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# At the store, Sam bought a shirt and a toaster. There was an 8% sales

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Math Expert
Joined: 02 Sep 2009
Posts: 50624
At the store, Sam bought a shirt and a toaster. There was an 8% sales  [#permalink]

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18 Feb 2015, 03:20
00:00

Difficulty:

45% (medium)

Question Stats:

65% (01:44) correct 35% (02:36) wrong based on 176 sessions

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At the store, Sam bought a shirt and a toaster. There was an 8% sales tax on each item, and with tax, Sam paid a total of K. If the price of the toaster before tax was T, what, in terms of K and T, is the price of the shirt before tax?

A. 0.92(K – T)
B. 0.92K – T
C. 0.92(K – 1.08T)
D. (K – T)/1.08
E. (K/1.08) – T

Kudos for a correct solution.

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Posts: 54
Re: At the store, Sam bought a shirt and a toaster. There was an 8% sales  [#permalink]

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18 Feb 2015, 05:00
2
1
Let, S be the amount of shirt before tax, then total amount paid with 8% sales tax is -
1.08(T + S) = K (sales tax = 8%)
=> S = (K/1.08) - T

Hence, Ans is (E).
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Re: At the store, Sam bought a shirt and a toaster. There was an 8% sales  [#permalink]

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18 Feb 2015, 22:14
2
Bunuel wrote:
At the store, Sam bought a shirt and a toaster. There was an 8% sales tax on each item, and with tax, Sam paid a total of K. If the price of the toaster before tax was T, what, in terms of K and T, is the price of the shirt before tax?

A. 0.92(K – T)
B. 0.92K – T
C. 0.92(K – 1.08T)
D. (K – T)/1.08
E. (K/1.08) – T

Kudos for a correct solution.

If you have aversion to algebra and writing down equations (the way I do!), just assume some very simple scenarios.

Say price of toaster is 0 so T = 0. So K is just the price of the shirt with tax. So price of shirt before tax = K/1.08.
If you put T = 0 in options, only (D) and (E) will give you K/1.08

Now, say the price of shirt is 0. So K is the price of toaster with tax. So K = 1.08*T. If you put this in (D) and (E), only (E) gives 0.

You can practice these tricks with this question though actually, making the equation and manipulating is faster here. But, in most questions, the algebra way would take more time.
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Re: At the store, Sam bought a shirt and a toaster. There was an 8% sales  [#permalink]

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18 Feb 2015, 22:14
Answer = E. (K/1.08) – T

If Total cost With Tax = k, then

total cost without tax $$= k*\frac{100}{108}$$

Let cost of shirt without tax = s, then

cost of toaster without tax $$= k*\frac{100}{108} - s = t$$

$$s = k*\frac{100}{108} - t = \frac{k}{\frac{108}{100}} - t = \frac{k}{1.08} - t$$
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Posts: 50624
Re: At the store, Sam bought a shirt and a toaster. There was an 8% sales  [#permalink]

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22 Feb 2015, 11:20
1
Bunuel wrote:
At the store, Sam bought a shirt and a toaster. There was an 8% sales tax on each item, and with tax, Sam paid a total of K. If the price of the toaster before tax was T, what, in terms of K and T, is the price of the shirt before tax?

A. 0.92(K – T)
B. 0.92K – T
C. 0.92(K – 1.08T)
D. (K – T)/1.08
E. (K/1.08) – T

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION

Algebraic Solution: Call the price of the shirt S. The price of the toaster is T. The total before tax is (S + T). Then an 8% tax was applied. For an 8% increase, we use the multiplier 1.08. Thus, K = 1.08*(S + T). Solve this for S.
S + T = K/1.08
S = K/1.08 – T

Numerical Solution: we make our lives much easier if we first recognize the percent trap. The multiplier 1.08 is the correct multiplier for an 8% increase, and it makes sense that this would appear somehow in the correct answer. BUT, 0.92 is the multiplier for an 8% decrease. This is tricky: an 8% decrease is not the opposite of an 8% increase; it does not “undo” an 8% increase. In other words, an 8% increase followed by an 8% decrease does NOT get us back to the original starting point. That’s a major percent trap. There is a 8% increase in the problem, but no 8% decrease: this means that any answer in which the multiplier for an 8% decrease, 0.92, appears, it is automatically wrong. We can immediately eliminate (A) & (B) & (C) without plugging in anything.

OK, let’s say T = 50, shirt = 150, so total before tax is $200. (Again, avoiding the cliché price of$100 for a percent.) Now, 8% of $200 is$16, for a total of K = 216. Because dividing by a decimal isn’t fun, I am going to change the division by 1.08 into multiplication by the fraction 100/108. We are looking for an answer that equals 150, the price of the shirt.

(D) (K – T) /1.08 = (216 – 50)/1.08 = 156*100/108 = 39*100/27 = 13*100/9
well, 13/9 doesn’t equal 1.5, so this doesn’t work.

(E) (K/1.08) – T = 216/1.08 – 50 = 216*(100/108) – 50 = 2*108*(100/108) – 50
= 2*100 – 50 = 200 – 50 = 150

That’s the price of the shirt! Choice (E) is the answer!

- See more at: http://magoosh.com/gmat/2014/gmat-pract ... QEkpA.dpuf
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Re: At the store, Sam bought a shirt and a toaster. There was an 8% sales  [#permalink]

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24 Oct 2016, 08:19
1
I found it was easier creating my own equation first and then searching for it in the answers...

Eq --> S+T+0.08(S+T) = K

0.08S+S+0.008T+T = K

S=(K-1.08T)/1.08

This is the same as E.
Director
Joined: 27 May 2012
Posts: 611
Re: At the store, Sam bought a shirt and a toaster. There was an 8% sales  [#permalink]

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12 Nov 2017, 01:57
VeritasPrepKarishma wrote:
Bunuel wrote:
At the store, Sam bought a shirt and a toaster. There was an 8% sales tax on each item, and with tax, Sam paid a total of K. If the price of the toaster before tax was T, what, in terms of K and T, is the price of the shirt before tax?

A. 0.92(K – T)
B. 0.92K – T
C. 0.92(K – 1.08T)
D. (K – T)/1.08
E. (K/1.08) – T

Kudos for a correct solution.

If you have aversion to algebra and writing down equations (the way I do!), just assume some very simple scenarios.

Say price of toaster is 0 so T = 0. So K is just the price of the shirt with tax. So price of shirt before tax = K/1.08.
If you put T = 0 in options, only (D) and (E) will give you K/1.08

Now, say the price of shirt is 0. So K is the price of toaster with tax. So K = 1.08*T. If you put this in (D) and (E), only (E) gives 0.

You can practice these tricks with this question though actually, making the equation and manipulating is faster here. But, in most questions, the algebra way would take more time.

Hi Karishma,

What am i missing?

Option B and E look the same to me !

0.92= 1/(1.08)
_________________

- Stne

Math Expert
Joined: 02 Sep 2009
Posts: 50624
Re: At the store, Sam bought a shirt and a toaster. There was an 8% sales  [#permalink]

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12 Nov 2017, 02:00
stne wrote:
VeritasPrepKarishma wrote:
Bunuel wrote:
At the store, Sam bought a shirt and a toaster. There was an 8% sales tax on each item, and with tax, Sam paid a total of K. If the price of the toaster before tax was T, what, in terms of K and T, is the price of the shirt before tax?

A. 0.92(K – T)
B. 0.92K – T
C. 0.92(K – 1.08T)
D. (K – T)/1.08
E. (K/1.08) – T

Kudos for a correct solution.

If you have aversion to algebra and writing down equations (the way I do!), just assume some very simple scenarios.

Say price of toaster is 0 so T = 0. So K is just the price of the shirt with tax. So price of shirt before tax = K/1.08.
If you put T = 0 in options, only (D) and (E) will give you K/1.08

Now, say the price of shirt is 0. So K is the price of toaster with tax. So K = 1.08*T. If you put this in (D) and (E), only (E) gives 0.

You can practice these tricks with this question though actually, making the equation and manipulating is faster here. But, in most questions, the algebra way would take more time.

Hi Karishma,

What am i missing?

Option B and E look the same to me !

0.92= 1/(1.08)

How did you get this? Did you try to actually calculate???

1/(1.08) = 0.925925....
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Joined: 27 May 2012
Posts: 611
Re: At the store, Sam bought a shirt and a toaster. There was an 8% sales  [#permalink]

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12 Nov 2017, 02:33
Bunuel wrote:
At the store, Sam bought a shirt and a toaster. There was an 8% sales tax on each item, and with tax, Sam paid a total of K. If the price of the toaster before tax was T, what, in terms of K and T, is the price of the shirt before tax?

A. 0.92(K – T)
B. 0.92K – T
C. 0.92(K – 1.08T)
D. (K – T)/1.08
E. (K/1.08) – T

Kudos for a correct solution.

Hi Bunuel,

Thank you for your question !

let me show you my calculation and approach !

(108/100)S +(108/100)T = K

(108/100)[ S +T]= K

S+T= K*(100/108)

S= K*(100/108) -T

S= (100K- 108T)/108
S=4(25K -27T) /108
S= (25K- 27T )/27
S= (25/27)K - T

After this I calculated 25/27 up to two decimal places and got 0.92
S= 0.92K - T

Then I realized that S= K*(100/108) -T can we easily rewritten as K/1.08 -T ( dividing both the numerator and denominator by 100 )

Then I again calculated 1/(1.08) up to two decimal places and realized I again got 0.92.

Please can you tell me where I went wrong ?

Thanks
_________________

- Stne

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8550
Location: Pune, India
Re: At the store, Sam bought a shirt and a toaster. There was an 8% sales  [#permalink]

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13 Nov 2017, 22:25
2
stne wrote:
Bunuel wrote:
At the store, Sam bought a shirt and a toaster. There was an 8% sales tax on each item, and with tax, Sam paid a total of K. If the price of the toaster before tax was T, what, in terms of K and T, is the price of the shirt before tax?

A. 0.92(K – T)
B. 0.92K – T
C. 0.92(K – 1.08T)
D. (K – T)/1.08
E. (K/1.08) – T

Kudos for a correct solution.

Hi Bunuel,

Thank you for your question !

let me show you my calculation and approach !

(108/100)S +(108/100)T = K

(108/100)[ S +T]= K

S+T= K*(100/108)

S= K*(100/108) -T

S= (100K- 108T)/108
S=4(25K -27T) /108
S= (25K- 27T )/27
S= (25/27)K - T

After this I calculated 25/27 up to two decimal places and got 0.92
S= 0.92K - T

Then I realized that S= K*(100/108) -T can we easily rewritten as K/1.08 -T ( dividing both the numerator and denominator by 100 )

Then I again calculated 1/(1.08) up to two decimal places and realized I again got 0.92.

Please can you tell me where I went wrong ?

Thanks

1/1.08 = .9259...
It is not the same as .92 though close

Note that 92/100 is not the same as 100/108
92/100 < 100/108
Just like 4/5 is not the same as 5/6. I agree that the difference is not much but it is about being exact.
_________________

Karishma
Veritas Prep GMAT Instructor

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Director
Joined: 27 May 2012
Posts: 611
Re: At the store, Sam bought a shirt and a toaster. There was an 8% sales  [#permalink]

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14 Nov 2017, 05:25
VeritasPrepKarishma wrote:
stne wrote:
Bunuel wrote:
At the store, Sam bought a shirt and a toaster. There was an 8% sales tax on each item, and with tax, Sam paid a total of K. If the price of the toaster before tax was T, what, in terms of K and T, is the price of the shirt before tax?

A. 0.92(K – T)
B. 0.92K – T
C. 0.92(K – 1.08T)
D. (K – T)/1.08
E. (K/1.08) – T

Kudos for a correct solution.

Hi Bunuel,

Thank you for your question !

let me show you my calculation and approach !

(108/100)S +(108/100)T = K

(108/100)[ S +T]= K

S+T= K*(100/108)

S= K*(100/108) -T

S= (100K- 108T)/108
S=4(25K -27T) /108
S= (25K- 27T )/27
S= (25/27)K - T

After this I calculated 25/27 up to two decimal places and got 0.92
S= 0.92K - T

Then I realized that S= K*(100/108) -T can we easily rewritten as K/1.08 -T ( dividing both the numerator and denominator by 100 )

Then I again calculated 1/(1.08) up to two decimal places and realized I again got 0.92.

Please can you tell me where I went wrong ?

Thanks

1/1.08 = .9259...
It is not the same as .92 though close

Note that 92/100 is not the same as 100/108
92/100 < 100/108
Just like 4/5 is not the same as 5/6. I agree that the difference is not much but it is about being exact.

Thank you Karishma,
Would you suggest to always calculate up to 4 or more decimal places just to be exact?
_________________

- Stne

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8550
Location: Pune, India
Re: At the store, Sam bought a shirt and a toaster. There was an 8% sales  [#permalink]

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14 Nov 2017, 21:43
stne wrote:
Thank you Karishma,
Would you suggest to always calculate up to 4 or more decimal places just to be exact?

I would suggest to keep it in fraction as much as possible. If a decimal is required, conversion should take place at the end and until and unless the question says "is closest to..", the exact value should be picked.
_________________

Karishma
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GMAT self-study has never been more personalized or more fun. Try ORION Free!

Re: At the store, Sam bought a shirt and a toaster. There was an 8% sales &nbs [#permalink] 14 Nov 2017, 21:43
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