There are two natural numbers m and n (m\gt n). When m is divided by 12, it leaves a remainder 4. When n is divided by 12, it leaves a remainder 6. Which of the following statements is/are correct?<br>I. The remainder when (m+n) is divided by 12 is 10.<br>II. The remainder when (m-n) is divided by 12 is 10.<br>Select the correct answer using the code given below :

  1. A. I only
  2. B. II only
  3. C. Both I and II ✓
  4. D. Neither I nor II

Correct Answer: C. Both I and II

Explanation

Let m = 12a+4 and n = 12b+6. For I: m+n = 12(a+b) + 10, which leaves a remainder of 10. For II: m-n = 12(a-b) - 2. Adding and subtracting 12 gives 12(a-b-1) + 10, which also leaves a remainder of 10. Both statements are correct.

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