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Q.

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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a

73

b

91

c

67

d

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 ⇒ 2x=62 ⇒ x=31 Numbers are 2, 31 and 67.
The highest prime number is 67.
Hence, the correct option is 3.
 
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