Question

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

• A. 73
• B. 91
• C. 67
• D. 57

Answer 1

The correct option is C 67

If the sum of 3 prime numbers is even, then one of the numbers must be 2.
Let the second number be x.
So, the numbers are x, (x+36) and 2.
Then as per the given condition,
$x+(x+36)+2=100$
$2x+38=100$
$2x=62$
$\Rightarrow x=31$
So, the number are 2, 31 and 67.
Hence, the largest number is 67.