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Distinct prime numbers p, q, and r satisfy the equation p(q + r) = 16.     

Which of the following prime numbers must either q or r be equal to?     
2 3 5 7 11     

 

For p(q + r) to produce a positive product – that is, 16 – both p and (q + r) have to be positive.     

The only way p can be positive is if it is 2.  The only way the product can be 16 is if (q + r) = 8.     

 

So p(q + r) is either 2(3 + 5) or 2(5 + 3).  Either q or r is either 3 or 5.     

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