Is the product of a certain pair of integers even?

Hi,

About statement 1: Why aren't we considering that one of the integer could be Zero. In that case product will be zero which is neither even nor odd.

Please clarify.

Regards
Devesh

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Check more here: number-properties-tips-and-hints-174996.html

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

Answer = D

Cheers,
Brent

1) only possible scenario is O+E and their product is even. Sufficient.
2) O x E is even. Sufficient.
Therefore answer is D.

new to the platform. can somebody tell me where the options are given, so that i can choose my answer

­Hi,

This is a data sufficiency question. Options for DS questions are always the same and usually omitted on the site.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hope this helps.­