CAT 2000 | Question: 94

Question

Let $\text{N} = 55^3 + 17^3 – 72^3.\; \text{N}$ is divisible by

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

Answer 1

Let x=72 and y=17

55 + 17 = 72

Use formula

$(x-y)^{3}=x^{3} -y^{3}-3x^{2}y+ 3xy^{2} = x^{3} -y^{3}-3xy(y-x)$

$(72-17)^{3}=72^{3} -17^{3}-3*72*17(17-72)$ 

$55^{3}+17^{3} -72^{3}=3*72*17*55$

N is divisible by both 3 and 17.

 

Hence,option (4).Both 3 and 17.