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# What is the maximum number of sheep that Ruben's pen will

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What is the maximum number of sheep that Ruben's pen will [#permalink]  02 Aug 2011, 19:54
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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.

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Re: Knewton DS [#permalink]  02 Aug 2011, 20:08
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'.

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Re: Knewton DS [#permalink]  02 Aug 2011, 20:28
1
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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, 01:01, edited 1 time in total.
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Re: Knewton DS [#permalink]  02 Aug 2011, 21:01
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.

1.
Let "x" be the number of sheep when the pen is full.
$$\frac{1}{4}*\frac{2}{3}*x=8$$
$$x=48$$
Sufficient.

Ans: "A"
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Re: Knewton DS [#permalink]  02 Aug 2011, 22:02
Gyanone, fluke, could you please explain in detail. I am not able to follow the explanation.
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Re: Knewton DS [#permalink]  02 Aug 2011, 22:03
.....................................
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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Re: Knewton DS [#permalink]  02 Aug 2011, 22:07
@ fluke:
--------------------------------------
Let "x" be the number of sheep when the pen is full.
\frac{1}{4}*\frac{2}{3}*x=8
--------------------------------------

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.

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Re: Knewton DS [#permalink]  02 Aug 2011, 22:10
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

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Re: Knewton DS [#permalink]  02 Aug 2011, 22:13
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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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Re: Knewton DS [#permalink]  02 Aug 2011, 22:32
@ 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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Re: Knewton DS [#permalink]  03 Aug 2011, 01:05
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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Re: Knewton DS [#permalink]  03 Aug 2011, 01:20
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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Re: Knewton DS [#permalink]  03 Aug 2011, 03:04
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Yes, assuming the x in your post is the capacity of the pen.
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Re: Knewton DS [#permalink]  03 Aug 2011, 05:36
@gyanone, I think you & fluke are right. I was thinking on different lines. Thanks for the clarifications.
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Re: Knewton DS [#permalink]  03 Aug 2011, 05:53
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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Re: Knewton DS [#permalink]  03 Aug 2011, 07:51
thanks fluke and GyanOne.. very detailed and clear explanation.. +1
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Re: Knewton DS   [#permalink] 03 Aug 2011, 07:51
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