Graduate Management Admission Test (GMAT) Practice Test

When is the product of two even numbers always true?

1. Odd

2. Even

3. Positive

4. Negative

The correct answer is: Even

The product of two even numbers is always even because of the mathematical property of even numbers. An even number can be defined as any integer that is divisible by 2, which means it can be expressed in the form of 2n, where n is an integer. When multiplying two even numbers, say 2a and 2b (where a and b are integers), the multiplication results in: (2a) * (2b) = 4ab = 2(2ab) This final expression, 2(2ab), clearly shows that the result is an integer multiplied by 2, thus confirming it is even. Since every time two even integers are multiplied together, the product can always be divided by 2 without leaving a remainder, it is categorically even. Other outcomes such as being odd, positive, or negative do not consistently apply to the product of two even numbers. While it is possible for the product to be positive or negative depending on the specific values of the even numbers, the one constant is that their product will always be even. Therefore, the assertion that the product of two even numbers is even is unequivocally true in all cases.