2022 · Q19
There are two natural numbers x and y, where x > y. When x is divided by 6, it leaves the remainder 2 and; when y is divided by 6, it leaves the remainder 3. What is the remainder when (x - y) is divided by 6?
Elementary MathematicsNumber System
- A1
- B3
- C5
- DRemainder cannot be determined
Explanation
x − y ≡ 2 − 3 ≡ −1 ≡ 5 (mod 6). Writing x = 6m+2 and y = 6n+3 gives x−y = 6(m−n)−1, whose least non-negative residue mod 6 is 5. The keyed option is C.