Data Sufficiency

ATI wrote:Q14 of DS section of OG 13 is:
Question: If i and j are integers, is i+j an even integer?
(1) i>10
(2) i=j

Answere given in OG is option B - i.e. Only statement 2 is sufficient to solve the question. And explanation is based on following logic: If i=j then i+j=2i, implies it will be even since i is getting multiplied by 2.

I think answer to this question should be E - information is not sufficient to answer since "i" can be zero as well. In question it is mentioned i and j are integer so they can be zero as well.

Please can someone help me to analyze this. What am I doing wrong?

Thanks,

It's a common mistake to believe that 0 is neither odd nor even.
0 is actually even.

EVENS: ...-4, -2, 0, 2, 4, 6, ...
ODDS: -3, -1, 1, 3,5,...

Cheers,
Brent

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

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

Target question: Is i+j an even integer?

Statement 1: i > 10
We have no information about j, so there's no way to determine whether or not i+j is an even integer.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: i = j
Since we're told that i and j are integers, there are two possibilities to consider here:
case a: i and j are both EVEN integers, in which case i+j = even + even = EVEN
case b: i and j are both ODD integers, in which case i+j = odd + odd = EVEN
In both possible cases, i+j = EVEN, so we can be certain that the sum of i+j is even
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

Hi ATI,

Brent's solution emphasizes the use of Number Properties, which can make it far easier to score at a high level in the Quant section.

It's worth noting that Number Property questions can almost always be solved by TESTing VALUES.

Here, we're told that I and J are INTEGERS. We're asked if I+J = an EVEN INTEGER. This is a YES/NO question.

Fact 1: I > 10

Your initial reaction would probably be to think that you don't know anything about J, so Fact 1 is probably insufficient. You can quickly prove it though:

If....
I = 11 and J = 0, then I+J = 11 and the answer to the question is NO.
I = 11 and J = 1, then I+J = 12 and the answer to the question is YES.
Fact 1 is INSUFFICIENT.

Fact 2: I=J

If....
I = 0 and J = 0, then I+J = 0 and the answer to the question is YES.
I = 1 and J = 1, then I+J = 2 and the answer to the question is YES.
I = 2 and J = 2, then I+J = 4 and the answer to the question is YES.
I = -3 and J = -3, then I+J = -6 and the answer to the question is YES.
Etc.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich