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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Thu Sep 12, 2019 5:04 pm

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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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Source: Beat The GMAT — Problem Solving | Thu Sep 12, 2019 5:04 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Thu Sep 12, 2019 9:03 pm

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

OA D

Source: Magoosh

So, in a nutshell, instead of getting 15% discount, George got 15 + 15 = 30% discount. So, George offered to pay back 15% to the store; however, the manager asked him to pay only half 15/2 = 7.5% of it. Thus, 7.5% of the Original price = 40.50.

Thus, Original price = (40.50/7.5)*100 = $540.

The correct answer: D

Hope this helps!

-Jay
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swerve: Legendary Member; Posts: 2548; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Sat Sep 14, 2019 2:26 am

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 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

Let original price of the item be $x$

15%$x$ - discount
30% $x$ - discount offered

Difference 15% $x$
$\frac{1}{2}\cdot$ Difference $=$ 7.5% $x = $ $40.5.
$x=\frac{40.5}{7.5\%} = $ $540.

Therefore, __D__

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8157; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sat Sep 21, 2019 11:15 am

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

OA D

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

Â½(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

Source: Magoosh

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