Last year, the five employees of Company X took an average of 16 vacation days

Question

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 their number of vacation days, and two employees had a 50% decrease.
2) Three employees had 10 more vacation days each, and two employees had 5 fewer vacation days each.

Options:

A . If the question can be answered with statement 1 alone

B . If the question can be answered with statement 2 alone

C . If both statement 1 and statement 2 are needed to answer the question and

D . If the question cannot be answered even with the help of both statements

Answer: Option B
:
B

The average number of vacation days taken this year can be calculated by dividing the total number of vacation days by the number of employees. Since we know the total number of employees, we can rephrase the question as: How many total vacation days did the employees of Company X take this year?

(1) INSUFFICIENT: Since we don't know the specific details of how many vacation days each employee took the year before, we cannot determine the actual numbers that a 50% increase or a 50% decrease represent. For example, a 50% increase for someone who took 40 vacation days last year is going to affect the overall average more than the same percentage increase for someone who took only 4 days of vacation last year.

(2) SUFFICIENT: If three employees took 10 more vacation days each, and two employees took 5 fewer vacation days each, then we can calculate how the number of vacation days taken this year differs from the number taken last year:
(10 more days/employee)(3 employees) - (5 fewer days/employee)(2 employees) = 20
Required Average = 16 + 4 = 20

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