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

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

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New post 27 Jul 2018, 00:14
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

38% (01:18) correct 62% (01:29) wrong based on 34 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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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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New post 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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New post 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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