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.

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

For more on Number Properties check:

math-number-theory-88376.htmlHope it helps.

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