George bought a large electronic item with a 15% off coupon, and paid

Question

George bought a large electronic item with a 15% off coupon, and paid a total bill. When he got outside, he studied the receipt and realize that he mistakenly had been given double the discount of the coupon, even though there was no double-coupon offer in effect that day. He went back inside and pointed this mistake out to the manager, offering to make the the difference between what he paid and what he should have paid. The manager was so grateful for George's honesty that he allowed George to pay just half that difference, so George paid him $40.50. What was the original price of the item, before any coupons? Assume that there was no tax at all in this scenario.

A) $135
B) $270
C) $405
D) $540
E) $810

A. $135
B. $270
C. $405
D. $540
E. $810

generis · Answer

Focus on  savings  (rightful and mistaken) from the discount

DID save/ SHOULD HAVE saved

x  = original price
Original discount is 15% off
He SHOULD save  .15x 
Mistaken doubled discount is 30% off
He DID save  .30x

Difference between mistaken and rightful savings 
The difference between what he should have saved and what he did save:
 (.30x - .15x) = .15x

Half that difference is paid back 
George paid back half of that amount:

\frac{.15x}{2} = .075x 
So  .075x  is half the difference of mistaken savings vs rightful savings
Half of the difference of mistaken savings vs. rightful savings also =  $40.50

TOTAL AMOUNT?  From above: 
 .075x = $40.50 
 x = \frac{$40.50}{.075} = \frac{$40,500}{75} = $540

ANSWER D

BrentGMATPrepNow · Answer

George was SUPPOSED to receive a 15% discount, but he received a 30% discount. So, he should have returned 15% of the original cost. However, the manager asked for half that amount (i.e., 7.5% of the original cost) In other words, 7.5% of the original cost = $40.50 IMPORTANT: at this point, we COULD divide $40.50 by 0.075 to determine the original cost. HOWEVER, since the answer choices are quite spread apart , we can apply some logic and estimation to answer the question without resorting to long division. Here's what I mean: 7.5% of the original cost ≈ $40 So, 15% of the original cost ≈ $80 So, 45% of the original cost ≈ $240 So, 90% of the original cost ≈ $480 This means 100% of the original cost (aka the ORIGINAL COST

must be a little more than $480 Answer: D Cheers, Brent

EMPOWERgmatRichC · Answer

Hi All,

We're told that George bought a large electronic item with a 15% off coupon and paid a total bill. When he got outside, he studied the receipt and realize that he mistakenly had been given DOUBLE the discount of the coupon, even though there was no double-coupon offer in effect that day. He went back inside and pointed this mistake out to the manager, offering to make the difference between what he paid and what he should have paid. The manager was so grateful for George's honesty that he allowed George to pay just half that difference, so George paid him $40.50. We're asked for the original price of the item, before any coupons? (and we're told to assume that there was no tax at all in this scenario). This question can be solved in a number of different ways, including by TESTing THE ANSWERS.

To start, since the end results of all of these math 'steps' is $40.50, it's likely that we're starting with a nice 'round' number, so the correct answer is probably NOT Answer A or Answer C. Let's TEST Answer D first:

Answer D: $540 
IF... the original item cost $540... 
then a 15% coupon would have saved George (.15)($540) = $81 
and a 30% coupon would have saved George (.3)($540) = $162 
The difference in those discounts = $162 - $81 = $81 
HALF of that 'extra' discount = $81/2 = $40.50 
This is an exact match for what we were told, so this must be the answer!

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

ScottTargetTestPrep · Answer

We can let the original price of the item = x dollars. After 15% off, and had the sale been done correctly, George should have paid 0.85x dollars. However, because of the mistake, he received 30% off, so he actually paid 0.7x dollars. Therefore, the difference is 0.85x - 0.7x = 0.15x dollars, which he should pay back to the store. However, since the manager allowed him to pay half the difference, which amounts to $40.50, we can create the equation

½(0.15x) = 40.5

0.15x = 81

x = 81/0.15 = 540

Alternate Solution:

The $40.50 payment that George paid back to the store represents half of the 15% discount, which is 7.5%. Thus, if we let x = the original price of the item, we can create the following equation:

0.075x = 40.5

75x = 40,500

x = 540

Answer: D

Kinshook · Answer

Let original price of the item be x
15% x - discount
30% x - discount offered
Difference = 15% x
1/2* Difference = 7.5% x = $40.5
x = 40.5/7.5% = $540

IMO D

Difference = 15%

George bought a large electronic item with a 15% off coupon, and paid

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