CDS 2026 (I) Elementary Mathematics, question 28

Topic: Number system

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Q28

Consider the following statements :

I. Two consecutive natural numbers are always co-prime.

II. If mm and nn are relatively prime, then m×nm\times n is always even.

Which of the statements given above is/are correct ?

  1. (a) I onlyCorrect answer
  2. (b) II only
  3. (c) Both I and II
  4. (d) Neither I nor II

Solution.

Answer: (a) I only

  1. I is true because any common divisor of n and n+1n + 1 divides their difference, 1.
  2. II is false: 3 and 5 are coprime, but their product 15 is odd.