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# Last year the average (arithmetic mean) salary of the 10

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Last year the average (arithmetic mean) salary of the 10 [#permalink]

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02 Dec 2006, 07:07
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Last year the average (arithmetic mean) salary of the 10 employees of Company X was \$42,800. What is the average salary of the same 10 employees this year?

1) For 8 of the 10 employees, this year's salary is 15 percent greater than last year's salary.
2) For 2 of the 10 employees, this year's salary is the same as last year's salary.

Official Guide 12 Question

 Question: 46 Page: 26 Difficulty: 700

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Video Explanations:

OPEN DISCUSSION OF THIS QUESTION IS HERE: last-year-the-average-arithmetic-mean-salary-of-the-135830.html
[Reveal] Spoiler: OA

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Re: Last year the average (arithmetic mean) salary of the 10 [#permalink]

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02 Dec 2006, 07:21
E for me

From 1) Depending on which two employees didn't get 15% increase would affect the overall total. Eg if top two salaries didn't get the 15% increase then it would yield a lower total and hence average than if the bottom two salaries didn't get a 15% increase. INSUFF

From 2) This tells us even less than 1). What % change in salary did others get? Which two salaries didn't get increase? INSUFF

Together,
Still dont know which two employees didn't get increase and the respective salaries of the others.

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Re: Last year the average (arithmetic mean) salary of the 10 [#permalink]

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02 Dec 2006, 07:21
Straight E.

If they were to mention in the second statement that, these 2 are excluding those 8, then something is possible.

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Re: Last year the average (arithmetic mean) salary of the 10 [#permalink]

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02 Dec 2006, 07:23
Can you please explain why? From statement 1 wouldn't you know that for 8 of the 10 employees, the salary is now \$49,220 (42,800 * 1.15)...and from statement 2 you would know that the salary of the remaining 2 is (still) 42,800? Thus you could do:

(49220*8) + (42800*2)
--------------------------- = average salary
10

..and thus the answer would be C. How is that wrong?

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Re: Last year the average (arithmetic mean) salary of the 10 [#permalink]

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02 Dec 2006, 07:27
aurobindo wrote:
Straight E.

If they were to mention in the second statement that, these 2 are excluding those 8, then something is possible.

It still wouldn't help - taking both together we know that 8 got 15% increase but 2 got no increase (or loss). However, we'd still need to know where in the range of salaries those two employees were.

Eg.
Take a set of numbers 2,3,5,6 Mean = 4

If you double the lowest 3 numbers you get 4,6,10,6 Mean = 6.5
If you double the highest 3 numbers you get 2,6,10,12 Mean = 7.5

So simply knowing that x number of employees got/didn't get an increase doesn't help

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Re: Last year the average (arithmetic mean) salary of the 10 [#permalink]

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02 Dec 2006, 07:30
Last year the average (arithmetic mean) salary of the 10 employees of Company X was \$42,800. What is the average salary of the same 10 employees this year?

1) For 8 of the 10 employees, this year's salary is 15 percent greater than last year's salary.

2) For 2 of the 10 employees, this year's salary is the same as last year's salary.

Let the salaries of the 10 be a1, a2...a10

given: 42800 = (a1+a2+..+a10)/10 => sum(a1...+a10) = 428000
also: a1+a2..a8 = (42800)-(a9+a10)

also given: a1(year2) = 1.15a1..similarly till a8

1.15a1+1.15a2.....1.15a8 = (a1...a8)+0.15(a1...a8)

from 2:

a9, a10 is same

combining
(a1+a2...a8)+a9+a10 + 0.15(a1...a8)/10

still cannot be determined. So E

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Re: Last year the average (arithmetic mean) salary of the 10 [#permalink]

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19 Apr 2010, 18:15
I'm really sorry to bump such an old thread but qant to play devil's advocate with this question.
If statement 2 stated that the lowest two salaries of the ten employees stayed the same, then the both of the statements together would be sufficient correct?

The average of the salaries would be ((42800*2)+(1.15*42800*8))/10= 47936

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Re: Last year the average (arithmetic mean) salary of the 10 [#permalink]

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20 Apr 2010, 12:26
You have no information on what the lowest 2 salaries were, just that the average was 42,800. What you assumed was the extra information tells us that the two lowest salaries stayed the same is not equivalent to they were the average values.

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Re: Last year the average (arithmetic mean) salary of the 10 [#permalink]

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04 Oct 2015, 12:29
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Re: Last year the average (arithmetic mean) salary of the 10 [#permalink]

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04 Oct 2015, 19:53
Expert's post
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ellisje22 wrote:
Last year the average (arithmetic mean) salary of the 10 employees of Company X was \$42,800. What is the average salary of the same 10 employees this year?

1) For 8 of the 10 employees, this year's salary is 15 percent greater than last year's salary.
2) For 2 of the 10 employees, this year's salary is the same as last year's salary.

Official Guide 12 Question

 Question: 46 Page: 26 Difficulty: 700

Find All Official Guide Questions

Video Explanations:

Last year the average (arithmetic mean) salary of the 10 employees of Company X was \$42,800. What is the average salary of the same 10 employees this year?

(1) For 8 of the 10 employees, this year’s salary is 15 percent greater than last year’s salary.
(2) For 2 of the 10 employees, this year’s salary is the same as last year’s salary.

Given: total salary is \$42,800*10. Question: new total salary=?

Each statement together is not sufficient.

When taken together. Consider two possible cases:
2 lowest salaries didn't change and 8 highest salaries increased by 15%;
2 highest salaries didn't change and 8 lowest salaries increased by 15%;

Ask yourself, would new total salary be the same for both cases? No, because increase in amount for the first case will be more than increase in amount for the second case. Hence even taken together statements are not sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: last-year-the-average-arithmetic-mean-salary-of-the-135830.html
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Re: Last year the average (arithmetic mean) salary of the 10   [#permalink] 04 Oct 2015, 19:53
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