Bunuel
The price per pair of brand X socks is $2 and the price per pair of brand Y socks is $3. If there is no sales tax and a customer chooses only from among these two brands, what is the greatest number of pairs of socks that he can buy with exactly $25?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 20
Let the number of brand X socks be x and number of brand Y socks be y
From the question stem, we have the following equation : 2x + 3y = 25 -> (1)
If Option E(20) is the greatest pair of socks he can buy, x + y = 20
This can be re-written as y = 20 - x. Using this in equation (1), 2x + 3(20 - x) = 25 -> x = 35(Not possible)
If Option E(12) is the greatest pair of socks he can buy, x + y = 12 -
This can be re-written as y = 12 - x. Using this in equation (1), 2x + 3(12 - x) = 25 -> x = 11(Possible)
Therefore, 12(Option D) is the greatest number of pairs of socks that he can buy with exactly $25.