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If the average of the consecutive even integers a, b, and c is less than ... ...

   If the average of the consecutive even integers a, b, and c is less than , which of the following best describes the value of a?
(A) a is prime    
(B) ...
(C) ...
(D) ...
(E) ...

*This question is included in Nova Press: Set E - Number Theory

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If the average of the consecutive even integers a, b, and c is less than ... ... 
Posted: 11/02/2013 03:49
I didn't get this, would you please help?
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Posted: 11/12/2013 15:31
Mohammad, have you followed the explanation? It's a very good one. Here I repeat: let a, b, and c be the consecutive even integers. well b=a+2, and c=a+4, so the average of a, b, and c is a+2. According to the problem, the average of a, b, and c is less then ⅓ a, so that means a+2 < ⅓ a. Reducing this inequality gives us a < -3. So a is negative, or (E).
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