Hi All,

DS questions are often built around patterns. To get to the correct answer, you don't necessarily have to be great at math....if you can do enough work to prove that a pattern exists (and you can prove whether there's a pattern or not by TESTing VALUES).

Here, we're told that N and K are INTEGERS. We're asked if N is divisible by 7. This is a YES/NO question.

Fact 1: N - 3 = 2K

IF....

K = 1, then N = 5 and the answer to the question is NO.

K = 2, then N = 7 and the answer to the question is YES.

Fact 1 is INSUFFICIENT

Fact 2: (2K - 4) is divisible by 7

This tells us NOTHING about N.

Fact 2 is INSUFFICIENT

Combined, we know:

N-3 = 2K

This first fact tells us that N MUST be ODD. Beyond our initial TESTs (that hint at this), there's a Number Property pattern here.....2(K) = EVEN, so 2K + 3 = ODD. N = 2K + 3, so N must be ODD.

(2K - 4) is divisible by 7

IF....

(2K-4) = 7 then K = 5.5 (this is NOT allowed though, since K MUST be an INTEGER).

(2K-4) = 14 then K = 9

(2K-4) = 21 then K = 12.5 (not allowed)

(2K-4) = 28 then K = 16

Notice from this pattern that K increases by 3.5 each time. We can use THIS pattern to quickly map out other possible values of K that are integers....

K COULD be...9, 16, 23, 30, 37, etc......

Using these values of K and the information in Fact 1....

IF....

K = 9, then N = 21 and the answer to the question is YES

K = 16, then N = 35 and the answer to the question is YES

K = 23, then N = 49 and the answer to the question is YES

Notice how N keeps increasing by 14 (and is always a multiple of 7)? This is another pattern.

Combined, SUFFICIENT.

Final Answer:

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

Rich

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