The largest four-digit number which when divided by 9, 18 and 23, leaves a remainder 5 in each case, is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 9941.
Let the number = N
LCM of 9, 18, 23 = 18 × 23 = 414
So, N − 5 = 414 × k
Largest four-digit number ⇒ N ≤ 9999
414 × k + 5 ≤ 9999
414 × k ≤ 9994
k = 9994 ÷ 414 = 24 (approx)
N = 414 × 24 + 5 = 9936 + 5 = 9941