guerrero wrote:If j and k are positive integers, and j + k is odd, what is the value of k?

(1) When j is divided by k, the remainder is 3
(2) j > 7 > 6 > k

Target question: What is the value of k?

Given: j and k are positive integers, and j + k is odd

Statement 1: When j is divided by k, the remainder is 3
There's a nice rule that says: the remainder is always less than the divisor. For example, if we divide an integer by 7, the remainder will be less than 7.
In this particular question, we're told that j divided by k leaves remainder 3, so we can be certain that the divisor (k) is greater than 3.

So, we know that k > 3, and we know a few other things (j+k is odd, etc.) This does not feel like enough information to find the exact value of k, so I'm going to look for different sets of values for j and k that satisfy the given conditions yet yield conflicting answers to the target question.
Here are two such sets of values:
Case a: j = 7 and k = 4, in which case k = 4
Case b: j = 8 and k = 5, in which case k = 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: j > 7 > 6 > k
This tells us that integer k is less than 6. This still leaves several possible values of k (i.e., k = 1 or 2 or 3 or 4 or 5)
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are still several sets of of values that satisfy both statements AND the given information. Here are two:
Case a: j = 11 and k = 4, in which case k = 4
Case b: j = 8 and k = 5, in which case k = 5
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

Hi guerrero,

Brent's explanation for this DS question is right-on; it's exactly how I would handle this question and the approach emphasizes a great way to tackle most DS questions: TEST Values and track the results.

There is one Number Property worth noting that Brent didn't discus, so I'll present it here:

We're told that J and K are positive integers and that J + K is ODD.

With those restrictions, we can deduce that one of the variables is EVEN and the other is ODD. Now, we don't know which is which, but that would be the only way for J + K to be ODD. With that deduction, TESTing values becomes a bit easier, since the possibilities become even more limited. Be on the lookout for these types of Number Property shortcuts; they show up often in DS questions.

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