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# If y<x<0, which of the following CANNOT be true?

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Math Expert
Joined: 02 Sep 2009
Posts: 52906
If y<x<0, which of the following CANNOT be true?  [#permalink]

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18 Nov 2016, 01:41
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Difficulty:

55% (hard)

Question Stats:

62% (01:51) correct 38% (01:45) wrong based on 215 sessions

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If y<x<0, which of the following CANNOT be true?

A. x·y > 2
B. x−y > 2
C. x/y > 2
D. x+y > −2
E. y/x < 2

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Joined: 05 Mar 2015
Posts: 1001
If y<x<0, which of the following CANNOT be true?  [#permalink]

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18 Nov 2016, 10:39
Bunuel wrote:
If y<x<0, which of the following CANNOT be true?

A. x·y > 2
B. x−y > 2
C. x/y > 2
D. x+y > −2
E. y/x < 2

A. if x=-1,y=-3.....true
B.if x=-1 , y=-7....true
D. if x=-0.5 , y=-0.6....true
E. if x=-1, y=-1.1.......true

Now why option C is correct..
As y has more magnitude than x thus making x/y never >1 or 2

Ans C
CEO
Joined: 11 Sep 2015
Posts: 3431
Re: If y<x<0, which of the following CANNOT be true?  [#permalink]

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20 Nov 2016, 06:25
1
Top Contributor
Bunuel wrote:
If y<x<0, which of the following CANNOT be true?

A. x·y > 2
B. x−y > 2
C. x/y > 2
D. x+y > −2
E. y/x < 2

I think rohit8865's approach is the best approach.
However, here's another way to show why answer choice C cannot be true.

First recognize that, if y is NEGATIVE, then we know that 2y < y
If you're not convinced, here's a quick proof:
Given: y < 0
Add y to both sides to get: y + y < y
Simplify: 2y < y

Now let's see why answer choice C (x/y > 2) cannot be true
Take x/y > 2
Multiply both sides by y to get: x < 2y [aside: y is negative, so we just multiplied both sides of the inequality by a negative value. Whenever we do this, we must reverse the direction of the inequality]
Now combine this inequality with the one we created earlier (2y < y)
We we do so, we get: x < 2y < y
If we ignore the 2y in the middle, we get x < y, HOWEVER this contradicts the given information that says y < x < 0.
As such, answer choice C can never be true.

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Re: If y<x<0, which of the following CANNOT be true?  [#permalink]

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18 Jan 2019, 08:07
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Re: If y<x<0, which of the following CANNOT be true?   [#permalink] 18 Jan 2019, 08:07
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