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

Question

Tough and Tricky questions: Word problems.

(1) If  8  sheep are removed from the pen when it is  \frac{2}{3}  full, the number of sheep in the pen will decrease by  \frac{1}{4} .

(2) Currently, there are 12 sheep in the pen.

Kudos for a correct  solution .

DangerPenguin · Answer

statement 1: sufficient
If 8 is 1/4 the # of sheep currently in the pen then there are currently 32 sheep in the pen. Since currently the pen is 2/3 full, then the maximum capacity must be 48.

statement 2: not sufficient
No info on how many his pen will hold.

Answer A!

devmillenium2k · Answer

Statement 1:
From the statement - If 8 sheep are removed from the pen, the number of sheep in the pen will decrease by \frac{1}{4}. 
Let's assume number of sheep in pen is S, than
8 = 1/4 *S => S = 32

Pen is  \frac{2}{3}  full, Let's assume capacity is C, than

2/3 * C = 32 => C = 48

Hence  Sufficient . Options B, C, E out.

Statement 2 :
Currently, there are 12 sheep in the pen
Nothing mentioned about the capacity of pen.

Insufficient .

Answer,  A .

Bunuel · Answer

Official Solution:

What is the maximum number of sheep that Ruben's pen will hold? 
 
The question asks us to find the maximum number of sheep that Ruben's pen can hold.

Statement 1 tells us that if 8 sheep are removed from the pen when it is  \frac{2}{3}  full, then the number of sheep in the pen will decrease by  \frac{1}{4} . This means that 8 is equal to  \frac{1}{4}  of  \frac{2}{3}  of the pen's maximum capacity. Let us call  m  the maximum capacity of Ruben's pen. Then  \frac{2}{3}m  is the number of sheep in a pen that is  \frac{2}{3}  full. Now we set up the equation  8 = \frac{1}{4} 	imes \frac{2}{3}m . (Remember that "of" means multiplication in math problems.) We can solve for the single variable  m  and thus for the maximum capacity of the pen. Statement 1 is sufficient to answer the question. Eliminate answer choices B, C, and E. The correct answer choice is either A or D.

Statement 2 tells us that the pen currently contains 12 sheep. This statement tells us that the pen can hold at least 12 sheep, but it gives us no clues as to what the maximum capacity of the pen is. Statement 2 alone is NOT sufficient to answer the question. Eliminate answer choice D.

Answer  choice A  is correct.

Though we do not need to solve for  m  explicitly, we will for illustration. From statement 1, we have the equation  8 = \frac{1}{4} 	imes \frac{2}{3}m . Multiplying the fractions on the right side together, we get  8 = \frac{2}{12}m = \frac{1}{6}m . Multiplying both sides by 6, we find that  m = 48  is the maximum capacity of Ruben's pen.
 
Answer: A.

bumpbot · Answer

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

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