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Question of the Week- 12 (For any purchase of less than $1000, a ...)

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Question of the Week- 12 (For any purchase of less than $1000, a ...)  [#permalink]

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New post 25 Aug 2018, 11:09
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e-GMAT Question of the Week #12


For any purchase of less than $1000, a person doesn’t need to pay any tax. However, if the purchase value is between $1000 and $2000 included, then the tax is 5% of the excess value over $1000. Also, if the purchase value is more than $2000, then one needs to pay an additional tax of 10% on the excess value over $2000. Which of the following can be the possible purchase value, such that the total tax paid is not more than 4% of the total purchase value?

    A. 2499
    B. 2599
    C. 2699
    D. 2799
    E. 2801

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Question of the Week- 12 (For any purchase of less than $1000, a ...)  [#permalink]

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New post 25 Aug 2018, 19:55
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EgmatQuantExpert wrote:
e-GMAT Question of the Week #12


For any purchase of less than $1000, a person doesn’t need to pay any tax. However, if the purchase value is between $1000 and $2000 included, then the tax is 5% of the excess value over $1000. Also, if the purchase value is more than $2000, then one needs to pay an additional tax of 10% on the excess value over $2000. Which of the following can be the possible purchase value, such that the total tax paid is not more than 4% of the total purchase value?

    A. 2499
    B. 2599
    C. 2699
    D. 2799
    E. 2801

Image



Hi..

The question asks for the value and surely ONLY one value should fit in. It has to be the lowest given.
A
Say B is possible, then A<B so A will also be possible and we will have two answers.
So No calculations required and you can press A


Otherwise, if you were to find SAY " max possible integer amount such that the % remains below 4%"

0-1000....Nil
1001-2000...5%
Above 2000....10%
4%of X=5% of 1000 + 10% of (x-2000)
0.04x=50+(0.1x-200)......0.04x=50+0.1x-200.....0.1x-0.04x=150
0.06x=150......6x=15000.....X=2500
So 2499 will be just below 4%

A
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Re: Question of the Week- 12 (For any purchase of less than $1000, a ...)  [#permalink]

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New post 25 Aug 2018, 20:19
EgmatQuantExpert wrote:
For any purchase of less than $1000, a person doesn’t need to pay any tax. However, if the purchase value is between $1000 and $2000 included, then the tax is 5% of the excess value over $1000. Also, if the purchase value is more than $2000, then one needs to pay an additional tax of 10% on the excess value over $2000. Which of the following can be the possible purchase value, such that the total tax paid is not more than 4% of the total purchase value?

    A. 2499
    B. 2599
    C. 2699
    D. 2799
    E. 2801



Going by answer options might be a good idea in this case

A. 2499 -> 5% of 1000 + 10% of 499 -> 50 + 49.9 = 99.9 which is less than 4% of 2499 = 24.99*0.4 = 99.96

Therefore, the tax paid is not more than 4% of the overall purchase value for $2499(Option A)
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Re: Question of the Week- 12 (For any purchase of less than $1000, a ...)  [#permalink]

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New post 25 Aug 2018, 21:10
EgmatQuantExpert wrote:
For any purchase of less than $1000, a person doesn’t need to pay any tax. However, if the purchase value is between $1000 and $2000 included, then the tax is 5% of the excess value over $1000. Also, if the purchase value is more than $2000, then one needs to pay an additional tax of 10% on the excess value over $2000. Which of the following can be the possible purchase value, such that the total tax paid is not more than 4% of the total purchase value?

    A. 2499
    B. 2599
    C. 2699
    D. 2799
    E. 2801


Since all the answer choices are between 2000 and 3000. let us assume that the value would be $(2000+x)
Now calculating the tax.
5% of 1000 + 10% of x. Now this tax should be less than 4% of the whole amount !
= 50 +0.1x < 4% of (2000+x)
= 50 +0.1x < 80 + 0.04x
=0.06x < 30
or x<500

Hence, Answer Choice A is the answer!
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Re: Question of the Week- 12 (For any purchase of less than $1000, a ...)  [#permalink]

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New post 14 Sep 2018, 01:10

Solution


Given:
    • We are given three cases,
      o Case 1: If the purchase value < $1000, then no need to pay tax
      o Case 2: If the purchase value is between $1000 and $2000, then the tax = 5% of the excess value over $1000
      o Case 3: If the purchase value > $2000, then the tax = 5% of ($2000 – $1000) + 10% of the excess value over $2000.

To find:
    • Possible purchase value, such that the total tax paid ≤ 4% of the total purchase value

Approach and Working:
    • So, if we observe, all the options given are greater than $2000
    • Thus, we can directly consider Case-2, where the purchase value is greater than $2000
    • Now, let us assume that the purchase value = $x, such that x > $2000
    • So, the total tax paid = 5% of $1000 + 10% of ($x – $2000)
    • This value should be less than or equal to 4% of x,
      o 5% of $1000 + 10% of ($x – $2000) ≤ 4% of x
      o \($50 + \frac{10x}{100} - $200 ≤ \frac{4x}{100}\)
      o Implies, \(\frac{6x}{100} ≤ $150\)
      o Thus, x ≤ $2500

Therefore, the purchase value must be less than or equal to $2500

Hence, the correct answer is option A.

Answer: A

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Re: Question of the Week- 12 (For any purchase of less than $1000, a ...) &nbs [#permalink] 14 Sep 2018, 01:10
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