Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 05 Apr 2012
Posts: 43

If a farmer sells 15 of his chickens, his stock of feed will last for [#permalink]
Show Tags
01 May 2012, 14:53
Question Stats:
65% (01:55) correct 35% (02:43) wrong based on 83 sessions
HideShow timer Statistics
If a farmer sells 15 of his chickens, his stock of feed will last for 4 more days than planned, but if he buys 20 more chickens, he will run out of feed 3 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have? A. 12 B. 24 C. 48 D. 55 E. 60 My approach is as follow the load be defined as the number of chicken x the number of day let x be the number of chicken and D the number of day
case 1 (X15) x (D+4) case 2 (X+20)x (D+3) from there I am stuck please help !
best regards
Official Answer and Stats are available only to registered users. Register/ Login.



Intern
Joined: 22 Jan 2012
Posts: 34

Re: If a farmer sells 15 of his chickens, his stock of feed will last for [#permalink]
Show Tags
01 May 2012, 16:59
Let x = total feed required for the planned period
n= number of chicken t = total time of the planned feed
x = nt
1) x = (n15) * (t+4)
2) x = (n+20) * (t3)
equating 1 & 2
(n15) * (t+4) = (n+20) * (t3)
7n = 35t n =5t
x= n * n/5
substituting this value in 1 n * n/5 = (n15) * (n/5+4)
5n = 300 n =60
Hence E is the answer



Intern
Joined: 02 Apr 2012
Posts: 2

Re: If a farmer sells 15 of his chickens, his stock of feed will last for [#permalink]
Show Tags
01 May 2012, 19:09
You are right with the approach..
But there is a mistake in your equation.
case 1 (X15) x (D+4) case 2 (X+20)x (D[highlight]+[/highlight]3)
It should be
case 1 (X15) x (D+4) case 2 (X+20)x (D[highlight][/highlight]3) , since he runs out of feed three days earlier.
Now, equate the cases you have got, cause the amount of the feed is the same in both the cases.
(X15) x (D+4) = (X+20)x (D3)
you will arrive at
X = 5*D
Since the amount of the feed is equal in all cases, we have,
(X15) * (D+4) = X*D
Substitute D = X/5 in the above equation, you will get the answer as,
X = 60.



Manager
Joined: 27 Dec 2011
Posts: 61

Re: If a farmer sells 15 of his chickens, his stock of feed will last for [#permalink]
Show Tags
14 Sep 2012, 00:26
Hi,
Instead of substituting values and all, we can do the following:
'x' be no. of chickens 't' be the time the feed last following normal schedule.
We two equations: (x15)(t+4)=1 [ Its like Rate*time=1 ('1' because the complete feed is done, i.e. complete work is done)]  eq. 1 (x+20)(t3)=1 [same explanation as above]  eq. 2
From eq.1 find t = .... (it will have x) From eq. 2 find t= ..... (it will also have x)
just equate 't' from above to equations and find x.
I must admit the calculations get hard as a quadratic equation is formed!
thanks,
Kartik



Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 616
Location: India
Concentration: Strategy, General Management
Schools: Olin  Wash U  Class of 2015
WE: Information Technology (Computer Software)

Re: If a farmer sells 15 of his chickens, his stock of feed will last for [#permalink]
Show Tags
12 Dec 2012, 23:54
gmatgeek wrote: If a farmer sells 15 of his chickens, his stock of feed will last for 4 more days than planned, but if he buys 20 more chickens, he will run out of feed 3 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have? 12 24 48 55 60 Say farmer has n chicken and he is good for d days.: We have 3 equations given in question: (n15) * d+4 =(n+20) *(d3) = n * d Solving these: (You can solve 1st and 3rd and 2nd and 3rd together) We get: 20d3n=60 4n15d =60 => n=60 Ans E it is!
_________________
Lets Kudos!!! Black Friday Debrief



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11970
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: If a farmer sells 15 of his chickens, his stock of feed will last for [#permalink]
Show Tags
14 Feb 2015, 13:55
Hi All, This question has a great 'concept shortcut' built into it. It's subtle, and you'll only notice it if you really think about how the numbers relate to one another, but here it is... We have an unknown number of chickens and exactly enough food to feed them all for a certain amount of time. IF....we sell 15 of the chickens, then there will be EXACTLY 4 more days of food than are needed. That's an INTERESTING piece of info  exactly 4 more days of food (not 3.999, not 3.5, not 2.7)  an INTEGER. IF...we buy 20 more chickens, there there will be EXACTLY 3 fewer days of food than are needed. Again, that's INTERESTING  it's an INTEGER. The ONLY way for those integers to appear is if the current number of chickens is a MULTIPLE of BOTH 15 and 20. Otherwise, the number of days of food would most likely end up as weird decimals or fractions. Looking at the answers, there's just one that's a multiple of 15 and 20.... Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



VP
Joined: 07 Dec 2014
Posts: 1032

Re: If a farmer sells 15 of his chickens, his stock of feed will last for [#permalink]
Show Tags
20 Sep 2016, 19:05
If a farmer sells 15 of his chickens, his stock of feed will last for 4 more days than planned, but if he buys 20 more chickens, he will run out of feed 3 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?
A. 12 B. 24 C. 48 D. 55 E. 60
total difference in chickens bought=20(15)=35 total difference in available feed days=4(3)=7 35/7=5/1=ratio of number of chickens to available feed days let c=current number of chickens c/5=available feed days c*c/5=(c15)(c/5+4) c=60 chickens E



NonHuman User
Joined: 09 Sep 2013
Posts: 7247

Re: If a farmer sells 15 of his chickens, his stock of feed will last for [#permalink]
Show Tags
06 Jul 2018, 11:37
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If a farmer sells 15 of his chickens, his stock of feed will last for
[#permalink]
06 Jul 2018, 11:37






