I'm visiting an unfamiliar state. This state has a sales tax of 6.1% but I don't know this. All I know is the tax rate is of the form a.b% where a and b are single digits.

I buy an item at a store and am able to deduce the tax rate from the item's price and the tax amount as listed on the receipt.

What is the minimum cost of the item that would allow me to make such a deduction?

Note: The tax amount listed on the receipt is rounded to the nearest cent.

I have not looked at the slew of other answers, but I like to imagine agreement. At 6.0, 6.1, and 6.2% tax rates a $5.41 item distinguishes itself with 3 unique prices: 

        program taxes

        implicit none

        real tax(3),cost(3)

        integer i,j,icost(3)

        data tax/.06,.061,.062/

           do i = 1,1000

                do j=1,3

                cost(j)=i*(1+tax(j))

                icost(j)=0.5+cost(j)

                enddo

                if(icost(1).ne.icost(2).and.icost(2).ne.icost(3))then

                print 2,i,icost,cost

                stop

                endif

2          format(i4,2x,3(i4,2x),2x,3(f7.2,2x))

           enddo

        end

rabbit-3:~ lord$ tax

 541   573   574   575     573.46   574.00   574.54 

Edited on August 22, 2018, 3:43 pm

Posted by Steven Lord on 2018-08-22 15:33:14