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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.

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. .....................................

@ 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.

I might not be capturing something. Please help me understand. Thanks in advance!

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. "

(2/3)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!

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. _________________

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