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

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

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

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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holdem
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

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

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