Find k such that a 7 -digit number 51032 kk is divisible by 12.

Correct option is C

Identity Used:

Divisibility by 4
- The last two digits (kk) must be divisible by 4. 

Divisibility by 3
- This sum must be divisible by 3

Solution:

Divisibility by 4
- The last two digits (kk) must be divisible by 4.
- Possible two-digit numbers formed by repeating k: 00, 11, 22, ..., 99.
- Check which are divisible by 4.
Divisibility by 3
- Sum of digits = 5 + 1 + 0 + 3 + 2 + k + k = 11 + 2k.
- This sum must be divisible by 3.Find suitable k
- Among the possible kk divisible by 4, only when k = 8, the sum of digits (11 + 16 = 27) is divisible by 3.
- Hence, k = 8.

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