GMAT10 wrote:
Last year, the five employees of company X took an average of 16 vacation days each. What was the average number of vacation days taken by the same employees this year?
(1) Three employees had a 50% increase in thier number of vacation days and two employees has a 50% decrease
(2) Three employees had 10 more vacation days each , and two employees has 5 fewer vacation days each.
Total number of vacation days last year = (number of employees)(average number of days per employee) = 5*16 = 80.
To determine the average number of vacations days for the 5 employees this year, we need to know the TOTAL NUMBER of vacation days this year.
Question stem, rephrased:
What was the total number of vacation days this year?
Statement 1: Three employees had a 50% increase in their number of vacation days, and two employees had a 50% decreaseCase 1: The 3 red employees took a total of 60 days last year, and the 2 blue employees took a total of 20 days last year, for a total of 80 vacation days last year
Total this year for the 3 red employees = 60 + (50% of 60) = 60 + 30 = 90.
Total this year for the 2 blue employees = 20 - (50% of 20) = 20 - 10 = 10.
Total this year for all 5 employees = 90 + 10 = 100.
Case 2: The 3 red employees took a total of 20 days last year, and the 2 blue employees took a total of 60 days last year, for a total of 80 vacation days last year
Total this year for the 3 red employees = 20 + (50% of 20) = 20 + 10 = 30.
Total this year for the 2 blue employees = 60 - (50% of 60) = 60 - 30 = 30.
Total this year for all 5 employees = 30 + 30 = 60.
Since the total this year can be different values, INSUFFICIENT.
Statement 2: Three employees had 10 more vacation days each, and two employees had 5 fewer vacation days each.Increase this year for the 3 red employees = 3*10 = 30.
Decrease this year for the 2 blue employees = 2*5 = 10.
Since last year's total = 80 days, we get:
Total this year for all 5 employees = 80 + 30 - 10 = 100.
SUFFICIENT.