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PS - LPV

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Director
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Joined: 25 Oct 2006
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Kudos [?]: 620 [0], given: 6

PS - LPV [#permalink]

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New post 06 Apr 2009, 19:42
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if xy = 165 where x>y, the least possible value of x-y is:
A. 2
B. 4
C. 8
D. 13
E. 15
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Kudos [?]: 620 [0], given: 6

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GMAT Tutor
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Joined: 24 Jun 2008
Posts: 1341

Kudos [?]: 1908 [0], given: 6

Re: PS - LPV [#permalink]

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New post 06 Apr 2009, 21:24
priyankur_saha@ml.com wrote:
if xy = 165 where x>y, the least possible value of x-y is:
A. 2
B. 4
C. 8
D. 13
E. 15


None of the above. Where is the question from? x - y can be as close to zero as you like. If x = root(165) and y = root(165), then xy = 165 and x - y = 0; if you make x just slightly larger than root(165), there will need to be value of y just slightly smaller than root(165) for which xy = 165, and x - y is very close to zero.

Now, if the question were to say that x and y are positive integers, the answer would be different. We would then need to think of how we might write 165 as a product of two positive integers. 165 = 3*5*11, so the only products of positive integers that give 165 are:

11* 15 = 165
5 * 33 = 165
3 * 55 = 165
1 * 165 = 165

and of these, we get the smallest difference from x = 15 and y = 11; x - y = 4.
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Kudos [?]: 1908 [0], given: 6

Director
Director
User avatar
Joined: 25 Oct 2006
Posts: 639

Kudos [?]: 620 [0], given: 6

Re: PS - LPV [#permalink]

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New post 06 Apr 2009, 21:51
IanStewart wrote:
None of the above. Where is the question from? x - y can be as close to zero as you like. If x = root(165) and y = root(165), then xy = 165 and x - y = 0; if you make x just slightly larger than root(165), there will need to be value of y just slightly smaller than root(165) for which xy = 165, and x - y is very close to zero.


This is the right approach because it is not given that x and y are integers. I missed this clue.... :(

Thanks Ian
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If You're Not Living On The Edge, You're Taking Up Too Much Space

Kudos [?]: 620 [0], given: 6

Re: PS - LPV   [#permalink] 06 Apr 2009, 21:51
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