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Math Expert V
Joined: 02 Sep 2009
Posts: 58454

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14 00:00

Difficulty:   75% (hard)

Question Stats: 58% (02:12) correct 42% (02:19) wrong based on 272 sessions

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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% of the cost of those returned, or $96, was reimbursed, how much money was spent on illuminating the gym? A.$160
B. $320 C.$360
D. $372 E.$384

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Math Expert V
Joined: 02 Sep 2009
Posts: 58454

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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% of the cost of those returned, 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 $$320*1 + 160*1*(100\% - 60\%) = 320 + 64 = 384$$.

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Manager  Joined: 14 Jul 2014
Posts: 88

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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 $$320*1 + 160*1*(100\% - 60\%) = 320 + 64 = 384$$.

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
Math Expert V
Joined: 02 Sep 2009
Posts: 58454

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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 $$320*1 + 160*1*(100\% - 60\%) = 320 + 64 = 384$$.

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. _________________ Manager  Joined: 14 Jul 2014 Posts: 88 Re: M02-37 [#permalink] Show Tags 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
Intern  Joined: 22 Apr 2015
Posts: 11
GMAT 1: 760 Q50 V44 Show Tags

1
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,
Intern  B
Joined: 09 Feb 2015
Posts: 20

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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$=> Spending cost: 480 - 96 (refund) = 384$.
Intern  Joined: 28 Oct 2015
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Can anyone please explain how the cost of one bulb has been calculated?
SVP  V
Joined: 26 Mar 2013
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Can anyone please explain how the cost of one bulb has been calculated?

Let's take it step by step.

Consider the Quantity of bulbs =X

2/3 of bulb used, it means 1/3 of the bulb left unused.

We have been told that left = 16, then............. (1/3)(X)= 160.........> X=480

It means 320 bulb used in gym

Now let's find price/bulb

consider cost/bulb= C

We have told that '60% of the COST of LEFT unused bulbs' have been returned, which equals to $96. Cost of left unused bulbs= 160C 60% of Cost of left unused bulbs = 0.6 * 160 C=$96

96C =96........... means C = $1 Total cost of bulbs ONLY used for gym =$320

However, there is still 40% of cost LEFT bulbs = $64 which not returned and incurred in total cost. Total cost= 320 + 64=$384

Intern  S
Joined: 20 Feb 2016
Posts: 6
Location: United States

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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
Current Student B
Joined: 28 Dec 2016
Posts: 88
Location: United States (IL)
Concentration: Marketing, General Management
Schools: Johnson '20 (M)
GMAT 1: 700 Q47 V38 Show Tags

I still understood the question correctly. For 'verbal-oriented' folks, I can understand how 'their' can hinder their understanding.
Maybe if we can say "60% of their cost" -> "60% of the cost" it helps them?
Manager  B
Joined: 17 Mar 2017
Posts: 55
Location: India
Concentration: Sustainability, Social Entrepreneurship
WE: Information Technology (Consulting)

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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.
Intern  B
Joined: 12 Aug 2017
Posts: 6

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An amazing question! Love that you have kept 320 as answer choice. I fell for the trap by calculating the cost of light bulbs that were used only. I forgot to factor in the 40% loss made during the refund process.  Re: M02-37   [#permalink] 25 Jun 2018, 11:39
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