N is the largest three digit number, which divided by 6 and 5 leaves remainder 4 and 3 respectively.  What will be the remainder when N is divided by 11?

8 9 6 10

9

LCM of 6 & 5 = 30 The largest three digits number = 999 After dividing 999 by 30, the remainder is 9 ∴ The largest three digits number divisible by 30 = 999 - 9 = 990 (N) Required number = 990 - 2 = 988 \(\frac{988}{11}\) = 9 remainder