Bunuel wrote:
Is integer N odd?
(1) N is a factor of 100.
(2) N is a factor of 135.
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Since we have 1 variable (N) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.
Condition 1)
Since \(1\) is a factor of \(100\) and \(1\) is an odd integer, the answer is 'yes'.
Since \(2\) is a factor of \(100\) and \(2\) is an even integer, the answer is 'no'.
Since condition 1) does not yield a unique solution, it is not sufficient.
Condition 2)
Since \(135=3^3 \cdot 5\) does not a prime factor \(2\), \(135\) does not have an even factor and N must be an odd number.
Since condition 2) yields a unique solution, it is sufficient.
Therefore, B is the answer.
If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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