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Is x < y? (1) 1/x < 1/y (2) x/y < 0

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Is x < y? (1) 1/x < 1/y (2) x/y < 0  [#permalink]

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New post 26 Nov 2017, 08:48
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Difficulty:

  55% (hard)

Question Stats:

55% (01:44) correct 45% (01:22) wrong based on 48 sessions

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Re: Is x < y? (1) 1/x < 1/y (2) x/y < 0  [#permalink]

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New post 26 Nov 2017, 08:58
Bunuel wrote:
Is x < y?

(1) 1/x < 1/y
(2) x/y < 0



lovely Q

(1) \(\frac{1}{x} < \frac{1}{y}\)..
\(\frac{1}{x} - \frac{1}{y}<0........................\frac{y-x}{xy}<0\)
so xy and y-x have opposite signs..
case I: xy >0, y-x<0....y<x
case II : xy<0, y-x>0...y>x
insuff

(2) \(\frac{x}{y}< 0\)
Just tells us that one is positive and one is negative
any of the two x and y can be negative
so x<y or y<x
insuff

combined
case II is left..
both x and y are of opposite sign, so xy<0 and therefore y>x
suff

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Is x < y? (1) 1/x < 1/y (2) x/y < 0 &nbs [#permalink] 26 Nov 2017, 08:58
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