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

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73

91

67

57

answer is C.

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Detailed Solution

Given, the sum of three non-zero prime numbers

= 100

(which is even).
We know that 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

100 - 2 = 98

.
According to the statement, we have,
⇒

x + x + 36 = 98

\Rightarrow 2 x = 62

\Rightarrow x = 31

Numbers are

2, 31

and

67

.
The highest prime number is

67

.
Hence, the correct option is 3.

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