Anne bought a computer for $2,000 . . .

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

Anne bought a computer for $2,000 . . .

by Vincen » Tue Nov 21, 2017 8:44 am

Anne bought a computer for $2,000 and then paid a 5 percent sales tax, and Henry bought a computer for $1,800 and then paid a 12 percent sales tax. The total amount that Henry paid, including sales tax, was what percent less than the total amount that Anne paid, including sales tax?

A. 3%
B. 4%
C. 7%
D.10%
E. 12%

The OA is B

Experts, I dont know what are the calculus I should do here. May you show me how to solve this PS question?

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Source: Beat The GMAT — Problem Solving | Tue Nov 21, 2017 8:44 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Tue Nov 21, 2017 9:35 am

Vincen wrote:Anne bought a computer for $2,000 and then paid a 5 percent sales tax, and Henry bought a computer for $1,800 and then paid a 12 percent sales tax. The total amount that Henry paid, including sales tax, was what percent less than the total amount that Anne paid, including sales tax?

A. 3%
B. 4%
C. 7%
D.10%
E. 12%

Anne bought a computer for $2,000 and then paid a 5 percent sales tax
10% of $2000 = $200
So, 5% of $2000 = $100
TOTAL that Anne paid = $2000 + $100 = $2100

Henry bought a computer for $1,800 and then paid a 12 percent sales tax
10% of $1800 = $180
So, 1% of $1800 = $18
And 1% of $1800 = $18
So, 12% of $1800 = $180 + $18 + $18 =$216
TOTAL that Henry paid = $1800 + $216 = $2016

The total amount that Henry paid, including sales tax, was what percent less than the total amount that Anne paid, including sales tax?
PERCENT difference = (100)(difference in payments)/(Anne's total payment)
= (100)(2100 - 2016)/(2100)
= (100)(84)/2100
= 8400/2100
= 4
Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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

by EconomistGMATTutor » Tue Nov 21, 2017 11:02 am

Anne bought a computer for $2,000 and then paid a 5 percent sales tax, and Henry bought a computer for $1,800 and then paid a 12 percent sales tax. The total amount that Henry paid, including sales tax, was what percent less than the total amount that Anne paid, including sales tax?

A. 3%
B. 4%
C. 7%
D.10%
E. 12%

The OA is B

Experts, I dont know what are the calculus I should do here. May you show me how to solve this PS question?

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

The price of the computer Anne bought = $2,000
Percentage of Sales tax Anne paid = 5%
Sales tax Anne paid will be:
$$=\ 2,000\times\frac{5}{100}=100$$

Therefore, the total amount Anne paid = 2,000 + 100 = $2,100

The price of the computer Henry bought = $1,800
Percentage of Sales tax Henry paid = 12%
Sales tax Henry paid will be:
$$=\ 1,800\times\frac{12}{100}=216$$

Therefore, the total amount Henry paid = 1,800 + 216 = $2,016

Now we are asked to find the percent decrease of Henry's payment than Anne's Payment.
Percent decrease = [(Anne's Payment - Henry's Payment)/Anne's Payment] * 100%
$$=\ \frac{2100-2016}{2100}\times100\%$$
$$=\ \frac{84}{2100}\times100\%$$
$$=\ \frac{84}{21}\%$$
$$=\ 4\%$$

Hence, the total amount that Henry paid, including sales tax, was 4% less than the total amount that Anne paid, including sales tax.
Therefore, Option B is correct.

Hope it helps.
I am available if you'd like any follow up.

GMAT Prep From The Economist
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Oct 12, 2019 4:05 pm

Vincen wrote:Anne bought a computer for $2,000 and then paid a 5 percent sales tax, and Henry bought a computer for $1,800 and then paid a 12 percent sales tax. The total amount that Henry paid, including sales tax, was what percent less than the total amount that Anne paid, including sales tax?

A. 3%
B. 4%
C. 7%
D.10%
E. 12%

The OA is B

Experts, I dont know what are the calculus I should do here. May you show me how to solve this PS question?

Anne paid 2000 x 1.05 = 2100 for her computer.

Henry paid 1800 x 1.12 = 2016 for his computer.

Now, we can determine the percent less:

(2016 - 2100)/2100 x 100 â‰ˆ -4% or 4% less.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
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