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Is the product of a certain pair of integers even?

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Is the product of a certain pair of integers even?  [#permalink]

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New post 12 May 2014, 12:54
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A
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D
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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.
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Re: Is the product of a certain pair of integers even?  [#permalink]

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New post 12 May 2014, 15:03
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holdem wrote:
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.

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 :-)
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Re: Is the product of a certain pair of integers even?  [#permalink]

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New post 12 May 2014, 16:58
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,
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Re: Is the product of a certain pair of integers even?  [#permalink]

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New post 19 May 2016, 03:10
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.

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Devesh
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Re: Is the product of a certain pair of integers even?  [#permalink]

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New post 19 May 2016, 03:15
deveshmalik wrote:
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
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Re: Is the product of a certain pair of integers even?  [#permalink]

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New post 20 Apr 2018, 07:22
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holdem wrote:
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.


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,
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Re: Is the product of a certain pair of integers even?  [#permalink]

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New post 25 Apr 2019, 09:50
holdem wrote:
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.



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

Please hit +1 Kudos :thumbup:
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Re: Is the product of a certain pair of integers even?   [#permalink] 25 Apr 2019, 09:50
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