Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
Let $N=55^{3}+17^{3}-72^{3}$. Then, $N$ is divisible by
(a)both 7 and 13
(b)both 3 and 13
(c)both 17 and 7
(d)both 3 and 17
Answer
Answer (as printed): D
Explanation
Let $a=55, b=17$. Then, $N=a^{3}+b^{3}-(a+b)^{3}=a^{3}+b^{3}-\left[a^{3}+b^{3}+3 a b(a+b)\right]$ $=-3 a b ~(a+b)=-3 \times 55 \times 17 \times 72$. Clearly, $N$ is divisible by both 3 and 17.
Explanation as extracted from the printed page; notation may be imperfect.