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chickens  algebra (m08q13) [#permalink]
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27 Dec 2007, 12:33
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This topic is locked. If you want to discuss this question please repost it in the respective forum. If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. how many chickens does he have? (A) 60 (B) 120 (C) 240 (D) 275 (E) 300 Source: GMAT Club Tests  hardest GMAT questions

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Re: chickens  algebra [#permalink]
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27 Dec 2007, 17:50
ashkrs wrote: bmwhype2 wrote: ashkrs wrote: bmwhype2 wrote: If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. how many chickens does he have? 500 chickens ? explnation please. Never mind . I am not sure if I got that right. Still working!
well finally got the answer to 300 and I am sure gmat's not going to ask to solve that equation because i had to use my calculator to solve the quadratic equations which I got.
And I am still not sure of I did that correct .
I tried multiple ways many times ..
x number of chickens
y  amount of food
days for which chickens can survive = y/x
if 75 decreased then days are increared by 20
y/(x75) = y/x + 20
if 100 increased then days are decreased
y/( x+100) = y/x  15
solving for x will give x = 300

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gmatnub wrote: can anyone try to solve this?
I solved it. 300.
x  number of chickens
y  number of days.
Then, (x75)(y+20)=(x+100)(y15).
So, x=5y, or y=x/5. (1)
We know, that xy=(x75)(y+20). Using (1), 5x=1500, or x=300.

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Re: chickens  algebra (m08q13) [#permalink]
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18 Feb 2010, 03:30
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hey what i can say is that the choice 1 is obviously redundant coz if farmer needs to sell 75 chickens there cant be 60 chickens in total.
Now total difference for days in/out of stock is 15+20 = 35 and total difference in chickens would be 100 and 75 so total chicken difference is 175 days.
So effective feed per chicken is 5 units i.e. 175/35 = 5
u can now easily calculate total chickens that comes out to 300

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Re: chickens  algebra (m08q13) [#permalink]
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18 Feb 2010, 08:42
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If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. how many chickens does he have? (A) 60 (B) 120 (C) 240 (D) 275 (E) 300 This question was posted in PS forum as well. Here is my solution from this forum: # of chickens  x # of days  d If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned > Amount of feed equals \(xd=(x75)(d+20)\); If he buys 100 more chickens, he will run out of feed 15 days earlier than planned > Amount of feed equals \(xd=(x+100)(d15)\). \((x75)(d+20)=(x+100)(d15)\) > \(\frac{d+20}{d15}=\frac{x+100}{x75}\) > \(x=5d\) \(xd=(x75)(d+20)\) > \(5d^2=(5d75)(d+20)\) > \(d^2=(d15)(d+20)\) > \(d=60\) > \(x=5d=300\). Answer: E (300) Hope it helps.
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Re: chickens  algebra (m08q13) [#permalink]
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03 Jun 2010, 11:26
Dear All  Thanks for all your efforts, with and without the calculator. Is this really a GMAT question by no means this can be solved under 3 mins.
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Re: chickens  algebra (m08q13) [#permalink]
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03 Jun 2010, 11:49
Can be solved under 3 mins.You don't really have to solve quadratic equations:
Chickens=x Feed=f No of days feed lasts= x/f
Eq 1) f/(x75)=f/x + 20 =>f=(4/15)x(x75) Eq 2) f/(x+100) = f/x 15 => f = (3/20)x(x+100)
equating 1 and 2 one x will cancel out 16(x75)= 9(x+100) =>x=300
Hope this helps!

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Re: chickens  algebra (m08q13) [#permalink]
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03 Jun 2010, 11:59
gauravsaxena03 wrote: Can be solved under 3 mins.You don't really have to solve quadratic equations:
Chickens=x Feed=f No of days feed lasts= x/f
Eq 1) f/(x75)=f/x + 20 =>f=(4/15)x(x75) Eq 2) f/(x+100) = f/x 15 => f = (3/20)x(x+100)
equating 1 and 2 one x will cancel out 16(x75)= 9(x+100) =>x=300
Hope this helps! I meant this is not a GMAT test (Real one), so you can take your own sweet time. Reading and understanding the questions takes around 45secs. Considering average time of 3 mins. you have only 2.15secs to solve. Mix a little bit of GMAT Real test tension as well. Here we know the answer so we can try lucid approaches, In GMAT we would be struggling...
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Re: chickens  algebra (m08q13) [#permalink]
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03 Jun 2010, 12:03
well thats another way to look at it.I was talking considering the time required to form the equation and solving them.Thanks anyways for the insight

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Re: chickens  algebra (m08q13) [#permalink]
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10 Jun 2010, 14:23
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bmwhype2 wrote: If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. how many chickens does he have? (A) 60 (B) 120 (C) 240 (D) 275 (E) 300 Source: GMAT Club Tests  hardest GMAT questions Let n = no of chickens Let d = no of days to finish all the feeds Total amount of feed = nd nd=(n75)(d+20) = (n+100)(d15) nd+20n75d 1500 = nd15n+100d1500 35n175d n=5d but nd = (n75)(d+20) => nd = nd+20n – 75d  1500 4n15d = 300 4n – 3(5d) = 300 4n – 3(n) = 300 N = 300 (OA = E)
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Re: chickens  algebra (m08q13) [#permalink]
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16 Aug 2010, 03:42
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x = No of chickens; n= No of days xn=(x75)(n+20)=(x+100)(n15)
Solving we get X = 300!

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Re: chickens  algebra (m08q13) [#permalink]
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17 Jan 2011, 15:55
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Bunuel wrote: # of chickens  x # of days  d
If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned > Amount of feed equals \(xd=(x75)(d+20)\); If he buys 100 more chickens, he will run out of feed 15 days earlier than planned > Amount of feed equals \(xd=(x+100)(d15)\).
\((x75)(d+20)=(x+100)(d15)\) > \(\frac{d+20}{d15}=\frac{x+100}{x75}\) > \(x=5d\)
Hi I got a question, why are you supposed to multiply no.chickens x no.of days ? xd ? hope someone can explain this, many thanks

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Re: chickens  algebra (m08q13) [#permalink]
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07 Jun 2011, 07:57
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Can be solved under 3 mins.You don't really have to solve quadratic equations:
Chickens=x Feed=f No of days feed lasts= x/f
Eq 1) f/(x75)=f/x + 20 =>f=(4/15)x(x75) Eq 2) f/(x+100) = f/x 15 => f = (3/20)x(x+100)
Can someone explain how you get from f/(x75)=f/x + 20 to f=(4/15)x(x75) ?

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Re: chickens  algebra (m08q13) [#permalink]
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07 Jun 2011, 11:24
brc310 wrote: Can be solved under 3 mins.You don't really have to solve quadratic equations:
Chickens=x Feed=f No of days feed lasts= x/f
Eq 1) f/(x75)=f/x + 20 =>f=(4/15)x(x75) Eq 2) f/(x+100) = f/x 15 => f = (3/20)x(x+100)
Can someone explain how you get from f/(x75)=f/x + 20 to f=(4/15)x(x75) ? bmwhype2, here you go 1. f/(x75)=f/x + 20 2. f/(x75)  f/x = 20 3. f(x  (x75)) = 20(x)(x75) 4. f(75) = 20(x)(x75) 5. f= (4/15)x(x75) I think the key to solving this question under 3 minutes is to realize that we should consider 'feed' and 'chickens' as variables and not 'days' and 'chickens'. With the later, we would end up with quadratics. The problem is that this (considering feed and not days) need not always strike us and this is what separates the highscorers from the lowscorers!

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Re: chickens  algebra (m08q13) [#permalink]
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07 Jun 2011, 11:37
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bmwhype2 wrote: If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. how many chickens does he have? (A) 60 (B) 120 (C) 240 (D) 275 (E) 300 Source: GMAT Club Tests  hardest GMAT questions I like this post by VeritasPrepKarishma: the food 75 chicken consumed in d days will last 20 days if consumed by (c  75) chickens So 75d = (c  75)20 ..... (I) What c chickens consumed in 15 days, 100 chickens will consume in (d  15) days 15c = 100(d  15) ......(II) Solve I and II to get c = 300 Original Post: feedingthechickens85752.html#p828191
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Re: chickens  algebra (m08q13) [#permalink]
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07 Jun 2011, 19:31
would this be considered a rate problem/word problem?
> i don't know how to put together the equations needed

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Re: chickens  algebra (m08q13) [#permalink]
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07 Jun 2011, 21:06
From the given condition we get two equations let 'x' be number of chickens and y be number of days (x75)*(y+20)=x*y(1) similarly (100+x)*(y15)=x*y(2)
simplifying we get 4x15y=300(i) and 3x20y=300(ii)
solving both simultaneous eqns we get ie (i) and (ii) x=300 and y=60 Hence number of chickens is 300

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Re: chickens  algebra (m08q13) [#permalink]
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07 Jun 2011, 23:37
\(f/(x75)=f/x + 20\) \(f/(x75) f/x = 20\) \(f(1/(x75)  1/x) = 20\) \(f((xx+75)/(x(x75))) = 20\) \(f=(20/75)x(x75)\) \(f=(4/15)x(x75)\) HTH

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Re: chickens  algebra (m08q13) [#permalink]
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11 Feb 2012, 16:47
Bunuel wrote: If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. how many chickens does he have?
(A) 60 (B) 120 (C) 240 (D) 275 (E) 300
This question was posted in PS forum as well. Here is my solution from this forum:
# of chickens  x # of days  d
If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned > Amount of feed equals \(xd=(x75)(d+20)\); If he buys 100 more chickens, he will run out of feed 15 days earlier than planned > Amount of feed equals \(xd=(x+100)(d15)\).
\((x75)(d+20)=(x+100)(d15)\) > \(\frac{d+20}{d15}=\frac{x+100}{x75}\) > \(x=5d\)
\(xd=(x75)(d+20)\) > \(5d^2=(5d75)(d+20)\) > \(d^2=(d15)(d+20)\) > \(d=60\) > \(x=5d=300\).
Answer: E (300)
Hope it helps. Can someone please explain why do you mulitply xd? "amount of feed" = "number of chicken" X "number of days" I don't see the logic. Also is there a shortcut to go from the fraction to x=5d ? \(\frac{d+20}{d15}=\frac{x+100}{x75}\) > \(x=5d\)

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Re: chickens  algebra (m08q13) [#permalink]
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22 Feb 2012, 14:41
SO... I'm not sure how to solve this & I'm still not able to follow the solution that others have posted...
I'm sure there has to be a simpler and smarter way to do this... But Here's how far I was able to get... Please tell me what I did wrong!!! Thanks
If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. how many chickens does he have?
(A) 60 (B) 120 (C) 240 (D) 275 (E) 300
c = Original # of chicken d = # of days of feed
If Sold 75 chicken > 20 more days than planned d/(c75) = (d/c) + 20 > Solve for (d/c) = d/(c75)  20 (1)
If Bought 100 chicken > 15 fewer days than planned d / (c+100) = (d / c)  15 > Solve for (d/c) = d/(c+100) + 15 (2)
Set (1) = (2) d/(c75)  20 = d/(c+100) + 15
d/(c75)  d/(c+100) = 15 + 20
d [1/(c75)  1/(c+100)] = 35
1/(c75)  1/(c+100) = 35/d
Cross multiple... (c+100)(c75) / (c75)(c+100) = 35/d
(175 / c^2+25c+7500) = 35/d
(175d/35) = c^2+25c+7500
5d = c^2+25c+7500.........
Not sure where to go from here... TOTALLY STUCK!!!

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Re: chickens  algebra (m08q13)
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