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# Is y!/x ! an integer? (1) (x + y)(x y) = 5! + 1 (2) x + y =

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SVP
Joined: 05 Apr 2005
Posts: 1710
Is y!/x ! an integer? (1) (x + y)(x y) = 5! + 1 (2) x + y = [#permalink]

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20 Sep 2005, 21:41
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Is y!/x ! an integer?

(1) (x + y)(x â€“ y) = 5! + 1
(2) x + y = 121

Last edited by HIMALAYA on 25 Sep 2005, 06:53, edited 1 time in total.
Manager
Joined: 15 Jul 2005
Posts: 105

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20 Sep 2005, 22:36
(a) statement I is sufficient

I am not sure whether this logic is correct, but here goes...

y!/x! is an integer if y>=x

also, I am assuming x and y are positive integers, as negative factorials are undefined.

statement I: (x-y)(x+y)=5!+1... or x^2-y^2=121. Since we are not counting negative integers for x and y, we can safely assume x>y, so sufficient (y!/x! is not an integer)

statement II: x+y=112, insufficient, as y may or may not be greater than or equal to x
Senior Manager
Joined: 07 Jul 2005
Posts: 404
Location: Sunnyvale, CA

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21 Sep 2005, 04:30
Excellent .. Choose C earlier. But this reasoning seems perfect.
Senior Manager
Joined: 13 Jan 2005
Posts: 331

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23 Sep 2005, 10:06
Chets, I used the same reasoning as yours and arrived at A. If x is indeed negative, I considered it as -(y!/x!) which still tells if K=(y!/x!) is an integer (-ve or +ve).

GA
SVP
Joined: 05 Apr 2005
Posts: 1710

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25 Sep 2005, 06:52
HIMALAYA wrote:
Is y!/x ! an integer?

(1) (x + y)(x â€“ y) = 5! + 1
(2) x + y = 112

i think the question is not correct as posted. it should be like this:

Is y!/x ! an integer?

(1) (x + y)(x â€“ y) = 5! + 1
(2) x + y = 121

Any way, OA given is A but i think it should be C.

from (i), the values that satisfy for x and y are 61 and 60 respectively. also -61 and -60 satisfy for x and y respectively...not suff.

from ii, values for x and y could be any positive numbers including 61 and 60. so not suff.

from i and ii, x and y are 61 and 60 respectively......
Intern
Joined: 08 Feb 2005
Posts: 15

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28 Sep 2005, 10:06
I think this is just one of those situations where you have to hope that the makers of the GMAT thought of that solution. Can they expect us to assume that this only refers to positive numbers... of course not, this is why I think something additional would have been added such as x>0 and y>0 to take care of an inconsistancy such as this one.
Manager
Joined: 06 Aug 2005
Posts: 197

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28 Sep 2005, 14:21
jrabenho wrote:
I think this is just one of those situations where you have to hope that the makers of the GMAT thought of that solution. Can they expect us to assume that this only refers to positive numbers... of course not, this is why I think something additional would have been added such as x>0 and y>0 to take care of an inconsistancy such as this one.

Yes you should assume x,y >=0, integers, because without use of gamma functions (off GMAT syllabus), factorial is undefined otherwise.
28 Sep 2005, 14:21
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