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For Jack, income tax is between 15 and 35 percent of total i

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For Jack, income tax is between 15 and 35 percent of total i [#permalink] New post 10 May 2020, 13:30
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For Jack, income tax is between 15 and 35 percent of total income after an "exclusion" amount has been subtracted (that is, Jack does not have to pay any income tax on the exclusion amount, only on the remainder of his total income). If the exclusion amount is between $5,200 and $9,800, and Jack's income tax was $8,700, which of the following could have been Jack's total income?

❑ $13,000

❑ $23,100

❑ $33,200

❑ $43,300

❑ $53,400

❑ $63,500

❑ $73,600


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Re: For Jack, income tax is between 15 and 35 percent of total i [#permalink] New post 10 May 2020, 14:02
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Re: For Jack, income tax is between 15 and 35 percent of total i [#permalink] New post 10 May 2020, 21:57
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We are given that income tax percent is between 15 and 35 and the amount of income tax is $8,700.
Thus, 8,700= 15/100 x, thus x= 24,857 and 8,700= 35/100 x, thus x= 58,000.
To find the range, add exclusion amount to these numbers.
Thus, 58,000 + 9,800 = 67,800 (high) and 24,857 + 5,200 = 30,057 (low).
Options C, D, E and F are inside this range.
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Re: For Jack, income tax is between 15 and 35 percent of total i [#permalink] New post 16 Jun 2020, 08:14
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I would start this sum by doing trial and error. I would randomly choose any number which is not too extreme maybe 23100 in the above sum. Irrespective of the exclusion amount he paid 8700 as tax. So, I would subtract 23100-8700=14400 35% of 14400 which is 5040 it is not between $5,200 and $9,800 so I can negate option A and B as A is smaller than B. Then rather than checking the next number that the value would at least rise to $5200 so C is in. I can then check last or the second last value if I consider $63,500-8700=54800*15%=8220 satisfies moving forward to 73600-8700=64900*15%=9735 negating my last option too and all the values between 33200 and 63500 are my answer. Thus C, D, E, F.
And a suggestion this question would definitely not be a sum I would like to do it in my first go until and unless I am good with arithmetic.
Re: For Jack, income tax is between 15 and 35 percent of total i   [#permalink] 16 Jun 2020, 08:14
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For Jack, income tax is between 15 and 35 percent of total i

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