If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?
I. a × b × c < a^3
II. a + b + c > a^3
III. 5b < bc
Select the correct option:	A) I only	B) II only	C) III only	D) II and III	E) I, II, and III
Given:   1) a is even prime. The only even prime number known is 2, so a must be equal to 2.   2) a,b,c are consecutive such that a&lt;b&lt;c. So, b must be 3 and c must be 4.   So, we know that a=2, b=3 and c=4.   Substituting the above values in the three equations,   I. abc<a^3 24<8.="" a+b+c="" false.="" ii.="" simplifies="" to="" which="">a^3   which simplifies to 9&gt;8. True.   III. 5b&lt;bc   which simplifies to 15&lt;12. False.   The only option correct is II, so the answer is II only.</a^3>
<result>B</result>
If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?
I. a × b × c < a^3
II. a + b + c > a^3
III. 5b < bc