A Farm has Chickens, Cows and Sheep. The Number of Chickens and Cows Combined is 3 Times the Number of Sheep.

Question: A farm has chickens, cows and sheep. The number of chickens and cows combined is 3 times the number of sheep. If there are more cows than chickens or sheep, and together, cows and chickens have a total of 100 feet and heads, how many sheep live at the farm?

1. 5
2. 8
3. 10
4. 14
5. 17

“A farm has chickens, cows and sheep. The number of chickens and cows combined is 3 times the number of sheep. If there are more cows than chickens or sheep, and together, cows and chickens have a total of 100 feet and heads, how many sheep live at the farm?” – This topic is a part of GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "Manhattan Prep's "GMAT Foundations of Math, 5th Edition"" published in the year 2007. GMAT Quant section consists a total of 31 questions. This is a GMAT Problem Solving question that allows the candidates to select the correct answer from the five answer choices provided. The total time allotted for this part is 62 minutes which allows the candidate 2 minutes to answer each question.

Answer:

Let us assume that

Number of chickens = C

Number of cows = W

Number of sheep = S

According to the question, it is given that:

Chickens and cows together have 100 feet and heads

This means:

100 = 1C + 1W+ 4W + 2C

In this we assumed that:

1 is the number of heads per either unit and 4 and 2 are number of legs per C and W accordingly.

Therefore, solving the above expression:

100 = 3C + 5W

In the question, it is given that W > C and we can also see that C should be a multiple of 5 for 3C + 5W to add up to 100. Picking up few numbers, we get two pairs: (5, 17) and (10, 14).

Therefore, S = (C + W)/3; 5 + 17 = 22 which is not divisible by 3, but 10 + 14 = 24 which is divisible by 3

Therefore, only 2\(^{nd}\) pair will work.

So, S = 8

Correct option: B

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