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A company wants to spend equal amounts of money for the purchase of [#permalink]

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08 Nov 2011, 19:02

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A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $600 and $375 per unit, respectively. What is the fewest number of computer printers that the company can purchase?

Re: A company wants to spend equal amounts of money for the purchase of [#permalink]

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08 Nov 2011, 20:39

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The smallest amount that the company can spend is the LCM of 600 and 375, which is 3000. The fewest number of computers they can purchase is therefore 3000/600 + 3000/375 = 13

Re: A company wants to spend equal amounts of money for the purchase of [#permalink]

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08 Nov 2011, 20:46

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The smallest amount that the company can spend is the LCM of 600 and 375, which is 3000 for each, which is total 6000. The number of 1st type of computers which costing $600 = 3000/600 = 5. The number of 2nd type of computers which costing $375 = 3000/375 = 8.

Total = 5+8 = 13 Answer is A.

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Re: A company wants to spend equal amounts of money for the purchase of [#permalink]

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09 Nov 2011, 05:59

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Another way:

As the total cost of 2 types of printers are same. Hence:

600*a = 375 * b (where a and b are the number of printers of each type). => 8a = 5b . The least value for which it is possible is for a = 5 and b = 8. So total 8+5 = 13

Re: A company wants to spend equal amounts of money for the purchase of [#permalink]

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11 Nov 2011, 15:39

GyanOne wrote:

The smallest amount that the company can spend is the LCM of 600 and 375, which is 3000. The fewest number of computers they can purchase is therefore 3000/600 + 3000/375 = 13

Option (A)

Nice job, didn't think about it

here's how I did it

600a=375b - divide 25 24a=15b -divide by 3 8a= 5b...5+8=13

Re: A company wants to spend equal amounts of money for the purchase of [#permalink]

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11 Nov 2011, 16:18

I found it just as easy to count by 375, until I recognized a number that would be divisible by 600. I knew it would come quick and by easily recognizable.

2 * 375 = 750 double that for 4 * 375 = 1500 double that for 8 * 375 = 3000 which is clearly the first number that is divisible by 600 (5 * 600).

8 @ 375 and 5 @ 600 = 13

Of course all of the previously mentioned solutions worked just as well, and probabaly as fast, but this is what worked best for me.

A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $600 and $375 per unit, respectively. What is the fewest number of computer printers that the company can purchase?

(A) 13 (B) 12 (C) 10 (D) 8 (E) 5

We can let a = the number of $600 printers purchased and b = the number of $365 printers purchased. Since the same number of dollars were spent purchasing each type of printer, we can create the following equation:

600a = 375b

24a = 15b

8a = 5b

In order for 8a to equal 5b, the smallest value of a is 5 and the smallest value of b is 8, and thus the minimum number of printers that can be purchased is 8 + 5 = 13.

Answer: A
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Re: A company wants to spend equal amounts of money for the purchase of [#permalink]

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19 Dec 2017, 17:19

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