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EQUATIONS + AVERAGE

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by candela.tartiere » Tue Feb 26, 2013 3:52 am
Fabio bought several pairs of socks, some woolen and the others cotton. The price of the each pair of woolen socks was $3 higher than the price of each pair of cotton socks. What was the average price of the pairs of socks that Fabio bought?

(1) He bought three times as many pairs of cotton socks as woolen socks.
(2) He spent twice as much money on cotton socks as he did on woolen socks.
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Source: — Data Sufficiency |

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by Anurag@Gurome » Tue Feb 26, 2013 4:28 am
candela.tartiere wrote:Fabio bought several pairs of socks, some woolen and the others cotton. The price of the each pair of woolen socks was $3 higher than the price of each pair of cotton socks. What was the average price of the pairs of socks that Fabio bought?

(1) He bought three times as many pairs of cotton socks as woolen socks.
(2) He spent twice as much money on cotton socks as he did on woolen socks.
Let us assume, he bough W pairs of woolen socks and C pairs of cotton socks.
And price of each pair of woolen socks and cotton socks are $n and $(n - 3), respectively.

Hence, average price of a pairs of socks = [nW + (n - 3)C]/(W + C)

Statement 1: C = 3W
Hence, average price = [nW + (n - 3)*(3W)]/(W + 3W) = [n + 3*(n - 3)]/4
We don't know the value of n.

Not sufficient

Statement 2: (n - 3)C = 2nW
Hence, average price = [nW + 2nW]/(W + C) = [3nW]/(W + C)

Not sufficient

1 & 2 Together: C = 3W
(n - 3)C = 2nW --> (n - 3)*(3W) = 2nW ---> 3(n - 3) = 2n
We can solve n from the above equation.

Now, average price = 3nW/(4W) = 3n/4

Sufficient

The correct answer is C.
Anurag Mairal, Ph.D., MBA
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