Question

At the beginning of the year, the Finance Committee and the Planning Committee of a certain company each had n members, and no one was a member of both committees. At the end of the year, 5 members left the Finance Committee and 3 members left the Planning Committee. How many members did the Finance Committee have at the beginning of the year?
(1) The ratio of the total number of members who left at the end of the year to the total number of members at the beginning of the year was 1:6.
(2) At the end of the year, 21 members remained on the Planning Committee.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is D Each statement alone is sufficient.

1. It is given that , since a total of $3+5=8$ members left at the end of the year and there were a total of $n+n=2n$ members at the beginning of the year. It follows that $\left(8\right)\left(6\right)=\left(2n\right)\left(1\right)$, or $n=24$; Thus, statement 1 is sufficient.
2. It is given that $n–3=21$, since $3$ members from the original n members left the Planning Committee at the end of the year. It follows that $n=21+3=24$. Thus, statement 2 is sufficient.