Data Sufficiency

In a certain school, teachers who lecture English and Spanish are there. If 2 teachers are selected randomly, what is the probability that at least one teacher selected lectures Spanish?
1) The ratio of Spanish teachers' number to English teachers' number is 3 to 1.
2) The sum of Spanish teachers' number and English teachers' number is less than 20.

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If we modify the original condition and the question, there are two variables (E and S). In order to match the number of variables and the number of equations, we need 2 equations. Hence, there is high chance that the correct answer is C. Using the condition 1) and the condition 2), since (E,S)=(2,6),(3,9),(4,12), the answer is not unique and the conditions are not sufficient. Thus, the correct answer is E.
- 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.