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George bought a large electronic item

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George bought a large electronic item  [#permalink]

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New post 06 Feb 2018, 08:21
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Difficulty:

  35% (medium)

Question Stats:

74% (02:39) correct 26% (03:03) wrong based on 52 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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New post 06 Feb 2018, 09:39
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:
\(.075x = $40.50\)
\(x = \frac{$40.50}{.075} = \frac{$40,500}{75} = $540\)

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

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New post 27 Aug 2018, 09:54
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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
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Re: George bought a large electronic item &nbs [#permalink] 27 Aug 2018, 09:54
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