Ravixxx wrote:
Is integer x odd?
(1) 2x+1 is odd
(2) x/2 is even
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Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.
Condition 1)
Whatever integer x is, 2x+1 is an odd integer.
If x = 1, then 2x+1=3, x is an odd integer and the answer is 'yes'.
If x = 2, then 2x+1=5, x is an even integer and the answer is 'no'.
Since condition 1) does not yield a unique solution, it is not sufficient.
Condition 2)
Since x/2 is an even integer, we have x/2 = 2k or x = 4k for an integer k.
Then x is an even integer and the answer is 'no' only.
Since condition 2) yields a unique solution, it is sufficient.
Therefore, B is the answer.
Since 'no' is also a unique answer by CMT (Common Mistake Type) 1, condition 2) is sufficient.
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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