Over the last three years a scientist had an average (arithmetic mean)

Question

Over the last three years a scientist had an average (arithmetic mean) yearly income of $45,000. The scientist earned $1\frac{1}{2}$ times as much the second year as the first year and $2\frac{1}{2}$ times as much the third year as the first year. What was the scientist's income the second year?

(A) $9,000
(B) $13,500
(e) $27,000
(D) $40,500
(E) $45,000

(A) $9,000
(B) $13,500
(e) $27,000
(D) $40,500
(E) $45,000

Chethan92 · Answer

Average of 3 years = 45,000$
Total income in 3 years = 135,000$

Let the income in first year be x.
Now, x+3/2x+5/x = 135,000
x = 27,000$

Income in second year = 1.5(27000) = 40,500$

D is the answer.

dollytaneja51 · Answer

Let first year salary be x
then second year salary = 1.5x
Third year = 2.5 x
Average salary for three years is 45000 which means total salary for 3 years = 45000(3)
x+1.5x+2.5x=135000
5x=135000
x=27000

Second year salary is 1.5x= 1.5*27000
=$40,500

D is the correct answer

dave13 · Answer

Average income for three months is 45000, then total income for three months is 45,000*3 = 135,000

"The scientist earned  1\frac{1}{2}  times as much the second year as the first year"

So,

Let First year be  x

Then second Year is  \frac{3x}{2}

"and  2\frac{1}{2}  times as much the third year as the first year"

So third Year is  \frac{5x}{2}

\frac{X}{1} +\frac{3x}{2}+\frac{5x}{2} = 135,000

\frac{10x}{2}  =  135,000

10x = 270,000

x = 27,000

Second year =  \frac{3}{2} * 27000 = 40,500

KanishkM · Answer

3 Years AM = 45000, Total Sum will be 135000

Given Y2 = 3/2 Y1
Y3 = 5/2 Y1

Y1 + Y2 + Y3 = 135000
substitute for above 
Y1 = 27000

Y2 = 3/2 Y1 = 40500

D

Shrey9 · Answer

Over the last three years a scientist had an average (arithmetic mean) yearly income of $45,000. The scientist earned $1\frac{1}{2}$ times as much the second year as the first year and $2\frac{1}{2}$ times as much the third year as the first year. What was the scientist's income the second year?

(A) $9,000
(B) $13,500
(e) $27,000
(D) $40,500
(E) $45,000

(A) $9,000
(B) $13,500
(e) $27,000
(D) $40,500
(E) $45,000

guys, I got this one right, but this sort of language always confuses me.. I am getting used to it, but not being a native leads me to a confusion. I sometimes think of it as
F = 3/2 S and then later on, thinking logically, I changed it to S= 3/2 F (as usually salary increments), but then its the GMAT, so one should be prepared...
can anyone help me find a way to debug such language ?

any help from language experts will be appreciated too..

bumpbot · Answer

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Over the last three years a scientist had an average (arithmetic mean)

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Over the last three years a scientist had an average (arithmetic mean)

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