Which of the following can be the value of ‘k’ so that the number 217924k is…

Step-by-Step Analysis
Divisibility Rule for 2:
A number is divisible by 2 if its last digit is even. The last digit here is 'k'. Therefore, k must be 0, 2, 4, 6, or 8.

Divisibility Rule for 3:
A number is divisible by 3 if the sum of its digits is divisible by 3.
Sum of the known digits: 2 + 1 + 7 + 9 + 2 + 4 = 25.
Including 'k', the total sum is 25 + k.

Testing the possible values of k:
We need 25 + k to be a multiple of 3. Let's test the even values of k identified in step 1:

If k = 0: 25 + 0 = 25 (Not divisible by 3)

If k = 2: 25 + 2 = 27 (Divisible by 3)

If k = 4: 25 + 4 = 29 (Not divisible by 3)

If k = 6: 25 + 6 = 31 (Not divisible by 3)

If k = 8: 25 + 8 = 33 (Divisible by 3)

The correct value for 'k' is 2, as it satisfies both the requirement for divisibility by 2 (being even) and divisibility by 3 (sum of digits equals 27).