Is the product of a certain pair of integers even?

Question

(1) The sum of the integers is odd.

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

mikemcgarry · Answer

Dear holdem I'm happy to help. :-)

Statement #1 : The only way the sum of two integers can be odd is if one is even and one is odd. This would yield an even product. The answer to the prompt question is "yes." This statement, alone and by itself, is sufficient . Statement #2 : One even, one odd: again, an even product. The answer to the prompt question is "yes." This statement, alone and by itself, is sufficient . Each statement is sufficient on its own. Answer = (D) . Does all this make sense? Mike :-)

holdem · Answer

Hi Mike,

thanks a lot, it totally does.

I basically just posted this question to complete the collection (didn't find this one), but still got an important information from your answer.

With kind regards,
holdem

deveshmalik · Answer

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

Bunuel · Answer

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

BrentGMATPrepNow · Answer

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

Rakesh1987 · Answer

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

singhpriyaansi · Answer

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

Bunuel · 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.

Is the product of a certain pair of integers even?

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