Of the people who attended a workshop, 60 percent were teachers and so

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.

Of the people who attended a workshop, 60 percent were teachers and some of the teachers were teachers of language arts. What percent of the people who attended the workshop were teachers of language arts?

(1) 200 people attended the workshop.

(2) 72 of the teachers who attended the workshop were not teachers of language arts.


Modify the original condition and the question. Suppose people attending a workshop 100p and then teachers are 60p. Then, suppose teachers of language arts np, there are 2 varibles(n,p), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2), it becomes 100p=200 and then (60-n)p=72. You can get a value of n in a unique way, which is sufficient. Therefore, the answer is C.


 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

(1) If 200 people attended the workshop, then 120 were teachers and x of the 120 teachers were teachers of language arts, where x < 120. The required percent is [x/200] X 100. We don’t know x, hence we cannot answer the required percent. Insufficient


(2) If y people attended the workshop, then 0.6 y were teachers and 0.6 y - 72 were teachers of language arts. The required percent is [(0.6 y - 72)/y] X 100. We don’t know y, hence we cannot answer the required percent. Insufficient

Taking together, we know y = 200, and hence the required percent is [(0.6 y - 72)/y] X 100 can be answered. Not to mention, you’ll get it equal to 24 percent. Sufficient

Take C

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