Bunuel wrote:
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.
Kudos for a correct solution.
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
Condition (1)
\(5 + 3 : 2n = 1: 6\)
\(2n = 48\)
Since we have 1 equation of \(n\), this is sufficient.
Condition (2)
\(n - 3 = 21\)
Since we have 1 equation of \(n\), this is also sufficient.
Therefore, D is the answer.
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.