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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

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.
_________________

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

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.

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.

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.

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???

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

Show Tags

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

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

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

Show Tags

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

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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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.
_________________