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

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Math Expert
Joined: 02 Sep 2009
Posts: 65761
For Jack, income tax is between 15 and 35 percent of total income afte  [#permalink]

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23 Jun 2020, 05:29
00:00

Difficulty:

45% (medium)

Question Stats:

80% (02:29) correct 20% (03:44) wrong based on 10 sessions

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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?

I. \$33,200
II. \$43,300
III. \$73,600

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

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Re: For Jack, income tax is between 15 and 35 percent of total income afte  [#permalink]

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23 Jun 2020, 06:13
Least value of income will be when Least amount is deducted and maximum percent of Income tax is charged.

Let total income = T
Least value deducted = 5200
And maximum percent of income tax = 35%

=> (T-5200)*0.35 = 8700
=> 0.35T - 1820 = 8700
=> 0.35T = 10520
=> T = 30057 (Least salary of jack)

Similarly,

Maximum value of income will be when most amount is deducted and minimum percent of Income tax is charged.

Let total income = T
Least value deducted = 9800
And maximum percent of income tax = 15%

=> (T-9800)*0.15 = 8700
=> 0.15T - 1470 = 8700
=> 0.15T = 10170
=> T = 67800 (maximum salary of jack)

Jack salary will lie in the bracket of 30057<Salary<67800

And only 1&2 fit the constraints.

IMO C

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Re: For Jack, income tax is between 15 and 35 percent of total income afte   [#permalink] 23 Jun 2020, 06:13