If a farmer sells 15 of his chickens, his stock of feed will : GMAT Problem Solving (PS)
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# If a farmer sells 15 of his chickens, his stock of feed will

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If a farmer sells 15 of his chickens, his stock of feed will [#permalink]

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01 May 2012, 13:53
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Question Stats:

66% (03:02) correct 34% (02:24) wrong based on 64 sessions

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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 (X-15) x (D+4)
case 2 (X+20)x (D+3)
from there I am stuck

best regards
[Reveal] Spoiler: OA
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Re: If a farmer sells 15 of his chickens, his stock of feed will [#permalink]

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01 May 2012, 15:59
Let x = total feed required for the planned period

n= number of chicken
t = total time of the planned feed

x = nt

1) x = (n-15) * (t+4)

2) x = (n+20) * (t-3)

equating 1 & 2

(n-15) * (t+4) = (n+20) * (t-3)

7n = 35t
n =5t

x= n * n/5

substituting this value in 1
n * n/5 = (n-15) * (n/5+4)

5n = 300
n =60

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Re: If a farmer sells 15 of his chickens, his stock of feed will [#permalink]

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01 May 2012, 18:09
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You are right with the approach..

But there is a mistake in your equation.

case 1 (X-15) x (D+4)
case 2 (X+20)x (D[highlight]+[/highlight]3)

It should be

case 1 (X-15) 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.

(X-15) x (D+4) = (X+20)x (D-3)

you will arrive at

X = 5*D

Since the amount of the feed is equal in all cases, we have,

(X-15) * (D+4) = X*D

Substitute D = X/5 in the above equation, you will get the answer as,

X = 60.
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Re: If a farmer sells 15 of his chickens, his stock of feed will [#permalink]

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13 Sep 2012, 23:26
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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:
(x-15)(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)(t-3)=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
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Re: If a farmer sells 15 of his chickens, his stock of feed will [#permalink]

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14 Feb 2015, 05:39
Hello from the GMAT Club BumpBot!

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Re: If a farmer sells 15 of his chickens, his stock of feed will [#permalink]

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14 Feb 2015, 12:55
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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....

[Reveal] Spoiler:
E

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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** GMAT Club Legend Joined: 09 Sep 2013 Posts: 13533 Followers: 577 Kudos [?]: 163 [0], given: 0 Re: If a farmer sells 15 of his chickens, his stock of feed will [#permalink] ### Show Tags 20 Sep 2016, 00:23 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. _________________ Director Joined: 07 Dec 2014 Posts: 500 Followers: 3 Kudos [?]: 82 [0], given: 2 If a farmer sells 15 of his chickens, his stock of feed will [#permalink] ### Show Tags 20 Sep 2016, 18:05 1 This post was BOOKMARKED 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 chickens to available feed days let c=number of chickens c/5=available feed days (c-15)(c/5+4)=c*c/5 c=60 chickens E. If a farmer sells 15 of his chickens, his stock of feed will [#permalink] 20 Sep 2016, 18:05 Similar topics Replies Last post Similar Topics: 6 A farmer constructs a fence along the northern edge of his property, u 2 03 Oct 2016, 05:27 2 A farmer ordered x tons of feed for his cattle. The feed supply compan 1 10 Jun 2016, 03:21 1 If a farmer sells 15 of his chickens, his stock of feed will 1 12 Dec 2012, 12:43 5 A farmer spent$35 on feed for chickens and goats. He spent 8 21 Apr 2012, 09:03
36 If the farmer sells 75 of his chickens, his stock of feed 15 25 Oct 2009, 01:41
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