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Option 1 : The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
From statement I:
M is not a multiple of 2. So, M is odd. It can be written as (2k + 1).
⇒ MN = (2k + 1)N
Using binomial theorem, if N is natural number, then all terms of expansion will be multiple of 2, except 1N. So, remainder will be 1.
∴ Statement I alone is sufficient to answer the question.
From statement II:
N is not a multiple of 2. M can be even or odd. Accordingly, MN can be even or odd, irrespective of value of N. And leave different remainders when divided by 2.
∴ Statement II alone is not sufficient to answer the question.
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