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# George bought a large electronic item

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Senior Manager
Joined: 29 Jun 2017
Posts: 454
GPA: 4
WE: Engineering (Transportation)
George bought a large electronic item  [#permalink]

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06 Feb 2018, 09:21
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Difficulty:

35% (medium)

Question Stats:

75% (02:34) correct 25% (02:59) wrong based on 51 sessions

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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

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George bought a large electronic item  [#permalink]

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06 Feb 2018, 10:39
sahilvijay wrote:
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

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:
$$.075x = 40.50$$
$$x = \frac{40.50}{.075} = \frac{40,500}{75} = 540$$

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Re: George bought a large electronic item  [#permalink]

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27 Aug 2018, 10:54
Top Contributor
sahilvijay wrote:
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

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 _________________ Test confidently with gmatprepnow.com EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14174 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: George bought a large electronic item [#permalink] ### Show Tags 19 Feb 2019, 16:31 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!

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Re: George bought a large electronic item   [#permalink] 19 Feb 2019, 16:31
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