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# If xy < 5, is x < 1 ? (1) | y | > 5 (2) x / y > 0

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Director
Joined: 07 Jun 2004
Posts: 555
Location: PA
If xy < 5, is x < 1 ? (1) | y | > 5 (2) x / y > 0  [#permalink]

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07 Feb 2012, 16:36
3
7
00:00

Difficulty:

75% (hard)

Question Stats:

52% (02:16) correct 48% (02:14) wrong based on 192 sessions

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If xy < 5, is x < 1 ?

(1) |y| > 5
(2) x/y > 0
Math Expert
Joined: 02 Sep 2009
Posts: 58427
Re: is x < 1 ?  [#permalink]

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07 Feb 2012, 16:49
If xy < 5, is x < 1 ?

(1) |y| > 5 --> if y=10 and x=0 then the answer is YES but if y=-10 and x=2 then the answer is NO. Not sufficient.

(2) x/y > 0 --> x and y have the same sign. Still insufficient: if y=-2 and x=-1 then the answer is YES but if y=2 and x=2 then the answer is NO.

(1)+(2) From (2) x and y have the same sign. Now, if from (1) y>5 then 0<x<1 (in order xy<5 to hold true) and if from (1) y<-5 then -1<x<0 (again in order xy<5 to hold true). So in both cases x<1. Sufficient.

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Re: If xy < 5, is x < 1 ? (1) | y | > 5 (2) x / y > 0  [#permalink]

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06 Aug 2018, 21:38
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Re: If xy < 5, is x < 1 ? (1) | y | > 5 (2) x / y > 0   [#permalink] 06 Aug 2018, 21:38
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