CDS 2025 · PYQ · Number Theory / Remainders · medium
There are two natural numbers m and n (m > 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? I. The remainder when (m + n) is divided by 12 is 10. II. The remainder when (m - n) is divided by 12 is 10.
A.I only
B.II only
C.Both I and II✓ Correct
D.Neither I nor II
Explanation
m = 12a + 4, n = 12b + 6. (m+n) = 12(a+b) + 10, remainder 10. ✓ Statement I correct. (m-n) = 12(a-b) + 4 - 6 = 12(a-b) - 2 = 12(a-b-1) + 10, remainder 10. ✓ Statement II correct. Both statements are correct.
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