Stereo sales tax

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EricKryk: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Tue Mar 31, 2009 11:03 am; Thanked: 3 times

by EricKryk » Tue Feb 11, 2014 6:03 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

A quick approach?

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Source: Beat The GMAT — Problem Solving | Tue Feb 11, 2014 6:03 am

Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Tue Feb 11, 2014 6:13 am

Retail price + 6% is 1.06r. Retail price + 5% is 1.05r. We're asked to find the difference between the two (0.01r), given that 1.06r = $530. To solve quickly, just divide 1.06r by 106 to get .01r. So the answer will be 530/106 = 5. The full solution below is taken from the GMATFix App.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Feb 11, 2014 1:48 pm

EricKryk 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

A quick approach?

Diane's state:
Here, the price with tax is an INTEGER.
Since the tax = 6% = 6/100 = 3/50, the retail price is almost certainly a MULTIPLE OF 50 just a bit less than $530.
If the retail price = 500, then the price with tax = 500 + 6% of 500 = $530.
This works!

Neighboring state:
Here, the price with tax = 500 + 5% of 500 = $525 -- a cost savings of $5.

The correct answer is D.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Feb 12, 2014 6:30 am

An alternate approach is to set up a PROPORTION.

In Diane's state -- where the tax is 6% -- $530 is equal to 106% of the retail price.
In the neighboring state -- where the tax is 5% -- $x is equal to 105% of the retail price.
Thus:
530/106 = x/105
5 = x/105
x = 525.

Amount saved = 530-525 = 5.

The correct answer is D.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Feb 12, 2014 10:50 am

EricKryk 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

Another 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

Brent Hanneson - Creator of GMATPrepNow.com

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Nupur.nk: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Sun Jan 08, 2012 6:30 pm; Thanked: 1 times

by Nupur.nk » Thu Feb 13, 2014 8:35 am

To Mitch Hunt:

I am not getting an intuitive understanding of the 106% and 105%.

Could you please explain it?

Thanks.

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Nupur.nk: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Sun Jan 08, 2012 6:30 pm; Thanked: 1 times

by Nupur.nk » Thu Feb 13, 2014 8:37 am

I am not getting an intuitive understanding
of the 106% and 105%.

Could someone please explain it?

GMATGuruNY wrote:An alternate approach is to set up a PROPORTION.

In Diane's state -- where the tax is 6% -- $530 is equal to 106% of the retail price.
In the neighboring state -- where the tax is 5% -- $x is equal to 105% of the retail price.
Thus:
530/106 = x/105
5 = x/105
x = 525.

Amount saved = 530-525 = 5.

The correct answer is D.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Feb 13, 2014 9:04 am

Nupur.nk wrote:To Mitch Hunt:

I am not getting an intuitive understanding of the 106% and 105%.

Could you please explain it?

Thanks.

A few more examples:

If 50% of the retail price of a printer is $100, what is 40% of the retail price?
Since $100 is equal to 50%, and we want to know what value is equal to 40%, we can set up the following proportion:
100/50 = x/40
2 = x/40
x = 80.
Thus, 40% of the retail price is $80.

If 40% of the retail price of a printer is $80, what is 50% of the retail price?
Since $80 is equal to 40%, and we want to know what value is equal to 50%, we can set up the following proportion:
80/40 = x/50
2 = x/50
x = 100.
Thus, 50% of the retail price is $100.

In the problem above:
The purchase price in Diane's state is equal to 100% of the retail price plus 6% tax.
In other words, the purchase price in Diane's state is equal to 106% of the retail price.
The purchase price in the neighboring state is equal to 100% of the retail price plus 5% tax.
In other words, the purchase price in the neighboring state is equal to 105% of the retail price.

Since $530 is equal to 106% of the retail price, and we want to know what value is equal to 105% of the retail price, we can set up the following proportion:
530/106 = x/105
5 = x/105
x = 525.
Thus, the purchase price in the neighboring state (525) is $5 less than the purchase price in Diane's state (530).

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Dec 08, 2017 11:08 am

EricKryk 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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