The East-17 pre-school is upgrading all of his classrooms by buying 46

Question

The East-17 pre-school is upgrading all of his classrooms by buying 46 computers, 6 printers and 5 fax machines. If a computer costs 4 times more than a printer and 2 times more than the fax machine, what percent of the cost of the entire purchase was the cost of one computer, 2 printers and 1 fax machine?

A. 1%.
B. 2%.
C. 3%.
D. 4%.
E. 5%.

A. 1%.
B. 2%.
C. 3%.
D. 4%.
E. 5%.

Abhishekgmat87 · Answer

Let price of 1 computer be c, one printer be p and 1 fax machine be f
We have to find  \frac{c+2p+f}{46c+6p+5f}  * 100

c = 4p = 2f So, f =2p
 \frac{c+2p+f}{46c+6p+5f}  =  \frac{4p+2p+2p}{ 184p+6p+10p}  = 4 %

Option D

rashminuligonda · Answer

when it is written more than, shouldnt it be 1C=5P=3F?

IF hats not the case, whats the diff btween 4 times as printer vs 4 times more than printer?

MarkGMATMentor · Answer

This problem gives us only relative, not concrete values, and asks for a percentage. In such cases, it's often helpful to pick 100 in order to simplify calculations.

Since 46 computers, 6 printers, and 5 fax machines represent the entire purchase (100%),  set their sum equal to 100: 
46c + 6p + 5f = 100

Then, since a computer costs 4 times as much as a printer and twice as much as a fax machine:
c = 4p = 2f

Now, pick one of the variables to convert the others in terms of. Choose whichever seems easiest. If we choose f, then we also know that:
p = f/2

Then replace c and p with f:
46(2f) + 6(f/2) + 5f = 100
92f + 3f + 5f = 100
100f = 100
f = 1

The question asks for the percentage of the entire cost represented by c + 2p + f. This is equivalent to:
2f + f + f = 4f = 4(1) = 4

Since you chose 100 as the total cost, the answer is simply 4/100 or 4%.  Choice D is correct.

On percent problems with no concrete values, picking 100 can make the problem easier to visualize and calculate.

Nick3105 · Answer

My solution path is probably not the most conventional as I directly converted the computers and fax machines in printers. As the total costs are given as 100% and not a defined as a specific total amount, the actual price of a printer doesen't matter.

Thus follows:

Total purchase: (46 * 4) + 6 + (5 * 2) = 184 + 10 + 6 = 200

Portion of the purchase: (1 * 4) + 2 + (1 * 2) = 8

=> 8/200 = 4/100 = 4%

Maybe it's not the most conventional solution path but it shows, that intuition can often lead to correct answers too (and in this case also in way under 2 minutes).

The East-17 pre-school is upgrading all of his classrooms by buying 46

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