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A number of light bulbs were purchased to illuminate a gym. However, only \(\normal\frac{2}{3}\) 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 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)

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.

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.

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

Total nr of bulbs bought initially - say n Of these bulbs, 2/3 of them were used and hence 1/3 (1-2/3) bulbs were returned to the retailer. This implies that 1/3 (of) n bulbs were returned.

1/3 of n = 160 bulbs ==> n = 480 (Remember n refers to the original nr and 160 refers to the number of bulbs that were returned) Lets determine the nr of bulbs that were used for lighting the gym.

2/3 of (480) = 320 bulbs were used to illuminate the gym.

Ok, now comes the tricky part. As per the question stem - 60% of the their cost was refunded.The trick is to understand identify the antecedent of the pronoun "their"

This interpretation makes sense. Think of if this way, some retailers sell products under the condition that on return, they will NOT refund 100 % of the amount paid by the customer.Instead they will refunded a reduced % - say 70 % of the initial price. This policy is to discourage people from buying large quantities and then return these products for a refund. Back to the question :- When 160 bulbs were returned, the retailer refunded only 60% of the COST of THESE 160 bulbs i.e .6x of (total cost of 160 bulbs that were returned) = $96 total cost of 160 bulbs that were returned = $160 Cost of 1 bulb = $1 Total Cost of lights used to decorate the gym= Cost of the 320 Bulbs that were not returned = 320 x $1 = $320
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A number of light bulbs were purchased to illuminate a gym. However, only \(\normal\frac{2}{3}\) 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 number of light bulbs were purchased to illuminate a gym. --------> say x

However, only \(\normal\frac{2}{3}\) 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
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A number of light bulbs were purchased to illuminate a gym. However, only \(\normal\frac{2}{3}\) 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?

Good one. Tricky question in terms that it is not difficult to solve but just that one needs to be careful in reading the question. I selected B and almost at that instant realized my mistake.

Nice. Need to focus more on the question asked.
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My attempt to capture my B-School Journey in a Blog : tranquilnomadgmat.blogspot.com

The question is not very clear. But since some of you got it correct, I shall not complain. I thought it was B, 320.

B could have been the answer if the question were "How much does it cost to illuminate the gym?" C is the answer to the actual question "How much money was spent on illuminating the gym?"

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

Total nr of bulbs bought initially - say n Of these bulbs, 2/3 of them were used and hence 1/3 (1-2/3) bulbs were returned to the retailer. This implies that 1/3 (of) n bulbs were returned.

1/3 of n = 160 bulbs ==> n = 480 (Remember n refers to the original nr and 160 refers to the number of bulbs that were returned) Lets determine the nr of bulbs that were used for lighting the gym.

2/3 of (480) = 320 bulbs were used to illuminate the gym.

Ok, now comes the tricky part. As per the question stem - 60% of the their cost was refunded.The trick is to understand identify the antecedent of the pronoun "their"

This interpretation makes sense. Think of if this way, some retailers sell products under the condition that on return, they will NOT refund 100 % of the amount paid by the customer.Instead they will refunded a reduced % - say 70 % of the initial price. This policy is to discourage people from buying large quantities and then return these products for a refund. Back to the question :- When 160 bulbs were returned, the retailer refunded only 60% of the COST of THESE 160 bulbs i.e .6x of (total cost of 160 bulbs that were returned) = $96 total cost of 160 bulbs that were returned = $160 Cost of 1 bulb = $1 Total Cost of lights used to decorate the gym= Cost of the 320 Bulbs that were not returned = 320 x $1 = $320

Looks easy question...but made a mistake ...this is the first question of the day that I started solving...

(1/3)x = 160, x= 480, 60 % is $96, so 100 % is 160, $160 are for 160 bulbs, so 1 bulb is for $1. for 480 bulbs $ 480 paid initially. $96 reimbursed. So, spending is $480 - $96 = $384 Hence C is the answer.