For a long time, the price of a certain console remained the same. Because of new tariffs, the price of this console

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

by BTGmoderatorDC » Sun Jul 10, 2022 9:40 pm

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For a long time, the price of a certain console remained the same. Because of new tariffs, the price of this console increased by 50% last week, and stayed at this new level. This week, Amanda purchased the console with a 50%-off coupon. Amanda paid $240. What was the original price, before the last week's price increase?

A. 90
B. 180
C. 240
D. 320
E. 360

OA D

Source: Magoosh

Source: Beat The GMAT — Problem Solving | Sun Jul 10, 2022 9:40 pm

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Re: For a long time, the price of a certain console remained the same. Because of new tariffs, the price of this console

by Brent@GMATPrepNow » Tue Jul 12, 2022 6:44 am

BTGmoderatorDC wrote: ↑
Sun Jul 10, 2022 9:40 pm
For a long time, the price of a certain console remained the same. Because of new tariffs, the price of this console increased by 50% last week, and stayed at this new level. This week, Amanda purchased the console with a 50%-off coupon. Amanda paid $240. What was the original price, before the last week's price increase?

A. 90
B. 180
C. 240
D. 320
E. 360

OA D

Source: Magoosh

Let x = the original price of the console (in dollars)

Because of new tariffs, the price of this console increased by 50% last week
The new price = x + (50% of x) = x + 0.5x = 1.5x

Amanda purchased the console with a 50%-off coupon. Amanda paid $240
Purchase price = 50% of 1.5x
= (0.5)(1.5x) = 0.75x

Since Amanda paid $240 we can write: 0.75x = 240

ASIDE: If you'd rather not divide 240 by 0.75, you can rewrite the above equation as follows: (3/4)x = 240
From here we can eliminate the fraction by multiplying both sides of the equation by 4/3 to get: (4/3)(3/4)x = (4/3)(240)
Simplify: x = 320

Answer: D

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