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# If x≠ 0 and y ≠ 0, is x < 1/y?

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Director
Joined: 18 Feb 2019
Posts: 817
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
If x≠ 0 and y ≠ 0, is x < 1/y?  [#permalink]

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26 Mar 2019, 00:05
2
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Difficulty:

45% (medium)

Question Stats:

53% (01:22) correct 47% (00:43) wrong based on 17 sessions

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If x≠ 0 and y ≠ 0, is x < 1/y?

I. xy < 1

II. y = 2
Math Expert
Joined: 02 Aug 2009
Posts: 8752
Re: If x≠ 0 and y ≠ 0, is x < 1/y?  [#permalink]

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26 Mar 2019, 08:09
If x≠ 0 and y ≠ 0, is x < 1/y?

I. xy < 1
Two cases..
(I) If y is positive, we can divide the two sides without changing the sign, so $$\frac{xy}{y}<\frac{1}{y}.....x<\frac{1}{y}$$
(II) If y is negative, we can divide the two sides but after changing the sign, so $$\frac{xy}{y}>\frac{1}{y}.....x>\frac{1}{y}$$
Thus insufficient.

II. y = 2
Insuff

Combined, we know y is positive , therefore $$\frac{xy}{y}<\frac{1}{y}.....x<\frac{1}{y}$$
Sufficient

C
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Re: If x≠ 0 and y ≠ 0, is x < 1/y?  [#permalink]

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29 May 2020, 09:38
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Re: If x≠ 0 and y ≠ 0, is x < 1/y?   [#permalink] 29 May 2020, 09:38