If A,B,C are three integers and AB+C is even . . . .

Hi VJesus12,

We're told that A, B, C are all integers and (A)(B)+C is EVEN. We're asked which of the following MUST be true (meaning "which of these things is ALWAYS TRUE no matter how many different examples we come up with?"). This question can be answered by TESTing VALUES or using Number Property Rules.

To start, since (A)(B) + C = an EVEN, there are a limited number of possible 'combinations' of Odds and Evens that will 'fit' here:

(Even)(Even) + (Even) = Even
(Even)(Odd) + (Even) = Even
(Odd)(Even) + (Even) = Even
(Odd)(Odd) + (Odd) = Even

A)A+C is even

In the 3rd example, this is NOT true. Eliminate Answer B and Answer D.

B)B+C is even

In the 2nd example, this is NOT true. Eliminate Answer C.

C)ABC is even

In the 4th example, this is NOT true. Eliminate Answer A.

There's only one answer remaining...

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

VJesus12 wrote:If A, B, C are three integers and AB+C is even; which of the following must be true?
A)A+C is even
B)B+C is even
C)ABC is even

1) Only C
2) Both A and B
3) Both B and C
4) All of them
5) None of them

Since AB + C is even, we can have:

Case 1: A, B, and C are all odd,

or

Case 2: A, B, and C are all even,

or

Case 3: A is odd and B and C are even,

or

Case 4: B is odd and A and C are even.

Now let’s analyze the three given statements.

If it’s case 3, A + C is odd and thus it’s not even.

If it’s case 4, B + C is odd and thus it’s not even.

If it’s case 1, ABC is odd and thus it’s not even.

Thus, none of the scenarios have to be true.

Answer: E