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

Hi Bunuel chetan2u GMATBusters VeritasKarishma

Why can't we take average of the two percentages i.e 15% increase for 8 people and no increase for 2 people which should give us an average increase of 12% over the last year's average irrespective of not knowing individual's salary.

What conceptual mistake am I making in this approach.

Will appreciate correction please.

You do not know the average of these 8 and these 2 separately.
Say average of these 10 was 100.
All 8 are 120 each, so increase of 15% means 18 more so 138 each
The remaining two would be 20 each.
New total 138*8+2*20
But there may be a case
All 8 are 20 each , so new =23
Remaining two would be (10*100-20*8)/2=420 each
Total 42*3+2*420

As you can see, the average can change

No, you cannot use weighted average concept here. Why? Because you have to be mindful of what the weights are in each case.

When I say 15% increase and 0% increase needs to averaged, what is my weight? It is the initial amount. A 15% increase of what and a 0% increase of what?
I need the total salary of the 8 people (which increased by 15%) and total salary of 2 people (which increased by 0%) to get the average increase in salary.

Check:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/1 ... -averages/

Average Increase = Total Increase/Total Initial Amount
Think of the physical quantity your weights represent and whether it makes sense as the denominator of the average.

This one is really conceptual

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.
Clearly insufficient. There's no way we can figure out what the new average is because we have no idea how much each person made previously in the last year.
e.g. Suppose 8/10 people each made 1 dollar last year...in that case the new average will barely change
e.g. Suppose 8/10 people made 42799 last year...in that case the average > 42800

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

Combined: Nothing has changed.

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 could vary.
Combined, INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Hi Bunuel,

How did you come to a conclusion that the 2 salaries which didn't change as per statement 1, were the lowest & the 2 salaries which didn't change as per statement 2 were the highest?

Dear Hemant611
it is never mind what places they hold. The matter is the average will be different.
Take into consideration a few examples:

1 10 10 10 10 10 10 10 10 19
or
5 5 10 10 10 10 10 10 15 15

Then the sum that comprises 15% growth for the first 8 places, for the middle or for the last will be always different. Hence, because you cannot get definite answer, even if combined with St.2, this statement is not sufficient.

Hope it helps.

KarishmaB
I had a similar question. I tried solving like this by back solving for the previous year, letting x equal the total sum for the eight individuals and y equaling the total sum for the 2 individuals. I realize that you cannot solve because there are two variables, but assuming I had the value of x or y, would be incorrect to set up the equation in this proportion?
(((8/10)*x)/1.15 + ((2/10)*y)/ 10) = 42,800

I apologize for the silly question. Thank you so much as always.

I am not sure how you got this equation.

Last year salary of all 10 people combined = 428,000 (total sum = avg * 10)
If I had the total salary of 8 people, say x, then x increased by 15% and (428,000 - x) increased by 0%

\(Avg increase = \frac{15*x + 0 * (428,000 - x)}{428000}\)
Say you have the value of x and you get avg increase as 3%.

Then total sum of salary this year = 1.03 * 428,000 and avg this year = 1.03 * 42,800

This is similar to calculating avg profit percentage and then SP given a 15% profit on certain part of CP and 0% on the rest of CP. We need the two parts of CP. We don't know what the salary of the 8 people who saw 15% increase was out of the total of $428,000.

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