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# Bill can dig a well in x! hours. Carlos can dig the same

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Bill can dig a well in x! hours. Carlos can dig the same [#permalink]  30 Mar 2005, 21:41
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Bill can dig a well in x! hours. Carlos can dig the same well in y! hours. If q is the number of hours that it takes Bill and Carlos to dig the well together, working at their respective rates, is q an integer?

(1) x-y=1
(2) y is a nonprime even number.
VP
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Re: work problem (DS) [#permalink]  30 Mar 2005, 22:38
I go with C.
q=(x!)(y!)/(x!+y!)

from i,
q=(x!)(y!)/(x!+y!)
= (x!)(y!)/(x*y!+y!)
=(x!)(y!)/y!(x+1)
=(x!)/(x+1)
if x=2,3, and 4, q is fraction otherwise not. note that x can not be 0 or negative.

from ii, y could be 4, 6,8 and so on but we do not know about x. if x=3, the value of q is in fraction.

from i and ii, x=y+1 and y is an even integer but not 2 and 0.
so if y=4, x=5 and q=(x!)/(x+1)=(5x4x3x2)/(5+1)=20.
if y=6, x=7, then q=(7x6x5x4x3x2)/(7+1)=630 or whatsoever.
VP
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I go with C

stat 1 insuff : (1) x-y=1
could be : x=2 and y=1 ; 1/2! + 1/1! = 1/Q ; Q = 2/3
could also be : x=5 and y=4 ; 1/5! + 1/4! = 1/Q ; 1/120 + 1/24 = 1/Q
6/120 = 1/Q ; Q = 20

stat 2 insuff : (2) y is a nonprime even number ( =even >2)
could be : x=3 and y=4 ; 1/3! + 1/4! = 1/Q ; 1/6 + 1/24 = 1/Q ; Q = 5/24
could be : x= and y=4 ; 1/5! + 1/4! = 1/Q ; 1/120 + 1/24 = 1/Q
6/120 = 1/Q ; Q = 20

stat 1+2 suff
x=7 and y=6 ; 1/7! + 1/6! = 1/Q ; 8/5040 = 1/Q ; Q = 630
x=5 and y=4 ; 1/5! + 1/4! = 1/Q ; 1/120 + 1/24 = 1/Q
6/120 = 1/Q ; Q = 20

I don't have the pattern and the algebra to prove it, I just did 2 tries but it seems correct

In addition to MA I would add that normally neither X nor Y should be equal 1 because in the question it is written X hourS and Y hourS Some Verbal in the Quant part
GMAT Club Legend
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That's right. (C) is the OA.
VP
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Re: work problem (DS) [#permalink]  04 Apr 2005, 12:29
Quote:
q=(x!)(y!)/(x!+y!)
= (x!)(y!)/(x*y!+y!)

can u plz explain this step ! thx
Intern
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Re: work problem (DS) [#permalink]  15 Apr 2005, 03:45
christoph wrote:
Quote:
q=(x!)(y!)/(x!+y!)
= (x!)(y!)/(x*y!+y!)

can u plz explain this step ! thx

Perhaps there is a formular that explains this better, but if you plug in nos you'll see that if x=y+1, x!=x*y!

Example 4=3+1, and 4!=4*3!. See da point?
Re: work problem (DS)   [#permalink] 15 Apr 2005, 03:45
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