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Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

Since we have 2 variables P(A) and P(B), and no equation, C is most likely to be the answer.

Since events A and B are independent, P(A∩B) = P(A) ∙P(B) and P(B) = P(A∩B) / P(A).

Condition 1) & 2)

Since P(only A) = 0.35 and P(A) = 0.5, we have P(A) ∙P(B) = P(A∩B) = 0.15.

Both conditions 1) and 2) together are sufficient.

Therefore, 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.

Answer: C

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