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

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chetan2u
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Is |x|/y>x/y, where x is not equal to 0? [#permalink] New post   27 Jul 2018, 00:14
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A
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D
E

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Question Stats:

39% (02:13) correct 61% (01:45) wrong based on 75 sessions
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Is \(\frac{|x|}{y}>\frac{x}{y}\), where \(xy\neq{0}\)?


(1) \(y<0\)

(2) \(x=y\)


New question!!!..
self made
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D
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Re: Is |x|/y>x/y, where x is not equal to 0? [#permalink] New post   27 Jul 2018, 00:32
Expert Reply
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] 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? [#permalink] New post   16 Apr 2020, 22:33
Where is it given that LHS is less than or EQUAL ?? to RHS?
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Is |x|/y>x/y, where x is not equal to 0? [#permalink] New post   16 Apr 2020, 22:57
Expert Reply
chetan2u wrote:
Is \(\frac{|x|}{y}>\frac{x}{y}\), where \(xy\neq{0}\)?


(1) \(y<0\)

(2) \(x=y\)


New question!!!..
self made


(1) \(y<0\)
Now, we can look at the main question asked and it deals with |x| and x apart from y...
So \(|x|\geq{x}\).....Divide this by y, a negative number, and the inequality sign will change
\(\frac{|x|}{y}\leq{\frac{x}{y}}\)..
So our answer for - Is \(\frac{|x|}{y}>\frac{x}{y}\)? - is always NO
Suff

(2) \(x=y\)
So either both are positive or negative..
a) Both positive....\(\frac{x}{y}=1\) and \(\frac{|x|}{y}=1\), ... Is 1>1..NO
b) Both negative....\(\frac{x}{y}=1\) and \(\frac{|x|}{y}\)=-1, ...Is -1>1...NO
So our answer for - Is \(\frac{|x|}{y}>\frac{x}{y}\)? - is always NO
Suff

D
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Re: Is |x|/y>x/y, where x is not equal to 0? [#permalink] New post   16 Apr 2020, 23:19
Since y < 0

Then we need to look at two possibilities for x either it is positive or negative.

If x is positive then they’re equal, which gives an answer of NO.

If x is negative it would reverse the relationship and make the right side larger than the left side. Again an answer of NO.

So statement 1 is sufficient. Now we eliminate the chance that B,C, or D can happen.

We look at statement 2

Similarly if x = +ve then y +ve and they’re both equal, giving an answer of NO.

If x = -ve then y is -ve

Making the right hand side larger than the left hand side. Again an answer of NO

Since both statements are sufficient, the answer is D.

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Re: Is |x|/y>x/y, where x is not equal to 0? [#permalink]
16 Apr 2020, 23:19
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Bunuel
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