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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
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If x > 1 and y > 1, is X < Y 1) x^2/(xy + x) < 1 [#permalink] New post 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
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Re: Inequality: [#permalink] New post 31 Jul 2008, 17:17
PatrickBateman wrote:
I get B.


please show your reasoning.
VP
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Re: Inequality: [#permalink] New post 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
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Director
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Re: Inequality: [#permalink] New post 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
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Re: Inequality: [#permalink] New post 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
inequality.JPG [ 14.43 KiB | Viewed 693 times ]
Senior Manager
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Re: Inequality: [#permalink] New post 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
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Re: Inequality: [#permalink] New post 01 Aug 2008, 03:47
@ alpha_plus_gamma: your graphical approach will be clear if you draw the line x=y
Answer is B
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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