Let N = 55³ + 17³ - 72³. N is divisible by

1. both 3 and 17
2. both 7 and 13
3. both 3 and 13
4. both 17 and 7

Answer

55 + 17 = 72

Use formula

(x - y)³ = x³ - y³ - 3xy(x-y)

(72 - 17)³ = 72³ - 17³ - 3(72)(17)(72 - 17)

55³ + 17³ - 72³ = 3(72)(17)(55)

N is divisible by both 3 and 17.

The correct option is A.