(x\neq{y}\), so if \(y=0\), then \(2x=y\) is not possible). Not sufficient.
(2) x^3 < 0
The above implies that \(x<0\). No info about \(y\). Not sufficient.
(1)+(2) Since from (2) \(x<0\), then we have the first case from (1) \(2x=y\). Sufficient.
Answer: C.
- Is \(\frac{x}{(y-x)}=1\)?
Is \(x=y-x\)?
Is \(2x=y\)?
(1) |x| = x - y
If \(x<0\), then we'd get \(-x=x-y\) and finally, \(2x=y\). In this case, the answer is YES.
However, if \(x\geq{0}\), then we'd get \(x=x-y\) and finally \(y=0\). Since \(x\neq{y}\) (given), then \(2x\neq{y}\). In this case, the answer is NO. (If \(y=0\), then for \(2x=y\) to hold true, \(x\) must also be 0. However, we are told that \(x\neq{y}\), so if \(y=0\), then \(2x=y\) is not possible). Not sufficient.
(2) x^3 < 0
The above implies that \(x<0\). No info about \(y\). Not sufficient.
(1)+(2) Since from (2) \(x<0\), then we have the first case from (1) \(2x=y\). Sufficient.
Answer: C.
General Discussion
09 Dec 2023, 22:46
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Bunuel
Hi Bunuel
A fundamental doubt:
Statement 1 gives two possibilities - either y =0 or y=2x.
If y=0, then x has to be equal to y, which is forbidden as per the question.
So y has to be 2x.
By this, Can't we not assume statement 1 is sufficient?
