Each of these questions consists of a problem followed by two statements numbered as I and II. Decide whether the data in the statements are sufficient to answer the question. Mark answer as
Committee X and Committee Y, which have no common members, will combine to form Committee Z. Does Committee X have more members than Committee Y?
I. The average (arithmetic mean) age of the members of Committee X is 25.7 years and the average age of the members of Committee Y is 29.3 years.
II. The average (arithmetic mean) age of the members of Committee Z will be 26.6 years.
Solution
Each of the statements is an independent fact, and we alone cannot make any inference about the number of people in Committees X and Y.
Let us say that the number of people in Committee X is x, and the number in Committee Y is y.
Statement 1 tells us that x people have an average age of 25.7 and y people have an average age of 29.3
This does not tell us anything
Statement 2 tells us that x+y people have an average age of 26.6 years.
Using the two statements together, we can equate it to get the needed equation,
$$25.7x+29.3y=26.6x+26.6y$$
$$2.7y=0.9x$$
$$3y=x$$
Hence, there are three times the number of people in x as in y, which we can find using both statements.
