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

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GMAT Expert