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M02-37

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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% 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
[Reveal] Spoiler: OA

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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% 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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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 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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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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: M02-37 [#permalink]

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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]

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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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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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New post 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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New post 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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New post 05 May 2016, 10:11
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?

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New post 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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New post 13 Jun 2016, 04:53
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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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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New post 27 May 2017, 15:19
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?

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New post 13 Jul 2017, 07:41
I think this is a poor-quality question. The wording is very confusing!
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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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Re: M02-37   [#permalink] 03 Sep 2017, 11:32
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