Gmatmachoman's solution is correct, although it's an interesting approach -- he used a very algebraic approach for the second statement, but didn't think about the first in terms of specific numbers. my approach is actually the exact opposite: i like to prove the insufficiency of the first statement by using specific numbers, but then i like to reason out the sufficiency of the second statement without bothering with the computation.
first, a very important realization:
if we can see what happens to the SUM of the five numbers, then that's also sufficient (because the sum is just 5 times the desired average).
this is a very common theme, especially on data sufficiency -- if the problem really wants you to work with the sum, then they'll ask you about the average, and vice versa.
statement 1:
as gmatmachoman stated above (in slightly different words), we need to have the actual numerical values here, since we want the NUMBER of vacation days in order to compute the average. the problem is that 50% of a larger number is, well, larger than 50% of a smaller number.
so, let's say that the employees took 14, 15, 16, 17, and 18 vacation days.
compare two situations:
1) the lowest three (14, 15, 16) receive 50% increases, while the top two (17 and 18) receive 50% decreases.
2) the highest three (18, 17, 16) receive 50% increases, while the bottom two (15 and 14) receive 50% decreases.
we don't need to compute the actual figures in this case, because we can see that, in situation #1, the increases are smaller and the decreases are larger than in situation #2. therefore, situation #1 will have a different impact on the overall sum than will situation #2. so, insufficient.
statement 2:
you can just reason this out as follows:
* we have the current SUM
* this SUM goes up by 3(10) - 2(5) = 20 days
* so, we have the new SUM
* so, sufficient.
no need to deal with actual numbers here at all.
answer = (b)
Ron has been teaching various standardized tests for 20 years.
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