Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 24 Oct 2016, 17:08

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5062
Location: Singapore
Followers: 30

Kudos [?]: 337 [0], given: 0

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

### Show Tags

30 Mar 2005, 22:41
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
Joined: 25 Nov 2004
Posts: 1493
Followers: 7

Kudos [?]: 93 [0], given: 0

### Show Tags

30 Mar 2005, 23:38
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
Joined: 13 Jun 2004
Posts: 1118
Location: London, UK
Schools: Tuck'08
Followers: 7

Kudos [?]: 45 [0], given: 0

### Show Tags

31 Mar 2005, 07:16
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
Joined: 07 Jul 2004
Posts: 5062
Location: Singapore
Followers: 30

Kudos [?]: 337 [0], given: 0

### Show Tags

31 Mar 2005, 22:50
That's right. (C) is the OA.
VP
Joined: 30 Sep 2004
Posts: 1488
Location: Germany
Followers: 6

Kudos [?]: 307 [0], given: 0

### Show Tags

04 Apr 2005, 13:29
Quote:
q=(x!)(y!)/(x!+y!)
= (x!)(y!)/(x*y!+y!)

can u plz explain this step ! thx
Intern
Joined: 11 Mar 2005
Posts: 23
Followers: 0

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

### Show Tags

15 Apr 2005, 04:45
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, 04:45
Display posts from previous: Sort by