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Explanation:

Given, 3k + 4k + 5k 
put k = 1, we have 3k + 4k + 5k = 3 + 4 + 5 = 12
put k = 2, we have 3k + 4k + 5k = 9 + 16 + 25 = 50

The only common factor between 12 and 50 is 2.

3k + 4k + 5k is always even for any value of k, and hence always divisible by 2.

∴ A = 2

Given, 4k + 3(4k) + 4k+2
= 4k(1 + 3 + 42)
= 4k × 20
For k ≥ 1, this number is always divisible by 4 × 20 = 80
∴ B = 80

⇒ A + B = 2 + 80 = 82.

Hence, 82.

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