M02-37

Official Solution:

A number of light bulbs were purchased to illuminate a gym. However, only \(\frac{2}{3}\) of them were needed and 160 leftover light bulbs were returned. If only 60% percent of their cost, or $96, was reimbursed, how much money was spent on illuminating the gym?

A. $160
B. $320
C. $360
D. $372
E. $384


First find the cost of a single light bulb, which is \(\frac{\frac{96}{160}}{60\%}=\frac{6}{10}*\frac{10}{6}=$1\), because only 60% of the cost was reimbursed.

Next find the number of light bulbs that were purchased: \(\frac{160}{1-\frac{2}{3}} = \frac{160}{\frac{1}{3}} = 160*3 = 480\). The number of bulbs that were used is equal to \(480*\frac{2}{3} = 320\). Multiply that number by the cost of a light bulb and add the money which was not reimbursed to find the answer, which is \(320*1 + 160*1*(100\% - 60\%) = 320 + 64 = $384\).


Answer: E

Hi Bunuel

I find the wordings bit confusing

1) If only 60% percent of their cost, or $96, was reimbursed,

So, basically 96 = 60% of Total cost
which gives us Total cost = 160

2) Now 160 was the cost for 480 bulbs ,

hence money was spent on illuminating the gym i.e. 320 bulbs = (160 * 320 ) / 480 = 320 / 3 = ~ $ 106

Where am I going wrong ???

Thanks

480 light bulbs purchased.
320 light bulbs used.
160 light bulbs returned. 60% percent of the cost of those 160, or $96, was reimbursed. Thus the cost of 160 light bulbs is $160 out of which 60%, or $96 were reimbursed and the remaining $64 were NOT reimbursed.

The cost of 320 light bulbs is $320, plus $64 that were NOT reimbursed = $384.