Question

What is the remainder when $({16}^3+{17}^3+{18}^3+{19}^3)$ is divided by 70?

• A. 10
• B. 20
• C. 30

Answer 1

${16}^3+{17}^3+{18}^3+{19}^3={16}^3+{19}^3+{17}^3+{18}^3$ is divisible by (16+19) i.e. 35 and is also divisible by (17+18) i.e. 35 as well. So, $({16}^3+{17}^3+{18}^3+{19}^3)=35x+35y$, as x+y must be even, hence the given expression is divisible by 70. So, the remainder will be 0.