M is the largest three digit number which when divided by 6 and 5 leaves remainder 5 and 3 respectively. What will be the remainder when M is divided by 11?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 4
X = 6m + 5 .....(1)
X = 5n + 3 .......(2)
From (1) and (2):
6m + 5 = 5n + 3
⇒ n = (6m + 2)/5
m = 3, 8, 13 ..... and n = 4, 10, 16 ..... satisfies the condition
According to question,
X must be largest 3 digit no. which satisfies both the conditions at m = 163 and n = 196
So, X = 983
Remainder = 983/11 = 4