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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

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VP
Joined: 03 Apr 2007
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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 [#permalink]  13 May 2008, 18:33
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Q29.
if X>1 and Y>1, is X<Y?
(1) X^2/(XY+X)<1
(2) XY/Y^2-Y<1

Please explain your work
Current Student
Joined: 28 Dec 2004
Posts: 3391
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 181 [0], given: 2

Re: DS:x<y [#permalink]  13 May 2008, 18:43
goalsnr wrote:
Q29.
if X>1 and Y>1, is X<Y?
(1) X^2/(XY+X)<1
(2) XY/Y^2-Y<1

Please explain your work

i would go with B..

1) basically boils down to x<(y+1)..suppose x=y..then yeah but x=y and not x<y..insuff
2) basically boils down to x<y-1 or x+1<y..this is clearly sufficient..x<y..
Director
Joined: 14 Jan 2007
Posts: 780
Followers: 2

Kudos [?]: 71 [0], given: 0

Re: DS:x<y [#permalink]  13 May 2008, 19:16
should be B.

Stmt1 reduces to x-y < 1
x=4.5, y=5 ==> x<y
x=5, y=4.5 ===> x>y
Insuff

Stmt2 reduces to y-x> 1
This ensures that y> x
Suff
Manager
Joined: 11 Apr 2008
Posts: 157
Schools: Kellogg(A), Wharton(W), Columbia(D)
Followers: 1

Kudos [?]: 55 [0], given: 0

Re: DS:x<y [#permalink]  13 May 2008, 23:31
I agree with the above explanations - IMO B.
SVP
Joined: 28 Dec 2005
Posts: 1583
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Kudos [?]: 88 [0], given: 2

Re: DS:x<y [#permalink]  14 May 2008, 03:49
B for me as well.

Now, I just want to absolutely confirm something with this quesion: for both the statements, we are able to rearrange the given inequality (i.e. cross multiply) only because we are told in the stem that x>1 and y>1, correct ?

If that was not the case, then we would have to consider multiple case of when the equality in the statement held ?
Senior Manager
Joined: 16 Aug 2004
Posts: 327
Location: India
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Kudos [?]: 40 [0], given: 0

Re: DS:x<y [#permalink]  14 May 2008, 04:04
Answer option B, similar to fresinha's working.
VP
Joined: 03 Apr 2007
Posts: 1376
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Kudos [?]: 263 [0], given: 10

Re: DS:x<y [#permalink]  14 May 2008, 09:39
Thank you All. I got B as well, but the OB stated was E.
The question is from Set 25.
Re: DS:x<y   [#permalink] 14 May 2008, 09:39
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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

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