Solution

Given:

• The price per pair of brand X socks is $2
• The price per pair of brand Y socks is $3
• There is no sales tax
• A customer chooses only from among these two brands

To find:

• The greatest number of pairs of socks that the customer can buy with exactly $25

Approach and Working:
As we are trying to maximise the total number of items, we should try to allocate maximum possible pairs of brand X socks, as it is cheaper than brand Y

• From $25, one can buy 12 pairs of X, but will be left with $1 unused

If 1 pair of X is reduced and 1 pair of Y is added, then

• The total cost = 11 * 2 + 1 * 3 = 22 + 3 = $25
• Therefore, the maximum number of pairs = 11 + 1 = 12

Hence, the correct answer is option D.

Answer: D
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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.
_________________

You've got what it takes, but it will take everything you've got

This is a question of Maximization and minimization...

So, The maximum no of X socks that can be bought is 25/2 = 12 and no y socks.

Further if she buys 11 X socks she can buy 1 y sock, hence, she can buy 12 socks, answer must be (D)
_________________

Thanks and Regards

Abhishek....

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