Divisibility of Algebraic Sum of Cubes

CAT 2000 Slot 1 · QA · Medium · Number Systems

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Let $N = 55^3 + 17^3 - 72^3$ . $N$ is divisible by:

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

Answer

Explanation

Using $a^3 + b^3 + c^3 = 3abc$ when $a + b + c = 0$ : Here $55 + 17 + (-72) = 0$ . So $N = 3 \times 55 \times 17 \times (-72)$ . Thus $N$ is divisible by $3$ and $17$ .

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