Question

# A number a has 7 as its smallest prime factor, and another number b has 3 as its smallest prime factor. What is the smallest prime factor of the number a+b?  3 2 7 5

Solution

## The correct option is B 2 Since 7 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 3 is the smallest prime factor of b, 2 cannot be a factor of b and thus b is also  odd.i.e., b=2m+1 for some m. Hence we have  a+b=(2n+1)+(2m+1)=2(n+m+1)=2k ( taking 2 common and assuming  k=n+m+1.) We can thus see that 2 is a factor of a+b, and hence  2 is the smallest prime factor of a+b.

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