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# If x > 1 and y > 1, is X < Y 1) x^2/(xy + x) < 1

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Senior Manager
Joined: 23 May 2006
Posts: 322
If x > 1 and y > 1, is X < Y 1) x^2/(xy + x) < 1 [#permalink]

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31 Jul 2008, 15:36
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If x > 1 and y > 1, is X < Y
1) x^2/(xy + x) < 1
2) xy/y^2-y < 1

I got E. I do not have the OA and want to veryify whether my answer is correct.
Senior Manager
Joined: 23 May 2006
Posts: 322

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31 Jul 2008, 17:17
PatrickBateman wrote:
I get B.

VP
Joined: 17 Jun 2008
Posts: 1373

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31 Jul 2008, 17:33
x97agarwal wrote:
If x > 1 and y > 1, is X < Y
1) x^2/(xy + x) < 1
2) xy/y^2-y < 1

I got E. I do not have the OA and want to veryify whether my answer is correct.

Clearly OA is B

Givn condns : x>1,y>1 hence no neg values and no fractions less than 1.

question : is x<y?
consider the cases :
(1) alone : x/(y+1) <1 =>x<y+1 => eithr x<y or x=y => insufficient
(2) alone : x<y-1 => x<y => sufficient
_________________

cheers
Its Now Or Never

Director
Joined: 20 Sep 2006
Posts: 653

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31 Jul 2008, 17:51
spriya wrote:
x97agarwal wrote:
If x > 1 and y > 1, is X < Y
1) x^2/(xy + x) < 1
2) xy/y^2-y < 1

I got E. I do not have the OA and want to veryify whether my answer is correct.

Clearly OA is B

Givn condns : x>1,y>1 hence no neg values and no fractions less than 1.

question : is x<y?
consider the cases :
(1) alone : x/(y+1) <1 =>x<y+1 => eithr x<y or x=y => insufficient
(2) alone : x<y-1 => x<y => sufficient

Good pt make sense. I donno when am I gonna stop doing these careless mistakes. I think the point here is that dont leave DS in middle try to solve to the point where you are sure rather its obvious that ans can be obtained.
Director
Joined: 14 Aug 2007
Posts: 726

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31 Jul 2008, 23:03
x97agarwal wrote:
If x > 1 and y > 1, is X < Y
1) x^2/(xy + x) < 1
2) xy/y^2-y < 1

I got E. I do not have the OA and want to veryify whether my answer is correct.

B

Using graphical approach.
[ I am bad at drawing in general and drawing with paintbrush at particular ...Ignore the blue dots in the figure; they don't have any meaning. Though the red dot implies the case where x can equal to y for 1) ...

Attachment:

inequality.JPG [ 14.43 KiB | Viewed 921 times ]
Senior Manager
Joined: 06 Apr 2008
Posts: 428

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01 Aug 2008, 02:02
x97agarwal wrote:
If x > 1 and y > 1, is X < Y
1) x^2/(xy + x) < 1
2) xy/y^2-y < 1

I got E. I do not have the OA and want to veryify whether my answer is correct.

Go with B)

Statement 1) is true even when x=y=2
Manager
Joined: 15 Jul 2008
Posts: 52

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01 Aug 2008, 03:47
@ alpha_plus_gamma: your graphical approach will be clear if you draw the line x=y
Re: Inequality:   [#permalink] 01 Aug 2008, 03:47
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# If x > 1 and y > 1, is X < Y 1) x^2/(xy + x) < 1

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