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tagged by: rolandprowess

This topic has 4 expert replies and 1 member reply

### Top Member

Vincen Legendary Member
Joined
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Posted:
550 messages
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#### An air-conditioning unit costs $470 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? ### GMAT/MBA Expert Matt@VeritasPrep GMAT Instructor Joined 12 Sep 2012 Posted: 2640 messages Followed by: 113 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 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! Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! ### GMAT/MBA Expert Scott@TargetTestPrep GMAT Instructor Joined 25 Apr 2015 Posted: 781 messages Followed by: 3 members Upvotes: 43 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 _________________ Scott Woodbury-Stewart Founder and CEO ### GMAT/MBA Expert Rich.C@EMPOWERgmat.com Elite Legendary Member Joined 23 Jun 2013 Posted: 9184 messages Followed by: 472 members Upvotes: 2867 GMAT Score: 800 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.

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

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### Top Member

Vincen Legendary Member
Joined
07 Sep 2017
Posted:
550 messages
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Tue Oct 03, 2017 6:18 pm
Oh. Thanks Rich. It was easier than I thought. Great explanation.

### GMAT/MBA Expert

EconomistGMATTutor GMAT Instructor
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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.

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