In the following examples, a number is coded as three digits — representing the remainders when the number is divided by 3, 7, and 11, respectively.
Examples: 1: 53 (53 3 = 17 R2, 53 7 = 7 R4, 53 11 = 4 R9) Code: 2, 4, 9
Example 2: 68 (68 3 = 22 R2, 68 7 = 9 R5, 68 11 = 6 R2) Code: 2, 5, 2
By following this method, which is the least number which would have the code - 2, 2, 2?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 233.
We need a number that leaves remainder 2 when divided by 3, 7, and 11.
Required code = 2, 2, 2
So the number leaves remainder 2 when divided by 3, 7, and 11.
Hence, N − 2
must be divisible by 3,7, and 11.
LCM(3, 7, 11) = 231
N = 231 + 2 = 233