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Given below is a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. You should use the given data and your knowledge of Mathematics to choose between the possible answers. How many factors will a natural number P have? I. P is an odd number. II. P is perfect square of a prime number.

Given below is a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. You should use the given data and your knowledge of Mathematics to choose between the possible answers. How many factors will a natural number P have? I. P is an odd number. II. P is perfect square of a prime number. Correct Answer 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.

From statement I:

P is an odd number, 1 has 1 factor, 3 has 2 factors. Both are odd. Number of factors cannot be determined uniquely.

∴ Statement I alone is not sufficient to answer the question.

From statement II:

P is perfect square of a prime number.

Let P = N × N, where N is prime.

So, its factors will be 1, N and P only, that is 3 factors.

∴ Statement II alone is sufficient to answer the question.

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