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Anne bought a computer for $2,000 and then paid a 5

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Anne bought a computer for $2,000 and then paid a 5  [#permalink]

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New post 23 Jul 2015, 03:10
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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%

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Anne bought a computer for $2,000 and then paid a 5  [#permalink]

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New post 23 Jul 2015, 03:40
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AbdurRakib 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%


For Anne
Cost of Computer = $2000
Sales tax = (5/100)*2000 = $100
Total Cost of Computer = 2000 + 100 = 2100

For Henry
Cost of Computer = $1800
Sales tax = (12/100)*1800 = $216
Total Cost of Computer = 1800 + 216 = 2016

% that Henry paid less than Anne = (2100 - 2016)*100/2100 = 4%

Answer: Option B
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Re: Anne bought a computer for $2,000 and then paid a 5  [#permalink]

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New post 23 Jul 2015, 06:48
Total amount paid by Anne = \($2,000 + 0.05 ($2,000) = $2,100\).
Total amount paid by Henry = \($1,800 + 0.12 ($1,800) = $2,016\).

\(\frac{$2,100 - $2,016}{$2,100} * 100 = 4%\). Ans (B).
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Re: Anne bought a computer for $2,000 and then paid a 5  [#permalink]

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New post 23 Jul 2015, 07:08
AbdurRakib 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%


Hi,
the straight method would be= (2100-2016)/2100*100=4%..

I also tried to come up with the answer before doing the calculation and landed up with correct answer..
the reasoning was the two amounts are both mutiples of 16 .. 2*1000 and 18*12*100 and the subtraction of the two should also be multiple of 16..
however the denominator is multiple of 4.. 2100, so the answer should be multiple of 4...
only 4 and 12 are there..
however one of the number is multiple of 3 and other 9, so their subtraction should be multiple of 3 and 2100 is also multiple of 3... therefore the answer will not be multiple of 3.. only 4 left ans B
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2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
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Anne bought a computer for $2,000 and then paid a 5  [#permalink]

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New post 05 Sep 2016, 11:50
A slightly different approach:

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?

Anne's computer cost $2,000 x 1.05 = $2100
Henry's computer cost $1,800 x 1.12 = $2016
A difference of $84
Henry paid x percent less than Anne paid: x = $84/$2100, x = 0.04 = 4%

Notes:
Define percent: parts of one hundred. $1 = 1 part of $100, or 1/100 or 0.01; $50 = 50 parts of $100, or 50/100 = 1/2 or 0.5; $100 = 100 parts of one hundred, or one one hundreds, or 100/100 or 1 or 1.00; $2000 = 20 one hundreds.

Therefore, 5% sales tax on a $2000 computer is $20 X 5 = $100 sales tax, Anne paid $2100 total.

Method: Divide dollars by 100 and multiply percentage decimal values by 100 when working with dollar values and percentages. Much easier to work with.

12% sales tax on a $1800 computer is $18 X 12 = $216 sales tax, total costs Henry paid $2016.

Difference:
$2100
-$2016
______
$ 84

Percent equals parts over sum. $84/$2100 = 0.04 percent.
Sanity Check: 4% x 25 = 100. 84 x 25 = 2100.
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Re: Anne bought a computer for $2,000 and then paid a 5   [#permalink] 15 Dec 2017, 05:38
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