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The price per pair of brand X socks is $2 and the price per pair of br

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The price per pair of brand X socks is $2 and the price per pair of br  [#permalink]

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New post 27 Jun 2018, 21:38
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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

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Re: The price per pair of brand X socks is $2 and the price per pair of br  [#permalink]

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New post 27 Jun 2018, 23:59

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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Re: The price per pair of brand X socks is $2 and the price per pair of br  [#permalink]

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New post 01 Jul 2018, 00:19
x2+y3=25

tryin different values we get max in case of x=11 , y = 1
so 12 pairs
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Re: The price per pair of brand X socks is $2 and the price per pair of br  [#permalink]

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New post 01 Jul 2018, 08:16
Bunuel wrote:
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.
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Re: The price per pair of brand X socks is $2 and the price per pair of br  [#permalink]

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New post 02 Jul 2018, 09:47
Bunuel wrote:
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


The greatest number of pairs can be purchased at the cheaper price. Since 25/2 = 12 remainder 1, the greatest number of pairs that can be purchased is 12. Or he can buy 11 pairs of the brand X socks and 1 pair of brand Y socks, which also result in a total of 12 pair of socks.

Note that the problem doesn’t specify that all $25 must be spent, so either approach to the solution is correct.

Answer: D
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Re: The price per pair of brand X socks is $2 and the price per pair of br  [#permalink]

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New post 02 Jul 2018, 12:01
Bunuel wrote:
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


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)
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Re: The price per pair of brand X socks is $2 and the price per pair of br &nbs [#permalink] 02 Jul 2018, 12:01
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