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

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

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.

10% of 2000 = 200
So, 5% of 2000 = 200/2 => 100

Amount including tax is 2100

10% of 1800 = 180
So, 1% of 1800 = 18
And 2% of 1800 = 36

Thus, 12% of 1800 = 180 + 36 =>216

So, Price after tax is 1800 + 216 = 2016

Required % is ( 2100 - 2016)/2100*100 => 84/21 => 4% , Answer must be (B)

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 ≈ -4% or 4% less.

Answer: B

OFFICIAL GMAT EXPLANATION

Anne paid a total amount of (1.05)($2000) = $2100, and Henry paid a total amount of (1.12)(1800) = $2016. Therefore, Henry paid $2100 - $2016 = $84 less than Anne paid, which was 84/2100 = 4 percent less. The best answer is B.

The best way to do this is backwards. Tbh I just guessed that it was 4% (bad idea), but after spending some time thinking about it, the best way to check is:

x / 2100 = 4/100
x = 84 <---the difference between 2100 and 2016

To find the percentage by which Henry's total amount paid is less than Anne's total amount paid, we need to compare the difference in the total amounts to Anne's total amount and express it as a percentage.

Anne's total amount paid, including sales tax, is $2,000 + 5% of $2,000.
Anne's total amount paid = $2,000 + 0.05 * $2,000 = $2,000 + $100 = $2,100.

Henry's total amount paid, including sales tax, is $1,800 + 12% of $1,800.
Henry's total amount paid = $1,800 + 0.12 * $1,800 = $1,800 + $216 = $2,016.

The difference between Anne's and Henry's total amounts paid is $2,100 - $2,016 = $84.

To find the percentage difference, we calculate (Difference / Anne's total amount paid) * 100:
($84 / $2,100) * 100 = 4%.

Therefore, Henry's total amount paid, including sales tax, is 4% less than Anne's total amount paid, including sales tax. This corresponds to option (B).