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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)  [#permalink]

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01 Dec 2018, 09:07
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35% (medium)

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69% (01:56) correct 31% (02:20) wrong based on 156 sessions

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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

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Re: Over the last three years a scientist had an average (arithmetic mean)  [#permalink]

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01 Dec 2018, 09:25
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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$Income in second year = 1.5(27000) = 40,500$

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Re: Over the last three years a scientist had an average (arithmetic mean)  [#permalink]

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01 Dec 2018, 16:21
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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 VP Joined: 09 Mar 2016 Posts: 1230 Over the last three years a scientist had an average (arithmetic mean) [#permalink] ### Show Tags 02 Dec 2018, 04:00 1 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 = $$\frac{3}{2} * 27000 = 40,500$$ Director Joined: 09 Mar 2018 Posts: 994 Location: India Re: Over the last three years a scientist had an average (arithmetic mean) [#permalink] ### Show Tags 10 Feb 2019, 21:09 HKD1710 wrote: 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 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 _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. Manager Joined: 23 Apr 2018 Posts: 139 Over the last three years a scientist had an average (arithmetic mean) [#permalink] ### Show Tags 17 Jun 2019, 05:42 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

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..
Over the last three years a scientist had an average (arithmetic mean)   [#permalink] 17 Jun 2019, 05:42
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