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What is the maximum number of sheep that Ruben's pen will [#permalink]
 02 Aug 2011, 20:54
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What is the maximum number of sheep that Ruben's pen will hold? 1. If 8 sheep are removed from the pen when it is 2/3 full, the number of sheep in the pen will decrease by 1/4. 2. Currently, there are 12 sheep in the pen. Please help solve this problem.
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Let the maximum capacity of pen = x and the number of sheep present as of now = 'y'.
so you cannot directly solve for 'x' & hence '1' is not sufficient. However, you will get following equation:
2/3(x) - 8 = y - 1/4(y) = 3/4(y)
Statement (2) alone is not sufficient (obviously).
Now, together the equations seem to be sufficient, but let us just solve the equations:
2/3(x) - 8 = 3/4(12) = 9, giving x = 25.5. We cannot have 25.5 sheep (sheep could be either 25 or 26), hence I will answer 'E'.
Any comments, anyone?
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The answer is (A). Using statement (1): If 8 sheep are removed from the pen when it is 2/3 full, the number of sheep in the pen will decrease by 1/4. Let the capacity of the pen be 'a' and the number of sheep currently in the pen be 'b'. Then (2/3)*a - 8 = b - (b/4) and b = (2/3)*a Solving these equations simultaneously gives us: a = 48 and b=32. Sufficient. Using statement (2): Just knowing the number of sheep currently in the pen is insufficient to tell us the capacity of the pen. Insufficient. Therefore (A) it is.
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Last edited by GyanOne on 03 Aug 2011, 02:01, edited 1 time in total.
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Asher wrote: What is the maximum number of sheep that Ruben's pen will hold?
1. If 8 sheep are removed from the pen when it is 2/3 full, the number of sheep in the pen will decrease by 1/4.
2. Currently, there are 12 sheep in the pen.
Please help solve this problem. 1. Let "x" be the number of sheep when the pen is full. \frac{1}{4}*\frac{2}{3}*x=8x=48Sufficient. Ans: "A"
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Gyanone, fluke, could you please explain in detail. I am not able to follow the explanation.
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Gyanone, please suggest on following:
.....................................
Let the capacity of the pen be 'a' and the number of sheep currently in the pen be 'b'.
Then (2/3)*a - 8 = b - (b/4)
and x = (2/3)*y ???
Solving these equations simultaneously gives us:
a = 48 and b=32. Sufficient.
.....................................
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@ fluke:
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Let "x" be the number of sheep when the pen is full.
\frac{1}{4}*\frac{2}{3}*x=8
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How could you arrive at equation in 1 variable? The stem says "the number of sheep in the pen will decrease by 1/4". We don't know how many sheep are in the pen (it does not say that the max. capacity of the pen will decrease by 1/4)? Both statements are different. So, you have to have two variables.
I might not be capturing something. Please help me understand. Thanks in advance!
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Also, to add on, 48 does not satisfy the stem "If 8 sheep are removed from the pen when it is 2/3 full, the number of sheep in the pen will decrease by 1/4. "
2/3x-8 gives = 24
and decrease by 1/4 gives 36
IMO, answer should be 'E'.
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puneet478 wrote: Gyanone, fluke, could you please explain in detail. I am not able to follow the explanation. 1. If 8 sheep are removed from the pen when it is 2/3 full, the number of sheep in the pen will decrease by 1/4. Let's take it one by one: If 8 sheep are removed from the pen when the pen is 2/3 full. (2/3)x-> This is 2/3 full because "x" is the number of sheep when the pen is full We got to remove 8 sheep from it (2/3)x-8 The number of sheep in the pen is decreased by 1/4. This statement means: If there were 100 sheep in the pen, it decreases by 25. If there were 20 sheep in the pen, it decreases by 5. So, (2/3)x-8=(2/3)x-(1/4)(2/3)x Or in other words: (1/4)(2/3)x=8. Because, you removed 8 sheep and the number decreased by (1/4)(2/3)x Thus, we know x, which is the total capacity. The question asks us to find just that.
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@ fluke...
(2/3)x-8=(2/3)x-(1/4)(2/3)x, how did you arrive at part highlighted in boldface?
Stem says number of sheep (in the pen at that particular time) decreases to 1/4. How can we assume that it was 2/3x at that time? We simply do not know!
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puneet478, apologies - my second statement was supposed to be: b = (2/3)*a (edited now in the original solution). This is valid because statement (1) says: If 8 sheep are removed from the pen when it is 2/3 full, the number of sheep in the pen will decrease by 1/4. Note the highlighted part. This means that the pen is 2/3 full when we remove the 8 sheep from it. This means the number of sheep currently in the pen is 2/3 of the pen's capacity. => b = (2/3)*a You can (rather must) take the number of sheep currently in the pen to be 2/3 of the pen's capacity because that is exactly what statement (1) says. Happy to explain further if you still have doubts.
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what i understand is that: 2/3x = total no. of sheep in the pen (assuming that sheep is the only animal in the pen) Am i right? 
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Yes, assuming the x in your post is the capacity of the pen.
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@gyanone, I think you & fluke are right. I was thinking on different lines. Thanks for the clarifications.
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Ans is A.
from option 1.
lets assume max numer of sheeps = x
so current no of sheeps = 2/3 x
now by reducing it by number 8 the total number of sheep reduces by 1/4 .
that means it reduces by 2/3 x * 1/4
now we can put this in equation
2/3 x * 1/4 = 8
and we can find the value of X
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thanks fluke and GyanOne.. very detailed and clear explanation.. +1
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