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salary of the 10 employees

by sanju09 » Mon Mar 12, 2012 2:49 am

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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 (arithmetic mean) 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.
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by killer1387 » Mon Mar 12, 2012 6:18 am

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IMO E
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by [email protected] » Tue Mar 13, 2012 3:31 am

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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 (arithmetic mean) 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.


Even my answer turns out to be E.

Statement 1: You know the average salary of all the 10 people of last year as $42800.

So you max you can come to know after all this is the total salary of the 10 people as $428000.

You do not know each one's salary so you cannot increase each by 15% and then find the average.

Also you do not know the minimum salary and the median salary or something like that to know the limits.

Neither do you know from statement 1 that the salary of the other 2 people whether increased or decreased or remained the same or if increase then by what % and if decrease then by what %.

Hence statement 1 insufficient...

Statement 2:
Same as above. Alone insufficient...


Combined 1 and 2:

when you combine the statements all you can find is that the average salary for this year is between

$42800 and 49220.

I got this by adding 15% increase of all the 10 people...

But other than that we clearly cannot find out as we do not know any limits of the salary of each person....

Hence E is the correct answer...


Hope i am right man...
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by sanju09 » Wed Mar 14, 2012 1:18 am

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Total salary of the 10 employees = $42,800 × 10 = $4, 28,000.

I. This statement means that 8 out of 10 employees are getting 15 percent more than $42,800 this year, or the total salary of those 8 employees is $42,800 × 8 × 1.15. in order to find the average salary of the same 10 employees this year, we need to know the total salary of the remaining 2 employees this year, which is not given. Insufficient

II. This statement means that 2 out of 10 employees are getting the same $42,800 each, this year too, hence this year's total salary of those 2 employees is $42,800 × 2. We need to know the total salary of the remaining 8 employees this year, which is not given. Insufficient

Taking I and II together, we can realize that the 8 employees mentioned in statement I have nothing to do with the 2 employees mentioned in statement II. Hence, total salary of the same 10 employees this year can be taken equal to $42,800 × 8 × 1.15 + $42,800 × 2 to answer the average (arithmetic mean) salary. [spoiler]Sufficient


OA C[/spoiler]
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by killer1387 » Wed Mar 14, 2012 1:28 am

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sanju09 wrote:Total salary of the 10 employees = $42,800 × 10 = $4, 28,000.

I. This statement means that 8 out of 10 employees are getting 15 percent more than $42,800 this year, or the total salary of those 8 employees is $42,800 × 8 × 1.15. in order to find the average salary of the same 10 employees this year, we need to know the total salary of the remaining 2 employees this year, which is not given. Insufficient

II. This statement means that 2 out of 10 employees are getting the same $42,800 each, this year too, hence this year's total salary of those 2 employees is $42,800 × 2. We need to know the total salary of the remaining 8 employees this year, which is not given. Insufficient

Taking I and II together, we can realize that the 8 employees mentioned in statement I have nothing to do with the 2 employees mentioned in statement II. Hence, total salary of the same 10 employees this year can be taken equal to $42,800 × 8 × 1.15 + $42,800 × 2 to answer the average (arithmetic mean) salary. [spoiler]Sufficient


OA C[/spoiler]
please elaborate on the part in bold.

I think its not possible to calculate from both 1 and 2

this yr's salary= 1.15 (a+b+c+d+e+f+g+h)+(i+j)

we only have a+b+c.....+j=428000

pls explain
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by sanju09 » Wed Mar 14, 2012 1:41 am

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killer1387 wrote:
sanju09 wrote:Total salary of the 10 employees = $42,800 × 10 = $4, 28,000.

I. This statement means that 8 out of 10 employees are getting 15 percent more than $42,800 this year, or the total salary of those 8 employees is $42,800 × 8 × 1.15. in order to find the average salary of the same 10 employees this year, we need to know the total salary of the remaining 2 employees this year, which is not given. Insufficient

II. This statement means that 2 out of 10 employees are getting the same $42,800 each, this year too, hence this year's total salary of those 2 employees is $42,800 × 2. We need to know the total salary of the remaining 8 employees this year, which is not given. Insufficient

Taking I and II together, we can realize that the 8 employees mentioned in statement I have nothing to do with the 2 employees mentioned in statement II. Hence, total salary of the same 10 employees this year can be taken equal to $42,800 × 8 × 1.15 + $42,800 × 2 to answer the average (arithmetic mean) salary. [spoiler]Sufficient


OA C[/spoiler]
please elaborate on the part in bold.

I think its not possible to calculate from both 1 and 2

this yr's salary= 1.15 (a+b+c+d+e+f+g+h)+(i+j)

we only have a+b+c.....+j=428000

pls explain
Please read what's in bold in my explanation above. If you agree, then (a + b + c + d + e + f + g + h) are all different from (i + j). The conclusion from stem "Total salary of the 10 employees = $42,800 X 10 = $4, 28,000." is not playing any role here.
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by killer1387 » Wed Mar 14, 2012 1:48 am

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sanju09 wrote:
killer1387 wrote:
sanju09 wrote:Total salary of the 10 employees = $42,800 × 10 = $4, 28,000.

I. This statement means that 8 out of 10 employees are getting 15 percent more than $42,800 this year, or the total salary of those 8 employees is $42,800 × 8 × 1.15. in order to find the average salary of the same 10 employees this year, we need to know the total salary of the remaining 2 employees this year, which is not given. Insufficient

II. This statement means that 2 out of 10 employees are getting the same $42,800 each, this year too, hence this year's total salary of those 2 employees is $42,800 × 2. We need to know the total salary of the remaining 8 employees this year, which is not given. Insufficient

Taking I and II together, we can realize that the 8 employees mentioned in statement I have nothing to do with the 2 employees mentioned in statement II. Hence, total salary of the same 10 employees this year can be taken equal to $42,800 × 8 × 1.15 + $42,800 × 2 to answer the average (arithmetic mean) salary. [spoiler]Sufficient


OA C[/spoiler]
please elaborate on the part in bold.

I think its not possible to calculate from both 1 and 2

this yr's salary= 1.15 (a+b+c+d+e+f+g+h)+(i+j)

we only have a+b+c.....+j=428000

pls explain
Please read what's in bold in my explanation above. If you agree, then (a + b + c + d + e + f + g + h) are all different from (i + j). The conclusion from stem "Total salary of the 10 employees = $42,800 X 10 = $4, 28,000." is not playing any role here.
That is ok i understand that but does this information makes us able to calculate the whole this year salary because we still dont know the break up of the grp of 8 and 2 people separately,

how can we reach this step: $42,800 × 8 × 1.15 + $42,800 × 2--> this means the average has been uniformly distributed among the 8 and 2 employees, which is not correct as no information states that in the question.

If possible could you please provide the procedure used to calculate this year salary from those two statements.


thnx
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by sanju09 » Wed Mar 14, 2012 2:02 am

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Oh dear...my dear...

Neither statement is talking about the average salary. Read the statements carefully and mind what "For 8 of the 10 employees" or "For 2 of the 10 employees" translate to. For your information, it translates to "each of 8" or "each of 2" mentioned respectively. Hence by multiplying new salary with the number of employees in each case, I am definitely not trying to distribute the average over number.
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by killer1387 » Wed Mar 14, 2012 3:08 am

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sanju09 wrote:Last year the average (arithmetic mean) salary of the 10 employees of Company X was $42,800. What is the average (arithmetic mean) 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 b1, b2...b10

given: 42800 = (b1+b2+..+b10)/10
=> b1+b2..+b8 = (428000)-(b9+b10)

statement 1:
also given: b1(year2) = 1.15b1..similarly till b8

1.15b1+1.15b2.....1.15b8 = (b1...b8)+0.15(b1...b8)
insufficient

statement 2:

b9, b10 is same
insufficient

1+2

(b1+b2...+b8)+b9+b10 + 0.15(b1...+b8)/10

0.15(b1...+b8) cant be determined

Insufficient
Hence E.

@sanju09
please point out what i am missing here. No offence but still i am not convinced by the distribution you provided. How can this part "0.15(b1...+b8)" be determined by the information available?

thnx
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by GMATGuruNY » Wed Mar 14, 2012 7:39 am

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sanju09 wrote:Last year the average (arithmetic mean) salary of the 10 employees of Company X was $42,800. What is the average (arithmetic mean) 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.
I received a PM asking me to comment.

Sum of the salaries last year = number*average = (10)(42,800) = 428,000.

Statements 1 and 2 combined:

Case 1: The 8 employees in statement 1 each earned $50,000 last year
Sum of their salaries last year = 8(50,000) = 400,000.
New sum this year = 1.15(400,000) = 460,000.
Sum of the salaries of the other 2 employees last year and this year = 428,000-400,000 = 28,000.
Average this year = (460,000+28,000)/10 = 48,800.

Case 2: The 8 employees in statement 1 each earned $1000 last year
Sum of their salaries last year = 8(1,000) = 8,000.
New sum this year = 1.15(8,000) = 9200.
Sum of the salaries of the other 2 employees last year and this year = 428,000-8,000 = 420,000.
Average this year = (9200+420,000)/10 = 42,920.

Since different averages this year are possible, INSUFFICIENT.

The correct answer is E.
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by sanju09 » Fri Mar 16, 2012 12:49 am

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killer1387 wrote:
sanju09 wrote:Last year the average (arithmetic mean) salary of the 10 employees of Company X was $42,800. What is the average (arithmetic mean) 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 b1, b2...b10

given: 42800 = (b1+b2+..+b10)/10
=> b1+b2..+b8 = (428000)-(b9+b10)

statement 1:
also given: b1(year2) = 1.15b1..similarly till b8

1.15b1+1.15b2.....1.15b8 = (b1...b8)+0.15(b1...b8)
insufficient

statement 2:

b9, b10 is same
insufficient

1+2

(b1+b2...+b8)+b9+b10 + 0.15(b1...+b8)/10

0.15(b1...+b8) cant be determined

Insufficient
Hence E.

@sanju09
please point out what i am missing here. No offence but still i am not convinced by the distribution you provided. How can this part "0.15(b1...+b8)" be determined by the information available?

thnx
Oh you are correct! The correct answer must be E; source is some GMAT Prep and the OA provided is definitely wrong.
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by voodoo_child » Mon Mar 19, 2012 8:58 am

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GMATGuruNY wrote:
sanju09 wrote:Last year the average (arithmetic mean) salary of the 10 employees of Company X was $42,800. What is the average (arithmetic mean) 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.
I received a PM asking me to comment.

Sum of the salaries last year = number*average = (10)(42,800) = 428,000.

Statements 1 and 2 combined:

Case 1: The 8 employees in statement 1 each earned $50,000 last year
Sum of their salaries last year = 8(50,000) = 400,000.
New sum this year = 1.15(400,000) = 460,000.
Sum of the salaries of the other 2 employees last year and this year = 428,000-400,000 = 28,000.
Average this year = (460,000+28,000)/10 = 48,800.

Case 2: The 8 employees in statement 1 each earned $1000 last year
Sum of their salaries last year = 8(1,000) = 8,000.
New sum this year = 1.15(8,000) = 9200.
Sum of the salaries of the other 2 employees last year and this year = 428,000-8,000 = 420,000.
Average this year = (9200+420,000)/10 = 42,920.

Since different averages this year are possible, INSUFFICIENT.

The correct answer is E.
Mitch,
why did you assume, in case b, that the salary of the other 8 people changed? It could be possible that the mean did not change at all this year. In other words, salary didn't change for two poeple and the other 8 guys. Correct? The question doesn't state that the mean has to change.

Please let me know your thoughts.

Thanks
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Re: salary of the 10 employees

by [email protected] » Sun Apr 18, 2021 3:29 pm

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Hi All,

We’re told that the AVERAGE salary of 10 employees last year was $42,800 (meaning that the TOTAL of those salaries was $428,000). We’re asked for the average salary of those same 10 employees this year. This is a great “concept” question – meaning that you do not actually have to do any math to answer it, as long as you understand the concepts involved.

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

To start, it’s worth noting that we do not know any of the actual salaries of the 10 employees, so in addition to not knowing what happened to the other 2 salaries, we don’t know how much these 8 salaries actually increased in absolute terms.

For example, if those 8 employees each earned $10,000 last year, then the increase in their salaries was (.15)($10,000) = $1500 each.

If those 8 employees each earned $20,000 last year though, then the increase in their salaries was (.15)($20,000) = $3000 each.

Those two outcomes would change the total of the 10 salaries in different ways, so the answer to the question would change.
Fact 1 is INSUFFICIENT.

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

While the information in Fact 2 is simpler to deal with than the information in Fact 1, the overall logic is the same: we don’t know what happened to the salaries of the other 8 people (nor any of the individual salaries or how they may have changed) – and the answer to the question will change based on that information.
Fact 2 is INSUFFICIENT.

Combined, we know:

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

Even combined, we run into the same issue that we faced with Fact 1 – we have no idea what any of the individual salaries are (and which ones were increased by 15%). Thus, the average salary this year will vary.
Combined, INSUFFICIENT

Final Answer: E

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