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.
  2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
  3. The data in statement I alone or in statement II alone is sufficient to answer the question.
  4. The data in both the statements I and II is not sufficient to answer the question.
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1 Answers

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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