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# If xy = 6, is x < y? (1) y ≥ 3 (2) y ≤ 3

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Math Expert
Joined: 02 Sep 2009
Posts: 58320
If xy = 6, is x < y? (1) y ≥ 3 (2) y ≤ 3  [#permalink]

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01 Nov 2018, 00:21
00:00

Difficulty:

25% (medium)

Question Stats:

81% (01:08) correct 19% (01:21) wrong based on 35 sessions

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If xy = 6, is x < y?

(1) y ≥ 3
(2) y ≤ 3

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Manager
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 104
Re: If xy = 6, is x < y? (1) y ≥ 3 (2) y ≤ 3  [#permalink]

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01 Nov 2018, 01:03
Statement 1 :

$$y=\frac{6}{x}$$

$$y ≥ 3$$ => $$\frac{6}{x}$$ ≥ 3 =>$$\frac{x}{6}$$ ≤ $$\frac{1}{3}$$ => $$x ≤ 2$$

$$x ≤ 2$$ and $$y ≥ 3$$ Hence $$x < y$$

(y is positive and $$xy = 6$$ so x is positive)

Sufficient

Statement 2 :

example 1 : $$x = 2$$ and $$y = 3$$ => $$x<y$$ (True)
example 2 : $$x =3$$ and $$y =2$$ => $$x>y$$ (False)

Not sufficient

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Re: If xy = 6, is x < y? (1) y ≥ 3 (2) y ≤ 3   [#permalink] 01 Nov 2018, 01:03
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