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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.

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

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.

Answer: B.

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 \(i+j=j+j=2j=2.2\neq{integer}\).

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.

The answer is B.
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Jeffery Miller Head of GMAT Instruction

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