An air-conditioning unit costs $470

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Tue Oct 03, 2017 5:17 pm

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

The OA is A.

It shouldn't be B? Why is A?

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Source: Beat The GMAT — Problem Solving | Tue Oct 03, 2017 5:17 pm

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by [email protected] » Tue Oct 03, 2017 6:10 pm

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

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Rich

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Tue Oct 03, 2017 6:18 pm

Oh. Thanks Rich. It was easier than I thought. Great explanation.

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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Sat Oct 07, 2017 12:26 pm

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

The OA is A.

It shouldn't be B? Why is A?

Hi Vicen,
Let's take a look at your question.

Air-conditioning unit costs $470.
Decrease in price = 470 x(16/100) = $75.2
Decreased cost of air-conditioning unit in December = $470 - $75.2 = $394.8

After six months the price was again raised by 16%.
The rise in price = 394.8 x (16/100) = $63.168
Increased cost of air-conditioning unit six months later = $394.8 + $63.168 = $457.968 approximately $458

Therefore, the cost of air-conditioning unit in November will be $458.

Option A is correct.

I am available if you'd like any followup.

GMAT Prep From The Economist
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Oct 09, 2017 4:22 pm

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

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Founder and CEO
[email protected]

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Wed Oct 11, 2017 5:43 pm

We could also use digit properties:

470 * .84 * 1.16 =>

10 * (47 * .84 * 1.16) =>

Since 7 * 4 * 6 ends in 8, this gets us =>

10 * (some decimal that ends in 8)

Only A ends in 8, so we're done!

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