Let p be the greatest number of 4-digits which when divided by 21, 22, 24 and 28, the remainder in each case is 8. What is the sum of the digits of p?

Correct option is C

​$$\textbf{Given:} \\p \text{ is the greatest 4-digit number} \\\text{Remainder} = 8 \\\text{Divisors} = 21,\;22,\;24,\;28 \\\textbf{Concept Used:} \\\text{LCM and remainder theorem} \\\textbf{Formula Used:} \\p - r = \text{LCM} \times k \\\textbf{Solution:} \\21 = 3 \times 7 \\22 = 2 \times 11 \\24 = 2^3 \times 3 \\28 = 2^2 \times 7 \\\text{LCM} = 2^3 \times 3 \times 7 \times 11 = 1848 \\p - 8 = 1848k \\1848k + 8 \le 9999 \\1848k \le 9991 \\k = 5 \\p - 8 = 1848 \times 5 = 9240 \\p = 9248 \\\text{Sum of digits} = 9 + 2 + 4 + 8 = 23 \\\textbf{Final Answer:} \\23$$​​