What is the highest number between 5000 and 5500, which when divided by 12,16 and 24, would leave a remainder 9?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 5481 .
We need a number N such that,
N ÷ 12 leaves remainder 9 → N = 12k + 9
N ÷ 16 leaves remainder 9 → N = 16m + 9
N ÷ 24 leaves remainder 9 → N = 24n + 9
So, N − 9 is divisible by 12, 16, 24.
LCM of 12, 16, 24 = 48
So, N − 9 = multiple of 48 → N = 48t + 9
We need N between 5000 and 5500 → 5000 ≤ 48t + 9 ≤ 5500
48t ≥ 4991 → t ≥ 104
48t ≤ 5491 → t ≤ 114
Highest t = 114 → N = 48 × 114 + 9 = 5472 + 9 = 5481