If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ?  Select
A) 141  B) 200  C) 312  D) 391  E) 412
The key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work).   We're told that a, b and c are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as...   A + (A+2) + (A+4) = 3A + 6   We know that 3A + 6 COULD equal one of those five answers; we just have to find it...   Could 3A + 6 = 141   3A = 135   A = 45   This is NOT an EVEN INTEGER, so 141 is NOT the answer   Could 3A + 6 = 200   3A = 194   A = 64.6666   This is NOT an EVEN INTEGER, so 200 is NOT the answer   Could 3A + 6 = 318   3A = 312   A = 102   This IS an EVEN INTEGER! The numbers would be 102, 104 and 106. This IS the answer   Final Answer:   312
<result>C</result>
If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ?