## Is the product of a certain pair of integers even?

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### Is the product of a certain pair of integers even?

by BTGmoderatorDC » Wed Apr 20, 2022 2:37 am

00:00

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## Global Stats

Is the product of a certain pair of integers even?

(1) The sum of the integers is odd.

(2) One of the integers is even and the other is odd.

OA D

Source: GMAT Prep

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### Re: Is the product of a certain pair of integers even?

by [email protected] » Wed Apr 20, 2022 6:27 am

00:00

A

B

C

D

E

## Global Stats

BTGmoderatorDC wrote:
Wed Apr 20, 2022 2:37 am
Is the product of a certain pair of integers even?

(1) The sum of the integers is odd.

(2) One of the integers is even and the other is odd.

OA D

Source: GMAT Prep
Some important rules:
1. ODD +/- ODD = EVEN
2. ODD +/- EVEN = ODD
3. EVEN +/- EVEN = EVEN

4. (ODD)(ODD) = ODD
5. (ODD)(EVEN) = EVEN
6. (EVEN)(EVEN) = EVEN

Target question: Is the product of a certain pair of integer even?

Statement 1: The sum of the integers is odd
So, if the sum is odd, we know that one integer is ODD, and one integer is EVEN (rule #2)
If one integer is ODD, and one integer is EVEN, then their product must be even (rule #5).
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: One of the integer is even and odd
If one integer is ODD, and one integer is EVEN, then their product must be even (rule #5).
Since we can answer the target question with certainty, statement 2 is SUFFICIENT