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M02-37

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Bunuel
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M02-37 [#permalink] New post   16 Sep 2014, 00:19
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Question Stats:

60% (02:14) correct 40% (02:17) wrong based on 963 sessions
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A gym purchased a certain number of light bulbs to illuminate the space but it turned out that only 2/3 of the bulbs were needed, so 160 bulbs were returned. If the returned light bulbs were reimbursed at 60% of their cost, resulting in a reimbursement of $96, what was the total amount of money spent on lighting the gym?

A. $160
B. $320
C. $360
D. $372
E. $384
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E
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Bunuel
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Re M02-37 [#permalink] New post   16 Sep 2014, 00:19
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Official Solution:

A gym purchased a certain number of light bulbs to illuminate the space but it turned out that only 2/3 of the bulbs were needed, so 160 bulbs were returned. If the returned light bulbs were reimbursed at 60% of their cost, resulting in a reimbursement of $96, what was the total amount of money spent on lighting the gym?

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


Assume the cost of one light bulb to be \($x\). Since \($96\) is 60% of the cost of 160 light bulbs, then the full cost of 160 bulbs can be determined by solving the equation \(160*x*0.6=96\), which gives \(x=$1\)

Next, since only 2/3 of the light bulbs were kept, 160 bulbs that were returned constitute 1/3 of the initial order. Therefore, the total number of bulbs purchased was 480. The initial cost of the order would be \($480\). However, \($96\) was reimbursed for the returned bulbs, resulting in a final cost of the order equal to \(480 - 96=$384\).


Answer: E
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Bunuel
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Re: M02-37 [#permalink] New post   18 Feb 2015, 04:12
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buddyisraelgmat wrote:
Bunuel wrote:
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.
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buddyisraelgmat
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Re: M02-37 [#permalink] New post   18 Feb 2015, 03:59
Bunuel wrote:
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
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buddyisraelgmat
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Re: M02-37 [#permalink] New post   18 Feb 2015, 04:21
Bunuel wrote:
buddyisraelgmat wrote:
Bunuel wrote:
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.



Ok Got it !

The highlighted part in yellow confused me initially - but now its clear - cool problem

Thanks
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Re: M02-37 [#permalink] New post   30 Apr 2015, 06:39
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Instead of that last step of finding the cost of the used bulbs and then adding the cost of the un-reimbursed sum to the total, I saved a bunch of time by just taking the total cost of the bulbs ($480) and subtracting how much was reimbursed ($96 and no math needed, since it was included in the question).

Cheers,
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Mrtinhnv
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Re: M02-37 [#permalink] New post   18 May 2015, 08:05
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Find cost of a bulb: 160*0.6*P = 96 => P=1.
Number of bulb: 1/3*X = 160 => X = 480
Total cost: 480*1 = 480$
=> Spending cost: 480 - 96 (refund) = 384$.
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Re: M02-37 [#permalink] New post   21 Sep 2016, 22:51
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60% of 160 bulbs =96
total cost of 160 bulbs = 96+160*(40/100)=96+64=160 =>1 bulb=1 rupee
Total number of bulbs= X
total cost => X*1=2/3X*1+160*1=>X=480
96 was reimbursed so 480-96 =384
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acacia
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Re: M02-37 [#permalink] New post   03 Sep 2017, 11:32
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I was able to find the cost of each bulb to be $1 using this - 60% of C =$96 , so Cost per bulb= $1

Next since there are a total of 480 bulbs purchased ( 1/3 * X = 160 , X=480) so total cost is $480.

Since they got a reimbursement of $96 , HENCE THE TOTAL COST TO LIGHT UP THE ROOM IS = 480- 96= $384.
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Everlasting32
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Re: M02-37 [#permalink] New post   11 Sep 2020, 20:36
I think this is a high-quality question and I agree with explanation.
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Bunuel
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Re: M02-37 [#permalink] New post   24 Feb 2023, 11:18
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M02-37 [#permalink] New post   15 Mar 2023, 01:22
it did take me 3 minutes to solve this, the reason is I saw that it is a 700 level question and as I was solving it I couldn't believe it's that simple and started looking for tricks. I'm a bit too cautious and I think that is stopping me from reaching my potential :(.

otherwise, really nice question with a simple easy trick.


1/3T = 160
T = 480
__________

3/5(cost)(160) -> returned, which equal to 96.
3/5(160) = 96
cost of each bulb = 1

total cost = 480
total cost after the refund = 480-96.
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Re: M02-37 [#permalink]
15 Mar 2023, 01:22
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