Last year the avg. salary of the 10 employees

[crrc]

Last year the avg. salary of the 10 employees of Company X was $42,800. What is the avg. 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

Taken together, why is it incorrect to think that we will be able to calculate this year's avg. given last year's avg.?
In other words, why isn't the answer C?

statement 1
1.15 (42.8) x 8
+
statement 2
(42.8) (2)
= the sum of the salaries.
That sum divided by 10 = the this year's avg.

OA however, is E

[Quizzy]

Can one (or two) of the 2 in statement (2) be a part of the group that is mentioned in 1? Yes....
Essentially the question never mentiones that the group of 8 is exclusive of the group of 2. + We are dealing with averages here. It would be incorrect to think of all values of a group to be equal to the average.

[JPG]

I believe it is E because given (1) and (2) together, we have no way of knowing the individual salaries and we cannot assume that the individual salaries are each equal to the previous year's average. For example, perhaps the highest 8 salaries increased by 15% and the lowest 2 did not change at all, the average would surely be different than if the highest 2 salaries did not change and the other 8 increased by 15%.

[RonPurewal]

I believe it is E because given (1) and (2) together, we have no way of knowing the individual salaries and we cannot assume that the individual salaries are each equal to the previous year's average. For example, perhaps the highest 8 salaries increased by 15% and the lowest 2 did not change at all, the average would surely be different than if the highest 2 salaries did not change and the other 8 increased by 15%.

yeah.

here's some more specific help:
remember that you can, and should, work easily back and forth between the AVERAGE of a set of data and the SUM of those data. remember, Average x # of Data Points = Sum, so, for sets in which the # of data points is known (such as this one), the SUM of the salaries will answer the data sufficiency problem just as well as the AVERAGE that's explicitly requested.

this is an extremely valuable observation, because, while it's somewhat difficult to process changes to the average conceptually, it's splendidly easy to think about changes to the sum.

to wit:
following JPG's lead, contrast the situation in which the 8 lowest salaries are augmented to that in which the 8 highest salaries are augmented.
since we're augmenting the salaries by a fixed percentage, it follows that the absolute dollar changes are smaller in the former case than in the latter case (because 15% of a smaller number is less than 15% of a larger number).
therefore, in the former case, the overall increase in the SUM will be smaller than it is in the latter case, because the individual salary changes are smaller.
that settles the issue; the sum could change by different amounts. therefore, the average could also change by different amounts. therefore, insufficient.

good times