M02-37

Question

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

Show Answer

Official Answer

E

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

Bunuel · Accepted Answer

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

Show Answer

Official Answer

E

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

Bunuel · Answer

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.

buddyisraelgmat · Answer

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

buddyisraelgmat · Answer

Ok Got it !

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

Thanks

bsattin1 · Answer

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,

Cheers,

Mrtinhnv · Answer

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$.

SB0512 · Answer

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

acacia · Answer

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.

Everlasting32 · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

joe123x · Answer

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.

Rance14 · Answer

2/3 of the bulbs were kept and 1/3 were returned

total number of returned bulbs = 160

hence the total number of bulbs = 480

they got only 60% of what they had paid for the bulb

hence if 60% -> 96
 10% -> 16
 100% -> 160

so they had originally paid a total of $160 for 160 bulbs, i.e. $1 per bulb

hence, they had paid $480 for all the bulbs

they got $96 back after reimbursement of 160 bulbs

so net total they spent = $480-$96 = $384

vn049636 · Answer

I think this is a  high-quality  question and I agree with explanation.

JSamp · Answer

I think this is a  poor-quality  question and I don't agree with the explanation. Maybe the wording is wrong, but the correct answer should be TOTAL Purchase quantity * Cost (540) - Returned quantity * 0.6 * Cost (96)

bb · Answer

How did you get 540? Did you multiply 180 by 3 instead of 160 by 3?

juanferloayza · Answer

This is a great question that’s helpful for learning and I like the solution - it’s helpful.

juanferloayza · Answer

This is a great question that’s helpful for learning and I like the solution - it’s helpful. Somehow I find easy this supposedly hard question. Instead, I find hard some supposedly easy numbers questions.

idlch · Answer

I like the solution - it’s helpful.

bomensah · Answer

I like the solution - it’s helpful.

M02-37

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