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Re M0237 [#permalink]
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16 Sep 2014, 00:19
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
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Re: M0237 [#permalink]
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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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Re: M0237 [#permalink]
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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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Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
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Re: M0237 [#permalink]
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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: M0237 [#permalink]
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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 unreimbursed 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 ($96 and no math needed, since it was included in the question).
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Find cost of a bulb: 160*0.6*P = 96 => P=1. Number of bulb: 1/3*X = 160 => X = 480 Total cost: 480*1 = 480$ => Spending cost: 480  96 (refund) = 384$.



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Re: M0237 [#permalink]
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21 Jul 2015, 08:28
The wording of the question are not very clear. This lead to my mistake. I got it now after reading solution.



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Re M0237 [#permalink]
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04 May 2016, 12:50
I think this the explanation isn't clear enough, please elaborate. Can this answer be elaborated?



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Re: M0237 [#permalink]
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04 May 2016, 12:53



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Bunuel wrote: 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 Dear Bunuel, This is good question. However, the wording is confusing. I did not understand what 'their' refer to. Does it refer to 60% of cost of leftover or to total cost of whole bulbs? Thanks



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Re: M0237 [#permalink]
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13 Jun 2016, 03:20
Can anyone please explain how the cost of one bulb has been calculated?



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rmadmit wrote: 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 Answer: E



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rmadmit wrote: Can anyone please explain how the cost of one bulb has been calculated? Thanks for the detailed explanation. Please let me know if this is the equation that is formed  60% of 160C=96? Yes, you are right. I just make it into 2 steps for detailed solution.



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Although I agree with explanation, the wording of the question at best is ambiguous. The "full stop" after "were returned" is doing the damage. I believe the wording of the question can be improved.
"Their cost" doesn't give a clear indication as to what light bulbs is it referring to.



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Re: M0237 [#permalink]
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21 Sep 2016, 22:51
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 48096 =384



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Re: M0237 [#permalink]
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27 May 2017, 15:19
I still understood the question correctly. For 'verbaloriented' 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?



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Re M0237 [#permalink]
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13 Jul 2017, 07:41
I think this is a poorquality question. The wording is very confusing!
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Re: M0237 [#permalink]
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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.










