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Question

# A number a has 3 as its smallest prime factor, and another number b has 5 as its smallest prime factor. What is the smallest prime factor of the number a+b?

A

10

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B

5

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C

3

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D

2

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Solution

## The correct option is D 2 Since 3 is the smallest prime factor of a, it is clear that 2 is not a factor of a. Thus, a is an odd number, i.e. a=2n+1 for some n. Similarly, when 5 is the smallest prime factor of b, 2 cannot be a factor of b and thus b too is odd.i.e., b=2m+1 for some m. Thus, a+b=(2n+1)+(2m+1)=2(n+m+1)=2k(say) where k=n+m+1. We can thus see that 2 is a factor of a+b, and clearly 2 is the smallest prime factor of a+b.

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