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# If i and j are integers, is i + j an even integer?

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If i and j are integers, is i + j an even integer? [#permalink]

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19 Jan 2009, 01:15
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If i and j are integers, is i + j an even integer?

(1) i < 10
(2) i = j

Official Guide 12 Question

 Question: 12 Page: 273 Difficulty: 600

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Re: OG pg.279 D/S No.25 [#permalink]

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19 Jan 2009, 02:10
sirrock wrote:
If i and j are integers, is i+j an even integer?
(1) i < 10
(2) i = j

OA is B

but what if i = j = 0?

Is 0 an even integer?

OG says 0 is an even integer.
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Re: OG pg.279 D/S No.25 [#permalink]

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19 Jan 2009, 04:18
sirrock wrote:
If i and j are integers, is i+j an even integer?
(1) i < 10
(2) i = j

OA is B

but what if i = j = 0?

Is 0 an even integer?

yes zero is even integer.
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Re: OG pg.279 D/S No.25 [#permalink]

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19 Jan 2009, 08:19
0 is even

0 + 1 = 1

(even) + (odd) = (odd)

0 + 2 = 2

(even) + (even) = (even)

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Re: OG pg.279 D/S No.25 [#permalink]

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19 Jan 2009, 09:06
selvae wrote:
0 is even

0 + 1 = 1

(even) + (odd) = (odd)

0 + 2 = 2

(even) + (even) = (even)

But what is the confusion here.

Second stmt says that i = j. If i, j = 0, then i + j = 0 + 0 = 0 which is even.

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Re: OG pg.279 D/S No.25 [#permalink]

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19 Jan 2009, 09:56
If i and j are integers, is i+j an even integer?
(1) i < 10
(2) i = j

OA is B

but what if i = j = 0?

Is 0 an even integer?

i and j either both should be even to get a even sum or both should be odd to get a even sum.
stmnt 1 : i < 10 which has no information abt j ..so its insufficient.

stmnt 2: i = j which means either i = j = even or i = j = odd which gives a even sum

yes 0 is an even integer.

i = j = 0 also gives a even sum. so its sufficient.

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Re: OG pg.279 D/S No.25 [#permalink]

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19 Jan 2009, 10:01
yes; sum of two odds or two evens is even. Hence, 2 is enough.

sirrock wrote:
If i and j are integers, is i+j an even integer?
(1) i < 10
(2) i = j

OA is B

but what if i = j = 0?

Is 0 an even integer?

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Re: If i and j are integers, is i + j an even integer? [#permalink]

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02 May 2012, 22:16
what if i and j are negative.
Its mentioned that i and j are integers but its not mentioned that i and j are positive integers.
what if i = j = -3 then i+j = -6 which is not even integer.
it should be 6 to be even integer ie i = j = 3
Please clarify where am i wrong

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Re: If i and j are integers, is i + j an even integer? [#permalink]

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03 May 2012, 00:28
apoorvpan wrote:
what if i and j are negative.
Its mentioned that i and j are integers but its not mentioned that i and j are positive integers.
what if i = j = -3 then i+j = -6 which is not even integer.
it should be 6 to be even integer ie i = j = 3
Please clarify where am i wrong

Negative integers can also be even or dd, for example -6 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 since -6/2=-3=integer then -6 is an even integer.

If i and j are integers, is i + j an even integer?

(1) i < 10 --> no info about j. Not sufficient.
(2) i = j --> $$i+j=j+j=2j$$, as $$j$$ is an integer then $$2j$$ is an even number. Sufficient.

As for zero:

The same way as above: 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 (in fact zero is divisible by every integer except zero itself).

Or in another way: an even number is an integer of the form $$n=2k$$, where $$k$$ is an integer. So for $$k=0$$ --> $$n=2*0=0$$.

Also note that if we were not told that $$i$$ and $$j$$ are integers then this statement would not be sufficient as in this case $$j$$ could be for example 1.5, so $$i+j=j+j=2j=3=odd$$ or $$j$$ could be for example 1.1, so $$i+j=j+j=2j=2.2\neq{integer}$$.

For more on Number Properties check: math-number-theory-88376.html

Hope it helps.
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Re: If i and j are integers, is i + j an even integer? [#permalink]

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30 Jul 2016, 08:34
sirrock wrote:
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If i and j are integers, is i + j an even integer?

(1) i < 10
(2) i = j

We need to determine whether i + j is an even integer. Remember:

even + even = even

odd + odd = even

Thus, if we can determine that i and j are either both even or both odd, we will be able to answer the question.

Statement One Alone:

i < 10

Knowing that i is less than 10 is not enough to determine whether i + j is an even integer. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

i = j

Since we know i = j, we know that i and j are both even or both odd. Following our addition rules for even and odd numbers, we see that i + j must be even.

Statement two alone is sufficient to answer the question.

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Re: If i and j are integers, is i + j an even integer?   [#permalink] 30 Jul 2016, 08:34
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