Bunuel wrote:
Is the positive integer N divisible by 4?
(1) N is a product of two even integers.
(2) N is a product of three consecutive integers.
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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)
We have N = (2a)(2b) = 4ab for some integers a and b.
Thus N is divisible by 4.
Since condition 1) yields a unique solution, it is sufficient.
Condition 2)
If N = 2*3*4 = 24, then N is divisible by 4 and the answer is "yes".
If N = 1*2*3 = 6, then N is not divisible by 4 and the answer is "no".
Since condition 2) does not yield a unique solution, it is not sufficient.
Therefore, A 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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