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# Discussion

The sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is:

• A.7
• B.29
• C.41
• D.67

$$x+(x+36)+y=100 \\ \Rightarrow 2x+y=64$$
Therefore $$y$$ must be even prime, which is 2.
Therefore,
$$2x+2=64 \\ \Rightarrow x=31$$
Third prime number
$$= (x+36)\\= (31+36)\\= 67$$

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