Given, N is the number, which when divided by 3 and 8 leaves the remainder 1 and 6. Formula: Largest two digit number is 99. Smallest three digit number is 100. Calculation: LCM of 3 and 8 3 = 1 × 3 8 = 2 × 2 × 2 LCM = 2 × 2 × 2 × 3 = 24 When we divide 99 by 24 we get 3 in remainder. The largest two digit number which when divided by 24 = 99 – 3 = 96 If N is divided by 3 and 8 leaves the remainder 1 and 6, then = 3 – 1 = 8 – 6 = 2 The largest two digit number which when divided by 3 and 8 leaves 1 and 6 remainder = 96 – 2 = 94 Statement C is correct because 94 is even number. The sum of 94 = 9 + 4 = 13 Statement A is wrong. When we divide 100 by 24 we get 4 in remainder. The smallest three digit number which when divided by 24 = 100 – 4 + 24 = 120 If N is divided by 3 and 8 leaves the remainder 1 and 6, then = 3 – 1 = 8 – 6 = 2 The smallest three digit number which when divided by 3 and 8 leaves 1 and 6 remainder = 120 – 2 = 118 When we divide 118 by 5 we get remainder 3. Statement B is correct. ∴ Only statement B and C are correct.