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
_________________
Contact Rich at: Rich.C@empowergmat.com The Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★