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An item cost $27.50 before tax. If the tax on the item was more than

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Bunuel
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An item cost $27.50 before tax. If the tax on the item was more than [#permalink] New post   20 Aug 2019, 06:41
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An item cost $27.50 before tax. If the tax on the item was more than 10 percent but less than 15 percent of the cost of the item before tax, then the total amount paid must have been between

A. $31 and $33

B. $30 and $32

C. $29 and $31

D. $28 and $30

E. $27 and $29
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B
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Re: An item cost $27.50 before tax. If the tax on the item was more than [#permalink] New post   20 Aug 2019, 07:22
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Cost before tax = $27.5.

Cost after tax:
27.5 * 1.1 < Cost < 27.5 * 1.15
$30.25 < Cost < $31.625
$30 < Cost < $32

Closest answer is (B): between $30 and $32
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Re: An item cost $27.50 before tax. If the tax on the item was more than [#permalink] New post   20 Aug 2019, 07:34
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Let the tax be T%

So Cost of the item with tax will be \(27.50 ( 1 + \frac{T}{100} )\)

Given: 10 < T < 15
So, \(0.1 < \frac{T}{100} < 0.15\)

Thus, Cost of item ranges from 27.50 (1.1) to 27.50 (1.15) = 30.25 to 31.625

B is the closest match.

Answer B
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Re: An item cost $27.50 before tax. If the tax on the item was more than [#permalink] New post   20 Aug 2019, 07:44
10% of 27.50 = 2.75
5% of 27.50 = 2.75/2 ~ 1.36

SO, 110% is 27.50 + 2. 75 => 30.25

And 115% of 27.50 = 27.50 + 2.75 + 1.36 ~ 31.61

SO, The value must lie between 30 and 32 , Answer must be (B)
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Re: An item cost $27.50 before tax. If the tax on the item was more than [#permalink] New post   20 Aug 2019, 07:49
IMO-B

CBT (Cost Before Tax)= $27.5
CAT (Cost After Tax)= $27.5+ Tax

10% (CBT) < Tax < 15% (CBT)
i.e, $ 2.75 < Tax < $ 4.125

$ (27.5+ 2.75) < $27.5 + Tax < $(27.5 + 4.125)

$ 30.25 < CAT < $ 31.625

Only option B satisfies this....
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Re: An item cost $27.50 before tax. If the tax on the item was more than [#permalink] New post   20 Aug 2019, 07:52
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cost before tax = $27.50

10% < tax < 15%
1.1(27.50) < total cost < 1.15(27.50)
$30.25 < total cost < $31.625
$31 < total cost < $32 (rounding off)
ans - B
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Re: An item cost $27.50 before tax. If the tax on the item was more than [#permalink] New post   20 Aug 2019, 08:42
An item cost $27.50 before tax. If the tax on the item was more than 10 percent but less than 15 percent of the cost of the item before tax, then the total amount paid must have been between

A. $31 and $33

B. $30 and $32

C. $29 and $31

D. $28 and $30

E. $27 and $29

least and max value of tax 10.1% and 14.9% ; $30.25 ;$ 31.5

IMO B
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Re: An item cost $27.50 before tax. If the tax on the item was more than [#permalink] New post   20 Aug 2019, 09:31
Quote:
An item cost $27.50 before tax. If the tax on the item was more than 10 percent but less than 15 percent of the cost of the item before tax, then the total amount paid must have been between

A. $31 and $33
B. $30 and $32
C. $29 and $31
D. $28 and $30
E. $27 and $29


0.10(27.5)<tax<0.15(27.5)
2.75<tax<4.125
27.50+2.75<total(=cost+tax)<27.50+4.125
30.25<total<31.625…

Answer (B).
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Re: An item cost $27.50 before tax. If the tax on the item was more than [#permalink] New post   20 Aug 2019, 09:57
An item cost $27.50 before tax. If the tax on the item was more than 10 percent but less than 15 percent of the cost of the item before tax, then the total amount paid must have been between

A. $31 and $33

B. $30 and $32

C. $29 and $31

D. $28 and $30

E. $27 and $29

C = 27.5. Total paid amount is between \(1.1*C\) to \(1.15*C\).
Thus \(1.1*C\) < C < \(1.15*C\)
30.25 < C < 31.625

Answer (B)
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Re: An item cost $27.50 before tax. If the tax on the item was more than [#permalink] New post   20 Aug 2019, 10:19
An item cost $27.50 before tax. If the tax on the item was more than 10 percent but less than 15 percent of the cost of the item before tax, then the total amount paid must have been between

min tax = 27.5*10% = $2.75
max tax = 27.5*15% = $4.125
Min total amount paid = 27.5 + 2.75 = $30.25
Max total amount paid = 27.5 + 4.125 = $31.625

\(30.25 \leq\) Total amount paid \(\leq 31.625\)
The Toal amount paid must have been between $30 and $32

IMO B
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Re: An item cost $27.50 before tax. If the tax on the item was more than [#permalink] New post   20 Aug 2019, 12:54
IMO B

Lets us take 10% and 15% as extremes of 2 tax slabs applicable:
27.5+ 10% of 27.5 = 30.25
27.5+15% of 27.5 = 31.62


so its between $30-$32
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Re: An item cost $27.50 before tax. If the tax on the item was more than [#permalink] New post   20 Aug 2019, 15:16
From the question stem we know price before tax is $27.5,and that tax on the item is more than 10% but less than 15%.
We are to find the range of the amount paid for the item.

Looking at the answer choices, every choice is unique in terms of the amount paid. Hence computing the possible lower bound or upper bound for the price should be sufficient.

I choose the lower bound for the price because it is easier for me to compute.

1.1*27.5 = 2.75 + 27.5 = 30.25.

Only option B has 30 as the possible lower price bound. The answer is therefore B.

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Re: An item cost $27.50 before tax. If the tax on the item was more than [#permalink]
20 Aug 2019, 15:16
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