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Diana bought a stereo for $530, which was the retail price plus a 6
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24 Nov 2015, 10:56
24 Nov 2015, 10:56
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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
(A) $1.00
(B) $2.65
(C) $4.30
(D) $5.00
(E) $5.30
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Joined: 12 Sep 2015
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Diana bought a stereo for $530, which was the retail price plus a 6
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Updated on: 19 Jan 2021, 11:26
Updated on: 19 Jan 2021, 11:26
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Bunuel
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
(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
Originally posted by BrentGMATPrepNow on 24 Nov 2015, 11:01.
Last edited by BrentGMATPrepNow on 19 Jan 2021, 11:26, edited 2 times in total.
Last edited by BrentGMATPrepNow on 19 Jan 2021, 11:26, edited 2 times in total.
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Re: Diana bought a stereo for $530, which was the retail price plus a 6
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13 Dec 2016, 17:52
13 Dec 2016, 17:52
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Bunuel
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
(A) $1.00
(B) $2.65
(C) $4.30
(D) $5.00
(E) $5.30
We are first given that Diana bought a stereo for $530, which was the retail price plus a 6 percent sales tax, so we can create the following equation to determine S, the retail price of the stereo before sales tax:
Retail Price + Sales Tax = Total
S + .06S = 530
1.06(S) = 530
106(S) = 530 x 100
S = (530 x 100)/106 = (530 x 50)/53 = 10 x 50 = 500
(Note: Although the above equation appeared somewhat complicated, we see that through careful simplification, we can fairly easily come up with a final value of 500.)
We need to determine how much Diana would have saved had she purchased a $530 dollar stereo with a 5 percent sales tax rather than the stereo with a 6 percent sales tax. Thus, we are essentially determining the difference in the amount of tax paid and can determine this using the formula: Sales Tax = Retail Price x Tax Rate
The amount of sales tax, when paying 6%, is 500 x 0.06 = 30 dollars.
The amount of sales tax, when paying 5%, is 500 x 0.05 = 25 dollars.
Thus, the money saved when paying 5% is 30 - 25 = 5 dollars.
Answer: D
