Problem Solving

AAPL wrote: ↑

Wed Mar 31, 2021 9:57 am

Magoosh

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

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