Bunuel wrote:

Of the high school students who participated in a recent survey, 110 had taken a course in biology and 230 had taken a course in history. How many students participated in the survey?

(1) Of the students who participated in the survey, 120 had taken neither a course in biology nor a course in history.

(2) Of the students who participated in the survey, 60 had taken both a course in biology and a course in history.

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.

We can use 2x2 matrix to set up this question.

..........| Bio | Not Bio

------------------------------

Hist.....| a | b

------------------------------

Not Hist | c | d

a + c = 110

a + b = 230

Q: a + b + c + d =?

Since we have 4 variables and 2 eqautions, C is most like to be the answer.

Condition 1) & 2)

We have d = 120 from the condition 1) and a = 60 from the condition 2)

c = 50 and b = 170

a + b + c + d = 60 + 170 + 50 + 120 = 400.

Condition 1)

d = 120

We can't figure out a + b + c.

This is not sufficient.

Condition 1)

a = 60

c = 50 and b = 170

We can't figure out d.

This is not sufficient, either.

Thus the answer is C as expected.

Normally 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 C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. 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 according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

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