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

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

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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

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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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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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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.

So answer must be (E)

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

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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
Answer = (E)

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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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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.

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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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New post 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.

So answer must be (E)

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)
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New post 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.

So answer must be (E)

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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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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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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New post 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
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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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New post 13 Nov 2017, 22:25
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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.
_________________

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Kudos [?]: 18128 [2], given: 236

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