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Updated on: 29 Nov 2018, 03:24
00:00

Difficulty:

85% (hard)

Question Stats:

45% (02:39) correct 55% (02:24) wrong based on 76 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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Originally posted by EgmatQuantExpert on 09 Oct 2018, 03:06.
Last edited by EgmatQuantExpert on 29 Nov 2018, 03:24, edited 2 times in total.
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: A person needs to pay a tax of 5% over the excess bill of $1000 ...... [#permalink] ### Show Tags 09 Oct 2018, 03:57 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 E _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html GMAT Expert e-GMAT Representative Joined: 04 Jan 2015 Posts: 2568 Re: A person needs to pay a tax of 5% over the excess bill of$1000 ......  [#permalink]

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11 Oct 2018, 03:34

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.

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