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A person needs to pay a tax of 5% over the excess bill of $1000 ......

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EgmatQuantExpert
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A person needs to pay a tax of 5% over the excess bill of $1000 ...... [#permalink] New post   Updated on: 29 Nov 2018, 04:24
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95% (hard)

Question Stats:

49% (02:41) correct 51% (02:35) wrong based on 203 sessions
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A person needs to pay a tax of 5% over the excess bill of $1000 purchase. However, if the total bill (i.e. purchase bill + tax) exceeds $1999, then he needs to pay a tax of 10% over the excess purchase of $1000. What can be the maximum purchase bill amount which will ensure that the person pays only 5% tax?

    A. $1001
    B. $1500
    C. $1543.24
    D. $1950
    E. $1951.43

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E

Originally posted by EgmatQuantExpert on 09 Oct 2018, 04:06.
Last edited by EgmatQuantExpert on 29 Nov 2018, 04:24, edited 2 times in total.
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Re: A person needs to pay a tax of 5% over the excess bill of $1000 ...... [#permalink] New post   09 Oct 2018, 04:57
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EgmatQuantExpert wrote:
A person needs to pay a tax of 5% over the excess bill of $1000 purchase. However, if the total bill (i.e. purchase bill + tax) exceeds $1999, then he needs to pay a tax of 10% over the excess purchase of $1000. What can be the maximum purchase bill amount which will ensure that the person pays only 5% tax?

    A. $1001
    B. $1500
    C. $1543.24
    D. $1950
    E. $1951.43


As there is no tax in 1000, we can deduct 1000 from 1999 to get 1999-1000=999
So \((1+\frac{5}{100})*x<999......105x<99900........x<951.5.\)
So 1000+951.43 is the correct answer..

How do we avoid calculations?
No tax on 1000 so 5% on 1000 is 50 thus amount increase above 1999...
So let us take 950 which is in choice D, 5% on 950 =47.5..
So add 47.5 on 1950=1950+47.5=1997.5
So 1950 is not the highest, we can increase by 1 and the increase in tax will be 0.05 so 1951 will give 1951+47.5+0.05=1998.55
So 1951.43 must be correct

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Re: A person needs to pay a tax of 5% over the excess bill of $1000 ...... [#permalink] New post   11 Oct 2018, 04:34
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Solution


Given:
    • A person needs to pay a tax of 5% over the excess bills of $1000 purchase
    • And if the total bill exceeds $1999, he needs to pay a tax of 10% over the excess purchase of $1000

To find:
    • Maximum purchase bill amount, such that he needs to pay only 5% tax

Approach and Working:
According to the given information, for him to pay a 5% tax over the excess bill, the purchase bill amount must be greater than $1000, and it cannot be greater than 1999

    • So, let us assume the purchase bill amount as x
    • Now, the total bill amount will be = purchase amount + tax
      o Where, purchase amount = x, and tax = 5% of (x -1000)

    • Thus, total bill amount = x + 5(x - 1000)/100 = 1.05x - 50
      o This must be maximum, which is equal to 1999, since if it exceeds 1999, then he needs to pay 10% tax

    • Therefore, 1.05x = 2049
      o Implies, x = 2049/1.05 = 1951.43

Hence, the correct answer is option E.

Answer: E

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Re: A person needs to pay a tax of 5% over the excess bill of $1000 ...... [#permalink] New post   22 Aug 2019, 01:42
EgmatQuantExpert wrote:

Solution


Given:
    • A person needs to pay a tax of 5% over the excess bills of $1000 purchase
    • And if the total bill exceeds $1999, he needs to pay a tax of 10% over the excess purchase of $1000

To find:
    • Maximum purchase bill amount, such that he needs to pay only 5% tax

Approach and Working:
According to the given information, for him to pay a 5% tax over the excess bill, the purchase bill amount must be greater than $1000, and it cannot be greater than 1999

    • So, let us assume the purchase bill amount as x
    • Now, the total bill amount will be = purchase amount + tax
      o Where, purchase amount = x, and tax = 5% of (x -1000)

    • Thus, total bill amount = x + 5(x - 1000)/100 = 1.05x - 50
      o This must be maximum, which is equal to 1999, since if it exceeds 1999, then he needs to pay 10% tax

    • Therefore, 1.05x = 2049
      o Implies, x = 2049/1.05 = 1951.43

Hence, the correct answer is option E.

Answer: E



How you get 2049/1.05 = 1951.43? It is 1951.428, so answer E is incorrect, as it exceeds this number. Correct answer should be D, as it is maximum possible number that is less than 1951.428
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Re: A person needs to pay a tax of 5% over the excess bill of $1000 ...... [#permalink] New post   22 Apr 2021, 09:45
So the question is asking what is the maximum amount so the patron does not have to pay the 10% excess tax that kicks in when the (bill + 5% tax paid) exceeds > $1,999

A problem solving MAX/MIN problem such as this, starting from the HIGHEST choice and working down is the smart way to approach testing the answer choices.

(E) If the bill is $1,951.43

Then for every dollar above $1,000 a 5% tax must be paid

951.43

10% move the decimal one place to the left

Then to get 5%, take 1/2 or that result

95.143

Tax paid = 47.5715


Does the (Bill) + (Tax Paid) > 1,999?

If so, then 10% tax will have to be paid and the number is too high

(1951.43) + (47.5715) ~ will be just around 1,999, and certainly will not exceed $1,999

Thus, E is the answer. This is the most the bill can be and only the 5% tax will be paid.


There are some good questions in the E-GMAT series. However, I wish the question stems were composed with an eye towards proper diction.

This is one of the better examples.

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Re: A person needs to pay a tax of 5% over the excess bill of $1000 ...... [#permalink]
22 Apr 2021, 09:45
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