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# Is |x|/y>x/y, where x is not equal to 0?

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Math Expert
Joined: 02 Aug 2009
Posts: 6554
Is |x|/y>x/y, where x is not equal to 0?  [#permalink]

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27 Jul 2018, 00:14
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Question Stats:

43% (01:18) correct 57% (01:19) wrong based on 30 sessions

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Is $$\frac{|x|}{y}>\frac{x}{y}$$, where $$xy\neq{0}$$?

(1) $$y<0$$

(2) $$x=y$$

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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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>x/y, where x is not equal to 0?  [#permalink]

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27 Jul 2018, 00:32
Given xy $$\neq$$ 0

=> x $$\neq$$ 0 and y $$\neq$$ 0

Statement 1

y < 0

=> $$\frac{1}{y}$$ < 0

We know for any value of x, |x| $$\geq$$ x

=> If we multiply above equation with $$\frac{1}{y}$$ which is < 0, the inequality sign reverses

=> $$\frac{|x|}{y} \leq \frac{x}{y}$$

Hence statement 1 is sufficient to say $$\frac{|x|}{y}$$ is not greater than $$\frac{x}{y}$$

Statement 2

x = y

=> $$\frac{x}{y}$$ = 1

=> $$\frac{x}{y}$$ is always positive

=> $$\frac{|x|}{y}$$ is either positive with a maximum value of $$\frac{x}{y}$$ or negative based on sign of y

In both the cases $$\frac{|x|}{y} \leq \frac{x}{y}$$

Statement 2 is sufficient

Hence statement s is sufficient to say $$\frac{|x|}{y}$$ is not greater than $$\frac{x}{y}$$

Hence option D
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Re: Is |x|/y>x/y, where x is not equal to 0?  [#permalink]

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27 Jul 2018, 00:41
I think it should be D.

Statement 1: y<0
x>0 or x<0
If x>0
$$\frac{|+x|}{-y} = \frac{+x}{-y}$$
If x<0
$$\frac{|-x|}{-y} < \frac{-x}{-y}$$
Sufficient.
$$\frac{|x|}{y} ≤ \frac{x}{y}$$

Statement 2: x=y
If x and y are less than 0
$$\frac{|-x|}{-y} < \frac{-x}{-y}$$

If x and y are greater than 0
$$\frac{|+x|}{+y} = \frac{+x}{+y}$$
Sufficient.
$$\frac{|x|}{y} ≤ \frac{x}{y}$$
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Re: Is |x|/y>x/y, where x is not equal to 0? &nbs [#permalink] 27 Jul 2018, 00:41
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