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If y≠0, is |x/y|=x/y? 1) |xy|=xy 2) |x/y|=|x|/|y|

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If y≠0, is |x/y|=x/y? 1) |xy|=xy 2) |x/y|=|x|/|y| [#permalink]

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New post 09 Aug 2017, 04:28
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If y≠0, is |x/y|=x/y?

1) |xy|=xy
2) |x/y|=|x|/|y|
[Reveal] Spoiler: OA

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Re: If y≠0, is |x/y|=x/y? 1) |xy|=xy 2) |x/y|=|x|/|y| [#permalink]

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New post 09 Aug 2017, 04:51
MathRevolution wrote:
If y≠0, is |x/y|=x/y?

The question is basically asking if x & y have the same sign i.e. Are x,y > 0 OR x,y <0?

Quote:
1) |xy|=xy
2) |x/y|=|x|/|y|


1) |xy| = xy
=> Both x and y have the same sign.
x = 1, y = 1
|xy| = 1
xy = 1
They are the same.

x = 1, y = -1
|xy| = 1
xy = -1
Not the same. Test Failed
=> x and y have the same sign.
=> |x/y| = \(\frac{x}{y}\)

So A is sufficient.

2) |x/y|=\(\frac{|x|}{|y|}\)
x = 1, y = 1
|x/y|=\(\frac{|x|}{|y|}\) = 1
=> |x/y| = \(\frac{x}{y}\) = 1 => YES

x = -1, y = 1
|x/y|=\(\frac{|x|}{|y|}\) = 1
BUT |x/y| = 1 ≠ \(\frac{x}{y}\) = -1
=> NO.

2 answers, hence Insufficient.

A is the answer.
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Re: If y≠0, is |x/y|=x/y? 1) |xy|=xy 2) |x/y|=|x|/|y| [#permalink]

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New post 09 Aug 2017, 05:24
MathRevolution wrote:
If y≠0, is |x/y|=x/y?

1) |xy|=xy
2) |x/y|=|x|/|y|



Hi..

\(\frac{x}{y}\)... Has to be EITHER 0 OR positive....
And for that any of conditions would be sufficient..
1) x and y are of the same SIGN
2) x is 0..

Let's see the statements..
1) |xy|=xy..
Clearly x*y is 0 or POSITIVE...
Sufficient
2) |x/y|=|x|/|y|
If x is zero ans is YES..
If x and y are of same sign, ans is YES
But if x and y are of opposite sign ans is NO
Insufficient

A
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Re: If y≠0, is |x/y|=x/y? 1) |xy|=xy 2) |x/y|=|x|/|y| [#permalink]

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New post 11 Aug 2017, 01:00
==> If you modify the original condition and the question, in order to get |x/y|=x/y, you get x/y≥0?, and if you multiply y^2 on both sides, you get xy≥0?. Then, for con 1), to satisfy |xy|=xy, you get xy≥0, hence yes, it is sufficient. For con 2), if x=y=2, yes, but if x=2 and y=-1, no, hence it is not sufficient.

The answer is A.
Answer: A
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Re: If y≠0, is |x/y|=x/y? 1) |xy|=xy 2) |x/y|=|x|/|y|   [#permalink] 11 Aug 2017, 01:00
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