Consider the following statements:
I. There exists a natural number which when increased by 50% can have its number of factors unchanged.
II. There exists a natural number which when increased by 150% can have its number of factors unchanged.
Which of the statements given above is/are correct?

Question

Accepted Answer

Both I and II. For statement I: Take N = 2. Increasing by 50% gives 3. Both 2 and 3 are primes and each has exactly 2 factors. So statement I is true. For statement II: Take N = 2. Increasing by 150% gives 2 + 3 = 5. Both 2 and 5 are primes with 2 factors each. So statement II is also true. Hence both statements are correct and option (c) is the answer.

Consider the following statements: I. There exists a natural number which when increased by 50% can have its number of factors unchanged. II. There exists a natural number which when increased by 150% can have its number of factors unchanged. Which of the statements given above is/are correct?

Explanation

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