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E
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Difficulty:
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Question Stats:
32% (02:35) correct
68%
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Is \(xy<0\)?
(1) \(\frac{x^3*y^5}{x*y^2}<0\)
(2) \(|x|-|y|<|x-y|\)
(1) \(\frac{x^3*y^5}{x*y^2}<0\)
(2) \(|x|-|y|<|x-y|\)
12 Nov 2009, 19:44
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Statement 1: \(\frac{x^3*y^5}{x*y^2} < 0\)
\(x^2*y^3 < 0\)
We know that \(x^2\) must be positive, so therefore y < 0. Since we do not know whether x is positive or negative, however, this is insufficient.
Statement 2: \(|x|-|y| < |x-y|\)
I'll approach this the way I would as if I was writing it on the GMAT with time constraints, by picking numbers:
(1) Is it possible for xy > 0 AND the above criteria to be satisfied? Yes. (i.e. x = 2, y = 3)
(2) Is it possible for xy < 0 AND the above criteria to be satisfied? Yes. (i.e. x = 2, y = -3)
Therefore, not sufficient.
Evaluating Both Statements
We know from Statement 1 that y < 0. Therefore we can revise the above approach for Statement 2 to specifics:
(1) Is it possible for y < 0, x < 0 (i.e. xy > 0) AND the above criteria to be satisfied? Yes. (i.e. x = -2, y = -3)
(2) Is it possible for y < 0, x > 0 (i.e. xy < 0) AND the above criteria to be satisfied? Yes. (i.e. x = 2, y = -3)
Therefore, insufficient.
The answer is E.
\(x^2*y^3 < 0\)
We know that \(x^2\) must be positive, so therefore y < 0. Since we do not know whether x is positive or negative, however, this is insufficient.
Statement 2: \(|x|-|y| < |x-y|\)
I'll approach this the way I would as if I was writing it on the GMAT with time constraints, by picking numbers:
(1) Is it possible for xy > 0 AND the above criteria to be satisfied? Yes. (i.e. x = 2, y = 3)
(2) Is it possible for xy < 0 AND the above criteria to be satisfied? Yes. (i.e. x = 2, y = -3)
Therefore, not sufficient.
Evaluating Both Statements
We know from Statement 1 that y < 0. Therefore we can revise the above approach for Statement 2 to specifics:
(1) Is it possible for y < 0, x < 0 (i.e. xy > 0) AND the above criteria to be satisfied? Yes. (i.e. x = -2, y = -3)
(2) Is it possible for y < 0, x > 0 (i.e. xy < 0) AND the above criteria to be satisfied? Yes. (i.e. x = 2, y = -3)
Therefore, insufficient.
The answer is E.
07 Mar 2012, 10:19
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pavanpuneet
Welcome to GMAT Club. Below is an answer to your question.
You can square both sides of an inequality if and only both sides are non-negative.
For |x|-|y|<|x-y| we know that |x-y| is non-negative, but |x|-|y| can be negative, as well as positive (non-negative), hence you cannot apply squaring.
GENERAL RULE:
A. We can raise both parts of an inequality to an even power if we know that both parts of an inequality are non-negative (the same for taking an even root of both sides of an inequality).
For example:
\(2<4\) --> we can square both sides and write: \(2^2<4^2\);
\(0\leq{x}<{y}\) --> we can square both sides and write: \(x^2<y^2\);
But if either of side is negative then raising to even power doesn't always work.
For example: \(1>-2\) if we square we'll get \(1>4\) which is not right. So if given that \(x>y\) then we can not square both sides and write \(x^2>y^2\) if we are not certain that both \(x\) and \(y\) are non-negative.
B. We can always raise both parts of an inequality to an odd power (the same for taking an odd root of both sides of an inequality).
For example:
\(-2<-1\) --> we can raise both sides to third power and write: \(-2^3=-8<-1=-1^3\) or \(-5<1\) --> \(-5^2=-125<1=1^3\);
\(x<y\) --> we can raise both sides to third power and write: \(x^3<y^3\).
Hope it helps.
