CMI2010-A-07

Question

For integer values of $n$, the expression $\frac{n(5n + 1)(10n + 1)}{6}$

• A. Is always divisible by 5.
• B. Is always divisible by 3.
• C. Is always an integer.
• D. None of the above

 

Answer 1

Let X=$\frac{n(5n+1)(10n+1)}{6}$

For n=1  X= $\frac{6*11}{6}=11$

For n=2  X=$\frac{2*11*21}{6}=77$

For n=3  X=$\frac{3*16*31}{6}=248$

For n=4  X=$\frac{4*21*41}{6}=574$

Here we can see X is not divisible 3 and 5 but  X is always an Integer.

 

Hence,Option(C)Is always an integer.