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21 Jun 2022, 01:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
71% (03:04) correct
29%
(02:38)
wrong
based on 156
sessions
History
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Time
Result
Not Attempted Yet
The state income tax where Kristin lives is levied at the rate of p% of the first $28000 of annual income plus (p + 2)% of any amount above $28000. Kristin noticed that the state income tax she paid amounted to (p + 0.25)% of her annual income. What was her annual income?
(A) $28000
(B) $32000
(C) $35000
(D) $42000
(E) $56000
Are You Up For the Challenge: 700 Level Questions
(A) $28000
(B) $32000
(C) $35000
(D) $42000
(E) $56000
Are You Up For the Challenge: 700 Level Questions
21 Jun 2022, 02:45
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Let A be her annual income.
The answer has no dependency on the value of p. Let's assume p to be 0%. And we have,
(A-28000)*2/100 = A*0.25/100
2A-56000=A/4
(7/4)A=56000
A=32000
The answer is thus (B).
The answer has no dependency on the value of p. Let's assume p to be 0%. And we have,
(A-28000)*2/100 = A*0.25/100
2A-56000=A/4
(7/4)A=56000
A=32000
The answer is thus (B).
General Discussion
21 Jun 2022, 07:00
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Bunuel
Let p=0. implying the following:
Percentage for the first $28000 = p = 0%
Percentage for the remaining amount = p+2 = 2%
Percentage for the MIXTURE of the two amounts = p+0.25 = 0.25%
Let F = the first $28000 and R = the remaining amount.
The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: Plot the 3 percentages on a number line, with the percentages for F and R on the ends and the percentage for the mixture in the middle.
F 0%-------------0.25%------------2% R
Step 2: Calculate the distances between the percentages.
F 0%-----0.25-----0.25%-----1.75-----2% R
Step 3: Determine the ratio for the mixture.
The ratio of F to R is equal to the RECIPROCAL of the distances in red.
F:R = 1.75 : 0.25 = 175:25 = 7:1
The sum of the parts of the ratio = 7+1 = 8
Implication:
Of every $8 of income, F constitutes $7 and R constitutes $1, with the result that F ($28000) must be equal to 7/8 of the total income:
\(28000 = \frac{7}{8}x\)
\(28000*8 = 7x\)
\(4000*8 = x\)
\(x = 32000\)
