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The total income of Mr. Teng in the years 2003, 2004, and 2005 was $36

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The total income of Mr. Teng in the years 2003, 2004, and 2005 was $36  [#permalink]

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New post 10 Apr 2019, 23:45
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (02:04) correct 31% (02:06) wrong based on 26 sessions

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Re: The total income of Mr. Teng in the years 2003, 2004, and 2005 was $36  [#permalink]

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New post 11 Apr 2019, 00:04
The total income of Mr. Teng in the years 2003, 2004, and 2005 was $36,400. His income increased by 20% each year. What was his income in 2005?

(A) 5,600
(B) 8,800
(C) 10,000
(D) 12,000
(E) 14,400

Let income in 2003 = x
implies,
income in 2004 = 1.2*x (20% greater than 2003)
income in 2005 = 1.2(1.2*x) ( 20% greater than 2004)

Total income = x + 1.2*x + 1.44*x = 36400 (given)
3.64*x = 36400
x = 10000

So, income in 2005 = 1.44*10000
= 14400

Option E is correct
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Re: The total income of Mr. Teng in the years 2003, 2004, and 2005 was $36  [#permalink]

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New post 11 Apr 2019, 00:07
2003 --> x income
2004 --> 1.2x income
2005 --> 1.2*1.2x=1.44x

According to the stem:
x+1.2x+1.44x=36400
x=10 000

1.44x=14400

IMO
ANs: E
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Re: The total income of Mr. Teng in the years 2003, 2004, and 2005 was $36  [#permalink]

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New post 11 Apr 2019, 00:10
Bunuel wrote:
The total income of Mr. Teng in the years 2003, 2004, and 2005 was $36,400. His income increased by 20% each year. What was his income in 2005?

(A) 5,600
(B) 8,800
(C) 10,000
(D) 12,000
(E) 14,400



suppose,

income in 2003 = 100

income in 2004 = 120

income in 2005 = 144.

Total = 364.

when total income 364, 2005's income is 144

when total income 1, 2005's income is 144/364

when total income 36400, 2005's income is = 144/364 * 36400 = 14400.

E is the correct answer.
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Re: The total income of Mr. Teng in the years 2003, 2004, and 2005 was $36  [#permalink]

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New post 11 Apr 2019, 03:05
Bunuel wrote:
The total income of Mr. Teng in the years 2003, 2004, and 2005 was $36,400. His income increased by 20% each year. What was his income in 2005?

(A) 5,600
(B) 8,800
(C) 10,000
(D) 12,000
(E) 14,400


income 2003 = x
2004 = 1.2x
2005 = 1.44 x
so total 3.64 x = 36400
x= 10,000
2005 income = 10,000*1.4 ; 14,400
IMO E
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Re: The total income of Mr. Teng in the years 2003, 2004, and 2005 was $36  [#permalink]

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New post 14 Apr 2019, 18:46
Bunuel wrote:
The total income of Mr. Teng in the years 2003, 2004, and 2005 was $36,400. His income increased by 20% each year. What was his income in 2005?

(A) 5,600
(B) 8,800
(C) 10,000
(D) 12,000
(E) 14,400


We can let n = his income in 2003; thus:

n + 1.2n + (1.2)^2 * n = 36,400

2.2n + 1.44n = 36,400

3.64n = 36,400

n = 36,400/3.64 = 3,640,000/364 = 10,000

Hence, his income in 2005 was (1.2)^2*10000 = 14,400.

Alternate Solution:

Notice that Mr. Teng’s income in 2005 was the greatest among the three years 2003, 2004 and 2005. Thus, his income in 2005 must be greater than the 3-year average of 36400/3 = 12133 1/3 . Only answer choice E is greater than 12133 1/3.

Answer: E
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Re: The total income of Mr. Teng in the years 2003, 2004, and 2005 was $36   [#permalink] 14 Apr 2019, 18:46
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