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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:

76% (01:35) correct 24% (03:56) wrong based on 17 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
[Reveal] Spoiler: OA

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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

x = original price
Original discount is 15% off: .85x
Mistaken doubled discount is 30% off: .70x

George paid back half of what he should have paid.

He got an extra 15 % off of x: (.85-.70)= .15x
15 percent divided in half = 7.5 percent of x.
In dollars, George paid back $40.50.

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

ANSWER D

Check:
Should have paid: (.85 * $540) = $459
Did pay: (.70 * $540) = $378
Difference: ($459 - $378) = $81.00
George pays half of that back. He pays back $40.50. Correct.

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George bought a large electronic item   [#permalink] 06 Feb 2018, 09:39
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