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25 Aug 2018, 11:09
00:00

Difficulty:

65% (hard)

Question Stats:

59% (02:47) correct 41% (03:04) wrong based on 110 sessions

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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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Math Expert
Joined: 02 Aug 2009
Posts: 7422

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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) _________________ You've got what it takes, but it will take everything you've got ISB, NUS, NTU Moderator Joined: 11 Aug 2016 Posts: 376 Re: Question of the Week- 12 (For any purchase of less than$1000, a ...)  [#permalink]

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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! _________________ ~R. If my post was of any help to you, You can thank me in the form of Kudos!! Applying to ISB ? Check out the ISB Application Kit. e-GMAT Representative Joined: 04 Jan 2015 Posts: 2710 Re: Question of the Week- 12 (For any purchase of less than$1000, a ...)  [#permalink]

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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.

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