Question

Let x be the greatest number of 4 digits which, when divided by 16, 28, 40 and 48, leaves remainder 11 in each case. What is the sum of the digit of x?
1. 17
2. 13
3. 14
4. 18

Answer 1

Correct Answer - Option 3 : 14

Given:

Four digit greatest number = x

Formula:

Dividend = divisor × quotient + remainder

Calculation:

LCM of 16, 28, 40 and 48

⇒ 16 = 2 × 2 × 2 × 2

⇒ 28 = 7 × 2 × 2

⇒ 40 = 2 × 2 × 2 × 5

⇒ 48 = 2 × 2 × 2 × 2 × 3

LCM = 2 × 2 × 2 × 2 × 7 × 5 × 3 = 1680

When, 9999/1680 = 5 and remainder = 1599

Required four digit number = (9999 - 1599) + 11 = 8411

∴ Sum of digits of number = 8 + 4 + 1 + 1 = 14