Question

Let $N={55}^3+{17}^3-{72}^3.$ N is divisible by : (CAT 2000)

• A. both 7 and 13
• B. both 3 and 13
• C. both 17 and 7
• D. both 3 and 17

Answer 1

The correct option is D both 3 and 17

Ans: (d).

$N={55}^3+{17}^3-{72}^3=(54+1{)}^3+(18-1{)}^3-{72}^3$

$=(51+4{)}^3+{17}^3-(68+4{)}^3.$

These two different forms of the expression are divisible by 3 and 17 both.

Elimination strategy:

Check the divisibility by 13, it is seen that it is not divisible, now check for 3, it is

divisible, hence the only option will be (d)