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# Fabio bought several pairs of socks, some woolen and the

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GMAT Instructor
Joined: 04 Jul 2006
Posts: 1266
Followers: 24

Kudos [?]: 167 [0], given: 0

Fabio bought several pairs of socks, some woolen and the [#permalink]  14 Oct 2007, 05:23
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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
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.
VP
Joined: 08 Jun 2005
Posts: 1146
Followers: 6

Kudos [?]: 136 [0], given: 0

Cotton socks price = x
Woolen socks price = x+3

Cotton socks amount = C
Woolen socks amount = W

statement 1

C/3 = W

C = 3W

insufficient

statement 2

Cx/2 = W(x+3)

Cx = 2Wx+6W

insufficient

both statements

C = 3W
Cx = 2Wx+6W

3Wx = 2Wx+6W

Wx = 6W

x = 6

6C/2 = W(6+3)

3C = 9W

C = 3W

sufficient

Director
Joined: 03 May 2007
Posts: 888
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 73 [0], given: 7

price of cotton socks = x
price of woolen socks = x+3

1: number of woolen socks = n
number of cotton socks = 3n

so total exp = n(x+3) + 3n(x) = 4nx + 3n
avg price of the pair of the socks = (4nx + 3n)/(4n) = (4x+3)/4..nsf

2: total purchase price of woolen = w
total purchase price of cotton = c

total purchase price of cotton = 2 (total purchase price of woolen)
c = 2w

so no relation between c and w....

from 1 and 2:

c = 2w
x (3n) = 2 n (x+3)
3x = 2x+6
x = 6

total exp = 4nx + 3n
avg = (4nx + 3n)/(n+3n)
avg = (4x + 3)/4 = (4 * 6 + 3)/4 = 27/4=6.75

C.
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