MGMAT average problem

[Redhorsep]

Hi,

My problem is that I thought statement 1 is sufficient because it looks like a weighted average thing, please tell me what I did wrong:

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Last year, the 5 employees took an average of 16 vacation days each. What was the average # of vacation days taken by the same employee this year?

1) 3 employees had a 50% increase in their # of vacation days, and 2 employees had a 50% decrease.

for weighted average, we need both the weight of data point (could be actual #'s or ratio to total) and data point, so am I wrong in thinking that this is weighted average because there's no data point in the statement?

[GmatMathPro]

yes. you can't use weighted average here because you don't know the average number of vacation days either group of employees took last year. in a case like this a good way to see that it is insufficient is to consider extreme cases. we know 80 vacation days were taken between the 5 employees, but we don't know how they're distributed. If they're distributed like this: 76 1 1 1 1, the new average will skyrocket if the 76 guy is included in the 50% increase group. But the average will drop dramatically if he is in the decrease group.

Note that if they had given you something like "the group that's increasing by 50% took an average of 30 vacation days each last year" you could use weighted averages:

Group of 3 would now take 45 vacation days each on average, group of 2 would now take 5 each on average, and then (3/5)*45+(2/5)*5=29