A number of light bulbs were purchased to illuminate a gym. However

Question

A number of light bulbs were purchased to illuminate a gym. However, only  
ormal\frac{2}{3}  of them were needed. The extra 160 light bulbs were returned. 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

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

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

walker · Answer

C x - money that was spent on illuminating the gym. (x+96)*\frac13*\frac{60}{100}=96 x=5*96-96=4*96=384 I think it is easy-medium level. But maybe I have wrong answer?

neeraj.kaushal · Answer

Answer is B

Extra bulbs 1/3 T = 160
 Total bulbs T=480
 (60/100) xcost of extra bulbs = 96

cost of extra bulbs=160
 cost of each bulb = 1
 cost of required bulbs=320

walker · Answer

I think we have to add losses 0.4*160=64
320+64=384.

jvaidya · Answer

A number of light bulbs were purchased to illuminate a gym. However, only of them were needed. The extra 160 light bulbs were returned. 60% percent of their cost, or $96, was reimbursed. How much money was spent on illuminating the gym?

(A) 360
(B) 320
(C) 384
(D) 364
(E) 160

Ans: C

Let Total Bulbs be X
1/3X=160 => X=480(Total)

Also,
Let Z=Price of 1 bulb
160*60*z/100=96
=>z=1(1 bulb price)

Thus Price Paid for illuminating gym= 480(Total Cost)-96(Refund)
=384 (C)

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mourinhogmat1 · Answer

I don't think the problem is tricky but I found the wording confusing. So, I interpreted the problem wrongly. One doubt : Does the reimbursement refer to the money for unused bulbs or the money used for the entire stock?

It has a sentence correction error: "Their" has no clear referent. :lol:

Narenn · Answer

Solve while reading...
 
A number of light bulbs were purchased to illuminate a gym. --------> say x

However, only  
ormal\frac{2}{3}  of them were needed. ------->  \frac{2}{3}x  used ------> means  \frac{1}{3}x  extra.

The extra 160 light bulbs ------>  \frac{1}{3}x =160 therefore x = 480 = total number of bulbs

Extra 160 bulbs Returned 60% percent of their cost, or $96, was reimbursed. ------> 0.6 X 160 X Rate = 96 --------> Rate = 1

How much money was spent on illuminating the gym? --------> Used Bulbs + 40% of unused bulbs --------> 320 + 0.40 X 160 -------> 384 = C

VeritasPrepRon · Answer

This question highlights one of the most important aspects of the GMAT: Correctly interpreting the question. If you consider that only 320 bulbs were used to light the gym, and each was 1$, then it's very easy to pick 320$ here. However the question asks how much money was spent on illuminating the gym, which includes waste since that money was spent and not recuperated. Sometimes students tell me: "I don't think this question is clear". Unfortunately, no one is there on exam day to help clarify the issue for you, so you have to figure out the intent of the question on your own. Practice will help a lot, but the stress of answering questions in ~2 minutes as well as tricky wording will always leave room for misinterpretation and missed points on this test.

I highly recommend rereading the question for 10-15 seconds before clicking on submit, particularly for Problem Solving questions in math. Whatever the right answer to the question is, you can bet there will also be the right answer to a misinterpreted question among the choices.

Hope this helps!
-Ron

I highly recommend rereading the question for 10-15 seconds before clicking on submit, particularly for Problem Solving questions in math. Whatever the right answer to the question is, you can bet there will also be the right answer to a misinterpreted question among the choices.

Hope this helps!
-Ron

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