VJesus12 wrote: ↑Tue Aug 17, 2021 8:14 am
Diana bought a stereo for $530, which was the retail price plus a 6 percent sales tax. How much money could she have saved if she had bought the stereo at the same retail price in a neighboring state where she would have paid a sales tax of 5 percent?
(A) $1.00
(B) $2.65
(C) $4.30
(D) $5.00
(E) $5.30
Answer:
D
Source: Official Guide
APPROACH #1: Algebra
Let x = the pre-tax price of the stereo Diana bought
Since the tax rate is 6%, the total
taxes = 6% of x = 0.06x
So we can write: x + 0.06x = $530
Simplify: 1.06x = $530
Solve: x = 530/1.06 = $500
IF Diana had travelled to a neighboring state (with a 5% tax rate), the taxes would have equaled 5% of $500, which is $25
So, the total amount Diana would have paid = $500 + $25 = $525
$530 - $525 = $5
So, Diana would have saved $5.
Answer: D
APPROACH #2:Number sense
The question asks us to determine how much Diana would have saved if the sales tax were decreased 1% (from 6% to 5%)
Keep in mind that the $530
includes the price of the stereo AND the sales tax. So, taking 1% of $530 (
$5.30) would be incorrect, because the stereo itself costs LESS THAN $530. So, the savings must be LESS THAN
$5.30, which means we can
eliminate answer choice E.
Now, those people who have real-life experience with 5% or 6% (or 8 or 9% even) sales tax know that the tax doesn't increase the final price by a whole lot. So, we should have a
gut feeling that the price of the stereo is a little bit less than $530. How much less?
Well, without performing any calculations (i.e., using only your experience with 5% or 6% sales tax), do you think the pre-tax price of the stereo is $430? If so, then 1% of $430 = $4.30 in which case the correct answer is C
ORRRRRR, do you think the pre-tax price of the stereo is $500? If so, then 1% of $500 = $5.00 in which case the correct answer is D
Our experience and number sense should tell us that the pre-tax price of the stereo is a lot closer to $500 than to $430. So, the correct answer MUST be D
Cheers,
Brent
