When ‘M’ is divided by 6 it leaves a remainder 2 and when ‘N’ is divided by 6…
2024
When ‘M’ is divided by 6 it leaves a remainder 2 and when ‘N’ is divided by 6 it leaves a remainder 3. What will be remainder if ‘M-N’ is divided by 6 ?
- A.
2
- B.
3
- C.
5
- D.
7
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Correct answer: C
Solution: Let M = 6a + 2 and N = 6b + 3 for integers a and b.
Compute M - N = (6a + 2) - (6b + 3) = 6(a - b) - 1.
Thus M - N = 6k - 1 for integer k = a - b, so it is one less than a multiple of 6 and leaves remainder 5 when divided by 6.
Alternatively, look at remainders directly: 2 - 3 = -1, and -1 ≡ 5 (mod 6), so the remainder is 5.
Therefore, the remainder when M - N is divided by 6 is 5.