Question

The mean of fifteen different natural numbers is 13. The maximum value for the second largest of these numbers is

• A. 46
• B. 51
• C. 52
• D. 53

Answer 1

The correct option is B 51

Let the $15$ different natural numbers for maximum value for second largest of number be $1,2,3,4,5,6,7,8,9,10,11,12,13,x$ and $y$

$\therefore \frac{1+2+3+4+5+6+7+8+9+10+11+12+13+x+y}{15}=13$

$⟹91+x+y=195$

$⟹x+y=104$

The second maximum will be $51$. It can't be $52$, because every number is different.

Hence, maximum value for the second largest number is $51$.