Question

N$={161}^3-{77}^3-{84}^3$ which of the following statements is not true?

• A. N is divisible by $4$ and $23$
• B. N is divisible by $23$ and $11$
• C. N is divisible by $4$ and $7$
• D. N is divisible by $8$ and $11$

Answer 1

The correct option is D N is divisible by $8$ and $11$

Let $a=77$ and $b=84$

$\Rightarrow a+b=77+84=161$

we k.n.t $(a+b{)}^3=a^3+b^3+3a{b}^2+3a^{2}b$

$N=(a+b{)}^3-a^3-b^3=3ab(a+b)=3\ast 77\ast 84\ast 161=2^2\ast 3^2\ast 7^3\ast 11\ast 23$

$N$ is not divisible by 8.

Hence Statement in Option (D) is not true