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# Is 1/x < 1/y for integers x,y ? (1) x^2 + y^2 = 25 (2) xy

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VP
Joined: 22 Aug 2005
Posts: 1112
Location: CA
Is 1/x < 1/y for integers x,y ? (1) x^2 + y^2 = 25 (2) xy [#permalink]

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04 Nov 2005, 19:05
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Is 1/x < 1/y for integers x,y ?

(1) x^2 + y^2 = 25
(2) xy = 12

Last edited by duttsit on 04 Nov 2005, 19:27, edited 1 time in total.
VP
Joined: 06 Jun 2004
Posts: 1053
Location: CA

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04 Nov 2005, 19:23
duttsit wrote:
Is 1/x < 1/y for integers x,y ?

(1) x^2 - y^2 = 25
(2) xy = 12

Is 1/x < 1/y for integers x,y?

1/x - 1/y < 0? --> (y-x)/xy < 0?

(1) x^2 - y^2 = 25 --> (x+y)(x-y) = 25. Insufficient.

(2) xy = 12. So for (y-x)/xy < 0, (y-x) has to be negative. Insufficient.

Together, still not sufficient. My answer is E
VP
Joined: 22 Aug 2005
Posts: 1112
Location: CA

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04 Nov 2005, 19:28
TeHCM wrote:
duttsit wrote:
Is 1/x < 1/y for integers x,y ?

(1) x^2 - y^2 = 25
(2) xy = 12

Is 1/x < 1/y for integers x,y?

1/x - 1/y < 0? --> (y-x)/xy < 0?

(1) x^2 - y^2 = 25 --> (x+y)(x-y) = 25. Insufficient.

(2) xy = 12. So for (y-x)/xy < 0, (y-x) has to be negative. Insufficient.

Together, still not sufficient. My answer is E

TeHCM, please look at question again. there was a typo in statement (1). sorry about that.
VP
Joined: 06 Jun 2004
Posts: 1053
Location: CA

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04 Nov 2005, 19:42
duttsit wrote:
Is 1/x < 1/y for integers x,y ?

(1) x^2 + y^2 = 25
(2) xy = 12

Is 1/x < 1/y?

Implies that x has to be bigger than y for the equation to hold.

(1) x or y could be +- 3 or +-4. Insufficient.
(2) xy = 12, which implies that both integers could either be negative or positive. But it still doesn't tell us if x or y is bigger. Insufficient.

Both together. Stil not sufficient. My answer is still E.
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

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04 Nov 2005, 19:49
folks...i am on a bad roll here totally out of stamina

though ....I am going with E

1/x < 1/y ?

well...DONT cross MULTIPLY as we dont know which side the equality sign points to

(1) clearly Insuff....

(2) xy=12, well then x=12/y

1/x=y/12

questions is asking is y/12<1/y Y is an integer...so eliminate fraction...

now we dont know the sign of Y is it positive or negative...so E...
Director
Joined: 27 Jun 2005
Posts: 504
Location: MS

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04 Nov 2005, 19:52
I am also with E ..

A ) take X =3 , Y = 4
1/X<1/Y No but if X=4 and Y =3 then 1/X< 1/Y so InSuff

B ) take X = 2 , Y =6
1/X<1/Y No but if X=6 and Y = 2 then 1/X<1/Y Yes so InSuff

both together also gives Yes and No with (3,4) and (4,3) so both together are also not sufficient .....Hence answer E
VP
Joined: 22 Aug 2005
Posts: 1112
Location: CA

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04 Nov 2005, 21:18
OA is E. Good work all the way.
Director
Joined: 14 Oct 2003
Posts: 583
Location: On Vacation at My Crawford, Texas Ranch

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04 Nov 2005, 22:22
Darn why didn't I see this thread earlier - good question Duttsit.
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04 Nov 2005, 22:22
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