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# If xy < 5, is x < 1 ?

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If xy < 5, is x < 1 ?  [#permalink]

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Updated on: 04 Dec 2012, 01:49
6
00:00

Difficulty:

75% (hard)

Question Stats:

58% (02:14) correct 42% (02:10) wrong based on 272 sessions

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If xy < 5, is x < 1 ?

(1) |y| > 5
(2) x/y > 0

I got the answer is C which is correct but it was a guess work. So here is how I did this question:

Statement 1

|y| > 5 i.e. y > 5 and y > -5 or y > 5 and y < -5.

As this statement doesn't say anything about x, its clearly insufficient.

Statement 2

x/y> 0 --> This statement only tells that x and y have the same sign. Therefore insufficient.

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Originally posted by enigma123 on 07 Mar 2012, 14:11.
Last edited by Bunuel on 04 Dec 2012, 01:49, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 51072
Re: Is x < 1?  [#permalink]

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07 Mar 2012, 14:24
1
4
enigma123 wrote:
If xy < 5, is x < 1 ?

(1) $$|y| > 5$$
(2) $$\frac{x}{y}> 0$$

I got the answer is C which is correct but it was a guess work. So here is how I did this question:

Statement 1

|y| > 5 i.e. y > 5 and y > -5 or y > 5 and y < -5.

As this statement doesn't say anything about x, its clearly insufficient.

Statement 2

x/y> 0 --> This statement only tells that x and y have the same sign. Therefore insufficient.

|y| > 5 means that y<-5 or y>5.

If xy < 5, is x < 1 ?

(1) $$|y| > 5$$ --> if $$y=10$$ and $$x=0$$ then the answer is YES but if $$y=-10$$ and $$x=2$$ then the answer is NO. Not sufficient.

(2) $$\frac{x}{y}>0$$ --> $$x$$ and $$y$$ have the same sign. Still insufficient: if $$y=-2$$ and $$x=-1$$ then the answer is YES but if $$y=2$$ and $$x=2$$ then the answer is NO. Not sufficient.

(1)+(2) From (2) $$x$$ and $$y$$ have the same sign. Now, if from (1) $$y>5$$ then $$0<x<1$$ (in order $$xy<5$$ to hold true) and if from (1) $$y<-5$$ then $$-1<x<0$$ (again in order $$xy<5$$ to hold true). So in both cases $$x<1$$. Sufficient.

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Re: If xy < 5, is x < 1 ?  [#permalink]

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13 Mar 2016, 07:45
1
Here Clearly statements 1 and two are not alone sufficient as x>1 and X<1
but combining them => x<1 as they should be of same sign and |y|>5 => if y is negative x is sufficient
if y is positive => x<<1 as Y>5
hence C
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Re: If xy < 5, is x < 1 ?  [#permalink]

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01 Jul 2017, 09:54
Bunuel wrote:
enigma123 wrote:
If xy < 5, is x < 1 ?

(1) $$|y| > 5$$
(2) $$\frac{x}{y}> 0$$

I got the answer is C which is correct but it was a guess work. So here is how I did this question:

Statement 1

|y| > 5 i.e. y > 5 and y > -5 or y > 5 and y < -5.

As this statement doesn't say anything about x, its clearly insufficient.

Statement 2

x/y> 0 --> This statement only tells that x and y have the same sign. Therefore insufficient.

|y| > 5 means that y<-5 or y>5.

If xy < 5, is x < 1 ?

(1) $$|y| > 5$$ --> if $$y=10$$ and $$x=0$$ then the answer is YES but if $$y=-10$$ and $$x=2$$ then the answer is NO. Not sufficient.

(2) $$\frac{x}{y}>0$$ --> $$x$$ and $$y$$ have the same sign. Still insufficient: if $$y=-2$$ and $$x=-1$$ then the answer is YES but if $$y=2$$ and $$x=2$$ then the answer is NO. Not sufficient.

(1)+(2) From (2) $$x$$ and $$y$$ have the same sign. Now, if from (1) $$y>5$$ then $$0<x<1$$ (in order $$xy<5$$ to hold true) and if from (1) $$y<-5$$ then $$-1<x<0$$ (again in order $$xy<5$$ to hold true). So in both cases $$x<1$$. Sufficient.

May not be the easiest solution, but I find it interesting that these inequalities can be rigorously solved using graphical visualisation.

Given : xy<5 is the area between the hyperbola.

1) |y| > 5: When y>5, x can only be less than 1. When y<-5, x can only be greater than -1. Thus not sufficient.
2) Same sign, so not sufficient.

Combining.
When y>5, x can only be less 1 BUT greater than 0. So x<1? YES
When y<-5, x can only be greater than -1 BUT less than 0. So, x<1? YES

E
Math Expert
Joined: 02 Aug 2009
Posts: 7100
Re: If xy < 5, is x < 1 ?  [#permalink]

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06 Aug 2018, 23:01
1) |y|>5
So y>5, then x<1 OR
y<-5, then x can be any value as say 10 so xy=10*-5=-50<5
Insufficient

2) x/y>0
Both X and y are of same sign
X could be 10 and y =1/3..
Or X could be -5 and y -1/2..
Insufficient

Combined
Y>5, and X>0, then x<1..
y<-5 and X<0, so X<1
Sufficient

C
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Re: If xy < 5, is x < 1 ? &nbs [#permalink] 06 Aug 2018, 23:01
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