Question

The sum of three non-zero prime numbers is $100$. One of them exceeds the other by $36$. Then the largest number is

• A. $73$
• B. $91$
• C. $67$
• D. $57$

Answer 1

Answer: (C)

$67$

The sum of three prime numbers can only be even if one of the prime numbers is even, the only prime number that is even is $2$.
So, the sum of the other two prime numbers must be $98$.
$x+x+36=98$
$\Rightarrow 2x=62$

$\Rightarrow x=31$
Numbers are $2,31$ and $67$.
The highest among them is $67$.