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

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

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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

OA D

Source: Magoosh

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BTGmoderatorDC 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
We can PLUG IN THE ANSWERS, which represent the original price of the item.
When the correct answer is plugged in, George reimburses the store $40.50.
Since the coupon discount = 15% = 15/100 = 3/20, the original price of the item is almost certainly a multiple of 20.
Of the 5 answer choices, only D is a multiple of 20.

D: 540
Coupon discount = (3/20)(540) = 81.
Since George is accidentally given double the coupon discount, the given discount = 2*81 = 162.
Since George reimburses the store for half the difference between the two discounts, the amount of the reimbursement = (1/2)(162-81) = (1/2)(81) = 40.50.
Success!

The correct answer is D.

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x = original price
Original discount is 15% off: 0.85x
Mistaken double discount is 30% off: 0.70x

George paid back half of what he should have paid.

He got an extra 15% off of x: (0.85-0.70)x = 0.15x.
15% divided in half = 7.5 percent of x.
In dollars, George paid back $40.50.

40.50 = 0.75x
x = 40.50/0.75 = 40500 / 75 = 540.

Hence, D is the correct answer. Regards!

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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 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 (assuming that there was no tax in this scenario)?

This question can be solved in a number of different ways, including by TESTing THE ANSWERS. Since the original discount was 15% - and the 'deal' George received was to pay back HALF of an extra 15% discount, the $40.50 he paid back was relatively small compared to the original price. Based on the answer choices, the overall price of the item had to be more than 10 times the $40.50 he paid back, so we should TEST one of the larger options first.

Answer D: $540
IF... the original price was $540,
a 15% discount would have been (.15)($540) = $81
half of $81 = $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

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Contact Rich at Rich.C@empowergmat.com

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BTGmoderatorDC 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
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 got 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

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Scott Woodbury-Stewart Founder and CEO

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BTGmoderatorDC 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 Smile must be a little more than $480

Answer: D

Cheers,
Brent

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Brent Hanneson – Creator of GMATPrepNow.com
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