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

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

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16 Jul 2012, 04:51
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Difficulty:

45% (medium)

Question Stats:

61% (00:58) correct 39% (00:57) wrong based on 1067 sessions

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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.

Diagnostic Test
Question: 46
Page: 26
Difficulty: 650
[Reveal] Spoiler: OA

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

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20 Jul 2012, 04:16
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SOLUTION

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?

Note that it's almost always better to express the average in terms of the sum.

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

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

(1)+(2) 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 the increase in amount for the first case will be greater than the increase in amount for the second case. Hence even taken together statements are not sufficient.

Hope it's clear.
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Re: Last year the average (arithmetic mean) salary of the 10 [#permalink]

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27 Sep 2013, 17:12
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Re: Last year the average (arithmetic mean) salary of the 10 [#permalink]

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26 Nov 2013, 01:19
Bunuel,
I chose E as well for this Q . However, my approach was as follows

Since we do not have information about individuals salary .. the \$42,8000 can be split in any way ( ie . one person might have earned 20000, another person 3000 etc etc ) . Had the question mentioned about the individuals salary being the same.. the answer would have been different . Hence we cannot assume which individual got a raise and who did not ..

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

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02 May 2014, 13:46
I chose C but the key point that helped me understand the issue was that we are being told the average salary of 10 people and not 8 so even if we combine the statements, we still do not get clarity on what is the average (or individual) salary of the 8 people mentioned in statement (1).
Thanks.

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

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13 May 2014, 01:22
thinktank wrote:
Bunuel,
I chose E as well for this Q . However, my approach was as follows

Since we do not have information about individuals salary .. the \$42,8000 can be split in any way ( ie . one person might have earned 20000, another person 3000 etc etc ) . Had the question mentioned about the individuals salary being the same.. the answer would have been different . Hence we cannot assume which individual got a raise and who did not ..

I have the same thought process Bunuel. Are we on right track ?

In others words we know that Total of 10 salary for Year 1 = 42800*10 = 428000. This is in no ways indicates that each employee had similar salary. it could be something like S(1) + S(2) .......S(10) = 428000. Here any of the 8 salaries could be increased by 15 % and any of the 2 could remain unchanged so finding the new average salary is impossible.

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

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13 May 2014, 07:42
himanshujovi wrote:
thinktank wrote:
Bunuel,
I chose E as well for this Q . However, my approach was as follows

Since we do not have information about individuals salary .. the \$42,8000 can be split in any way ( ie . one person might have earned 20000, another person 3000 etc etc ) . Had the question mentioned about the individuals salary being the same.. the answer would have been different . Hence we cannot assume which individual got a raise and who did not ..

I have the same thought process Bunuel. Are we on right track ?

In others words we know that Total of 10 salary for Year 1 = 42800*10 = 428000. This is in no ways indicates that each employee had similar salary. it could be something like S(1) + S(2) .......S(10) = 428000. Here any of the 8 salaries could be increased by 15 % and any of the 2 could remain unchanged so finding the new average salary is impossible.

Yes, that's correct.
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Re: Last year the average (arithmetic mean) salary of the 10 [#permalink]

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12 Jul 2015, 02:22
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Re: Last year the average (arithmetic mean) salary of the 10 [#permalink]

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21 Jul 2015, 14:42
@Brunuel I looked at it logically, the employees could get a raise next year since it was last years total, thats how i looked at it.
Moreover, I am confused on data sufficency of when to use logic and when to solve if it goes to the right idea? can you please help me thanks (any experts)

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

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14 Dec 2015, 02:47
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if the CEO and the CFO get increases of 15% then this should be a huge increase on average but the poorest in the company would not feel that.

the mean would not be that high if those 2 the richest would not get the increase still the mean is different so insufficient taken together.

BUT this question once again proves sufficient to show how mean can be the mean salary or mean income
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Re: Last year the average (arithmetic mean) salary of the 10 [#permalink]

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25 Dec 2016, 23:21
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Last year the average (arithmetic mean) salary of the 10 [#permalink]

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28 Dec 2016, 09:09
One of the Best Questions from the OG.
Here is what i did in this one =>

Clearly statement 1 and statement 2 are not sufficient on their own.
Combing the two statements =>
I used test cases ->

Case 1 => Let 2 employees be working for free whose value haven't changed and the rest of the values be very very big.=> Mean=> 15 percent increase.
Case 2=> Let the 8 employees be working for free and the two leftovers have very high salary => Mean would stay the same.

Hence E

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

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02 Jun 2017, 09:50
Bunuel 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.

Diagnostic Test
Question: 46
Page: 26
Difficulty: 650

This problem opens itself up nicely to testing cases if the intuition isn't obvious.

The goal is to determine the exact value of the average salary of the 10 employees this year.

Statement 1) Did the salaries of the other two employees increase or decrease? Insufficient.

Statement 2) Did the salaries of the other eight employees increase or decrease? Insufficient.

Statements 1+2) Let's assume they each have an equal salary (\$48,000). Then this statement would be sufficient. However, if the salaries are not equal, and 9 employees had a salary of \$1 and one employee had a salary of \$479,991, then clearly it matters which group this outlier employee falls into.

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Re: Last year the average (arithmetic mean) salary of the 10   [#permalink] 02 Jun 2017, 09:50
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