Percentages and Applied Problems

Expert replies

britney89: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Wed Sep 21, 2011 4:24 pm

by britney89 » Sat Oct 08, 2011 5:46 pm

Question: Diana bought a stereo for $530, which was the retail price plus a 6% sales tax. How much money could she have saved if she bought the stereo at the same retail price in the neighbouring state where she would have paid a sales tax of 5%?

I have the same process, but the percentage being multiplied by the price is different, the answer has the equation to be 530=1.06r, I'm just wondering how/why the percentage multiplied by the retail price is 1.06 and not 0.06?

Thanks!!

Like this post

Source: Beat The GMAT — Problem Solving | Sat Oct 08, 2011 5:46 pm

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Oct 08, 2011 7:38 pm

britney89 wrote:Question: Diana bought a stereo for $530, which was the retail price plus a 6% sales tax. How much money could she have saved if she bought the stereo at the same retail price in the neighbouring state where she would have paid a sales tax of 5%?

Say the retail price is R%

Hence, price of the stereo = Retail price + 6% tax on the retail price = R + 6% of R = R + 0.06R = 1.06R

Now, 1.06R = 530 ---> R = 500

Price of the stereo in the neighboring state = 1.05R = $525

Hence, she could have saved $(530 - 525) = $5

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/

Like this post

factor26: Senior | Next Rank: 100 Posts; Posts: 99; Joined: Sun Mar 13, 2011 12:42 pm

by factor26 » Sat Oct 08, 2011 9:10 pm

i used to be confused on this topic too!

just think of it this way ... if i gave you $100 to invest in a bond whose yield is 6% (dont worry about compounding now

) when i ask you how much will you have at the end of the year you can say

orig inv = $100.00
6% return $6.00
Total = $106.00

other ways to look at this

x = orig inv

x + .06x = answer

combine terms ...

1.06x = answer ... i used to solve at first by using the x + .06x equation ... but in an effort to save time i adapted and used the 1.06x equation ... saves me a step in the calculation which is really meaningful when taking the gmat considering it is a timed test!!

Like this post

fcabanski: Master | Next Rank: 500 Posts; Posts: 104; Joined: Fri Oct 07, 2011 10:23 pmFollowed by: 4 members; Thanked: 36 times

by fcabanski » Sat Oct 08, 2011 9:26 pm

Whenever you see problems like this, including work problems and d=rt problems, write down the general formula, and then a formula for each situation - there are usually 2, but sometimes 3.

Identify the problem type. Set up your solution. Make sure you know what is being asked, and that you've set up correctly. Execute.

Identify - Sale Price, original price, sales tax problem.

General formula: P=(1+r)*C

Situation 1: 530=(1.06)*C
Situation 2: P = (1.05)*C

Make sure - the problem asks to find what she could have saved, so P (from situation 1) which is 530 - P (situation 2).

Note situation one contains only one variable. Note situation two can be solved if C is known. Situation one can provide C.

Do the math.

530/1.06=C=500

Sit. 2: P = (1.05)*500=525

Answer: 530-525= 5

Like this post

Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Sun Oct 09, 2011 2:32 am

britney89 wrote:Question: Diana bought a stereo for $530, which was the retail price plus a 6% sales tax. How much money could she have saved if she bought the stereo at the same retail price in the neighbouring state where she would have paid a sales tax of 5%?

I have the same process, but the percentage being multiplied by the price is different, the answer has the equation to be 530=1.06r, I'm just wondering how/why the percentage multiplied by the retail price is 1.06 and not 0.06?

Thanks!!

Let the price of the stereo be 100

Sales tax is 6

So, price after sales tax is 106

Now 106 represents 530

so 100 represents (530/106)*100

So, Actual price of the stereo is $500

Sales tax in the other state is 5%

So price of the stereo after the tax is 500 * 105/100 => $ 525

So total savings is $ 5

Coming to your query -

let the price of the stereo be 100

Tax is 6% => 6

So price after the tax is 106

Hence the multiplicand is 1.06 not 0.6!!!!

Abhishek

Like this post

fcabanski: Master | Next Rank: 500 Posts; Posts: 104; Joined: Fri Oct 07, 2011 10:23 pmFollowed by: 4 members; Thanked: 36 times

by fcabanski » Sun Oct 09, 2011 7:44 pm

The formula is

P = (1=r) * C

Where C is the cost before tax, and P is the final price and r is the sales tax.

Another way to write this is:

P = C +rC

Price is the cost plus the sales tax rate times the cost. rC is the sales tax in dollars.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review