Bunuel wrote:
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
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
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing -
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