Paper can be purchased for $10 per pack of 500, $3 per pack of 200 and

Question

Paper can be purchased for $10 per pack of 500, $3 per pack of 200 and $0.30 per 10 sheets. If one needs to purchase exactly 5640 sheets of paper, what the lowest possible price one must pay?

A. $119.20
B. $114.20
C. $110.20
D. $85.20
E. $56.20

GMATinsight · Answer

$10 per pack of 500 i.e Price of 1 sheet of paper = 10*100/500 = 2 cents

$3 per pack of 200 i.e Price of 1 sheet of paper = 3*100/200 = 1.5 cents

$0.3 per pack of 10 i.e Price of 1 sheet of paper = 0.3*100/10 = 3 cents

Cheapest paper is purchased when pack of 200 is bought @$3 per pack

Total Sheets to be purchased = 5640

i.e. Pack of 200 in 5640 sheets = 28 packs and 4 sheets left

Price of 28 packs of 200 sheets each pack = 28*$3 = $84

Price of 40 sheets @$0.3 per 10 sheets = 0.3*4 = $1.2

Total Price of 5640 sheets = $84+$1.2 = $85.2

Answer: option D

JeffTargetTestPrep · Answer

Let’s calculate the unit (per sheet) cost of each option:

Packs of 500: unit cost = $10/500 = $0.02

Packs of 200: unit cost = $3/200 = $0.015

Single sheets: unit cost = $0.30/10 = $0.03

We see that the greatest savings occurs with packs of 200, then packs of 500, and, finally, single sheets.

Thus, to maximize savings, we should buy as many packs of 200 as possible. Since 5640/200 = 28.2, we can buy 28 packs of 200, which will cost us:

$3 x 28 = $84

So now we have 5640 - (28 x 200) = 40 sheets left. For these 40 sheets, we must buy them as single sheets, and they will cost us:

$0.03 x 40 = $1.20

Thus, the lowest possible price we have to pay is $84 + $1.20 = $85.20.
 
Answer: D

giovannisumano · Answer

I think one of the easiest ways to know which package has the lower cost by sheet is to find a common denominator and then compare the numerators, it is visually easy to see that 1000 can be a common denominator among the options, so

\frac{10(2)}{500(2)} vs \frac{3(5)}{200(5)} vs \frac{.3(100)}{10(100)} = \frac{20}{1000} vs \frac{15}{1000} vs \frac{30}{1000}

now you can see that the package of 200 sheets has the best price per sheet followed by the package of 500 sheets and the package of 10 sheets, and you can proceed answering the question

Paper can be purchased for $10 per pack of 500, $3 per pack of 200 and

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Paper can be purchased for $10 per pack of 500, $3 per pack of 200 and

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