Problem Solving

Hi Vincen,

This question has a great 'concept shortcut' built into it - and if you recognize it, then you avoid doing math altogether.

When dealing with 'percent change' questions, it's important to remember that the percent is based on the 'starting number.' Here, the first calculation (the 16% decrease) is based off of the initial $470 cost of the air-conditioner. However, the second calculation (a 16% increase) is based on the DISCOUNTED price of the air-conditioner (which is smaller than $470). Whatever 16% of $470 is, 16% of (less than $470) will be less than that. Thus, the increase will be LESS than the initial decrease... so the total price would have to be LESS than $470. There's only one answer that fits.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Vincen wrote:An air-conditioning unit costs $470. On December there was a discount for Christmas of 16%. Six months later, the holiday season was over so the company raised the price of the air-conditioning by 16%. How much will an air-conditioning unit cost in November?

A. $458
B. $470
C. $472
D. $484
E. $491

When a positive number is decreased by a certain percentage and then increased by the same percentage (or vice versa), the result will be always less than the original number. Thus, the correct answer should be a number that is less than $470. Since $458 is the only number in the given answer choices that is less than $470, it must be the correct answer.

Alternate Solution:

The price after the 16% discount will be 470 x 0.84 = 394.80.

If the discounted price is increased by 16%, the new price will be 394.80 x 1.16 = 457.97, which rounds to $458.

Answer: A