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Diana bought a stereo for $530, which was the retail price plus a 6

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Diana bought a stereo for $530, which was the retail price plus a 6  [#permalink]

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New post 24 Nov 2015, 10:56
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Question Stats:

69% (01:55) correct 31% (01:47) wrong based on 223 sessions

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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

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Re: Diana bought a stereo for $530, which was the retail price plus a 6  [#permalink]

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New post 24 Nov 2015, 11:01
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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

One approach is to apply a bit of 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
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Re: Diana bought a stereo for $530, which was the retail price plus a 6  [#permalink]

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New post 24 Nov 2015, 11:10
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Answer D
p+ tax = 106%
Price = 530/106 * 100 = 500
105% = 525
She will be saving 5 dollars. It just took me over two minutes, lame
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Re: Diana bought a stereo for $530, which was the retail price plus a 6  [#permalink]

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New post 24 Nov 2015, 11:20
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R=Retail Price

Store 1:

R(106/100)=530
R=(530*100)/(106) and recognize 106*5=530
Therefore R=500

Store 2:
500*(105/100)=5*105=$525

Savings=$530-$525=$5 (D)
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Re: Diana bought a stereo for $530, which was the retail price plus a 6  [#permalink]

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New post 24 Nov 2015, 11:25
Price at which Diana bought a stereo = 530$
Let the retail price = R
Percent of sales tax = 6%
R+.06R = 530
=>1.06R = 530
=> R = 500
Money spent in sales tax = 30$

In the neighboring state , she would have paid sales tax = 5%
Sales tax amount in neighboring state = (5/100)* 500 = 25 $
Diana could have saved = 30 - 25 = 5$

Answer D
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Re: Diana bought a stereo for $530, which was the retail price plus a 6  [#permalink]

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New post 24 Nov 2015, 12:20
Bunuel wrote:
Diana bought a stereo for $530, which was the retail price plus a 6 percent sales tax.


Let the retail price of the stereo be 100
Diana bought the stereo at 106

Bunuel wrote:
in a neighboring state where she would have paid a sales tax of 5 percent?


Price of the stereo in neighboring state is 105

Bunuel wrote:
How much money could she have saved if she had bought the stereo at the same retail price in a neighboring state


Savings possible by buying the stereo from the neighboring state is 106 - 105 = 1

Bunuel wrote:
Diana bought a stereo for $530, which was the retail price plus a 6 percent sales tax.


We know that when retail price is 106 , price of stereo is $530
When retail price is 1 , price of the stereo is 530/106 = $5

IMHO (D) $5.00
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Re: Diana bought a stereo for $530, which was the retail price plus a 6  [#permalink]

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New post 13 Dec 2016, 17:52
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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


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
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Re: Diana bought a stereo for $530, which was the retail price plus a 6  [#permalink]

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New post 20 Dec 2016, 04:59
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To find the actual price of the item: 530/106*100=500
Adding 5% tax: 500/100*105= 525
To find the difference: 530-525=5
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Re: Diana bought a stereo for $530, which was the retail price plus a 6  [#permalink]

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New post 09 Jan 2017, 09:46
Icecream87 wrote:
Answer D
p+ tax = 106%
Price = 530/106 * 100 = 500
105% = 525
She will be saving 5 dollars. It just took me over two minutes, lame



Can somebody refer to me a video on how to simplifiy 530/106 to 500?
what i am doing is
1% of 530 = 5.3
5.3*6= 31.8 ...
530-31.8= 498.2 ...

where am i making the mistake?
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Re: Diana bought a stereo for $530, which was the retail price plus a 6  [#permalink]

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