Bunuel wrote:

For real numbers a, b, and c, is ab = bc + 3?

(1) ab = 3b

(2) b + 3 = c

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

Since we have 3 variables and 0 equations, E is most likely to be the answer. So, we should consider 1) & 2) first.

Conditions 1) & 2):

ab = 3b

⇔ ab - 3b = 0

⇔ (a-3)b = 0

⇔ a = 3 or b = 0

Case 1: \(a = 3\)

\(ab = 3b\) and \(bc + 3 = b(b+3)+3\)

\(ab = bc + 3\)

\(⇔ 3b = b(b+3)+3\)

\(⇔ 3b = b^2 + 3b + 3\)

\(⇔ 0 = b^2 + 3\), which is false.

The answer is "No".

Case 2: \(b = 0\)

\(ab = bc + 3\)

\(⇔ 0a = 0c + 3\)

\(⇔ 0 = 0 + 3\), which is false.

The answer is "No".

The answer is always "No".

They are sufficient by CMT (Common Mistake Type) 1, since the answer "no" also means the condition is sufficient.

The answer is C.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.

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