If k and n are integers, is n divisible by 7 ?

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From Statement 1, 2k must be even, so we also know that n is odd because 2k + 3 must be odd. n could be any odd multiple of 7 (21, 35, etc.), but it could also be an odd number that is not a multiple of 7 (like 11). Insufficient.

From Statement 2, there is nothing about n, so it is clearly insufficient.

Combined, 2k - 4 is a multiple of 7, so 2k + 3 (which is equal to n) must also be a multiple, since (2k - 4) + 7 = 2k + 3. Sufficient.

As in the st.1 , can we work with smart numbers in the Stmt. 2 and the combined one (1 + 2 ) . Please help.

For (2) we cannot use plugging because no info is given about n. When we combine we get that n = 7q + 7. You can plug-in integer values for q there to see that all of them will give n which is in fact divisible by 7.

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

What if I just noticed since 1) says 2K+3 and 2) says 2K-4 they have a difference of 7? Is that sufficient enough?

Hi fiel9882,

You've caught one of the hidden patterns in this question. From Fact 2, we know that (2K-4) is divisible by 7, which means that it's a multiple of 7. Adding or subtracting any other multiple of 7 to (2K-4) will give you a new number that is ALSO divisible by 7.

So... (2K-4) + 7 = 2K+3.... so that term must also be a multiple of 7.

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

How is 2k becoming 7 when you add (1)+(2)? Please explain

\((n-3)+(2k-4) = 2k+7q\);

\(n+2k-7 = 2k+7q\);

Cancel 2k: \(n-7 = 7q\);

Add 7 to both sides: \(n= 7q+7\);

\(n=7(q+1)\).

Dear Experts
while solving, I came up with below understanding to solve this problem,
Requesting for guidance, is this method correct / if wrong, why?

is n divisible by 7?

Statement 1: n=2k+3 ---------not sufficient
Statement 2: (2k-4) is divisible by 7
Dividend = Divisor × Quotient + Remainder
7 = (2k-4) +3
2k = 11 ------------------not suffcient

substitude in statement (1)
n=2k+3
n=11+3
n=14
14 is divisible by 7 - "Option C"

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