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?
An air-conditioning unit costs $470
This topic has expert replies
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
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
- EconomistGMATTutor
- GMAT Instructor
- Posts: 555
- Joined: Wed Oct 04, 2017 4:18 pm
- Thanked: 180 times
- Followed by:12 members
Hi Vicen,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?
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
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7245
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
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.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
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
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
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!
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!