Question

Last year, the five employees of Alpha Ltd. 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.

• A. If Statement (1) alone is sufficient, but statement (2) alone is not sufficient. Or If Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• B. If BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• C. If Each statement ALONE is sufficient
• D. If Statements (1) and (2) TOGETHER are NOT sufficient.

Answer 1

The correct option is A

If Statement (1) alone is sufficient, but statement (2) alone is not sufficient. Or If Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

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 Alpha Ltd. 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) = 30days - 10 days = 20 days
20 additional vacation days were taken this year.
In order to determine the total number of vacation days taken this year (i.e., in order to answer the rephrased question), we need to determine the number of vacation days taken last year. The 5 employees took an average of 16 vacation days each last year, so the total number of vacation days taken last year can be determine by taking the product of the two:

(5 employees)(16 days/employee) = 80 days
80 vacation days were taken last year. Hence, the total number of vacation days taken this year was 100 days.
Note: It is not necessary to make the above calculations -- it is simply enough to know that you have enough information in order to do so (i.e., the information given is sufficient)! The correct answer is (a).