If k is a Positive Integer and n = k(k + 7), is n Divisible by 6? GMAT Data Sufficiency

Question: If k is a positive integer and n = k(k + 7), is n divisible by 6?

(1) k is odd.
(2) When k is divided by 3, the remainder is 2.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: B

Solution and Explanation:
Approach Solution 1:

The problem statement states that:

Given:

k is a positive integer
n = k(k + 7)

Find out:

If n is divisible by 6

Since, n = k(k + 7), therefore, we can say, n = 8k^2

Now, we can say, for n to be divisible by 6, the value of k must be divisible by 3.

The statement implies that k is odd.

Therefore, for k=1, the answer is No whereas, for k=3, the answer is Yes.
Thus the statement alone is not sufficient.

The statement suggests that when k is divided by 3, the remainder is 2.

This means the value of k cannot be divisible by 3 since there exists a remainder of 2.
Therefore, the value of n will not be divisible by 6.
Hence the statement alone is sufficient.

Approach Solution 2:

The problem statement informs that:

Given:

k is a positive integer
n = k(k + 7)

The problem statement asked to find whether n is divisible by 6 or not.

(1) k is odd.

If the value of k=1, then n= k(k+7)= 8
Therefore, n is not divisible by 6
However, if k=3, then n=k(k+7)=30
Therefore, the value of n is divisible by 6.
Hence the statement alone is insufficient.

(2) When k is divided by 3, the remainder is 2.

Therefore we can say, k=3x+2;
As given in the question, n=k(k+7)

Therefore, we get,
=> n = (3x + 2)(3x + 9)
=> n = 9x^2 + 33x + 18
=> n = 3(3x^2 + 11x) + 18.
It is required to note that 3x^2+11x is even no matter whether the value of x is even or odd. Therefore, we can say:

n = 3(3x^2 + 11x)+18
= 3∗ even + (a multiple of 6)
= (a multiple of 6)+(a multiple of 6)
= (a multiple of 6)

Therefore, the statement alone is sufficient.

Approach Solution 3:

The question states that n=k (k+7)
Statement (1) implies that k is odd then
=> odd * (odd + odd) = Odd * Even.
Therefore, we can not ensure that it is a multiple of 6 or not.
Hence, the statement is insufficient.

Statement (2) implies that when k is divided by 3, the remainder is 2
Therefore we can say, k = 3m +2.
As given in the question, n=k (k+7)
=>n = (3m+2)(3m+9)
=>n = 3(3m+2)(m+3) => multiple of 3.

If the value of m is odd then m+3 is even.
Therefore, it is a multiple of 2. Also, it is a multiple of 3. Hence the term n is a multiple of 6.

If the value of m is even then 3m+2 is even.
Therefore, it is a multiple of 2. Also, it is a multiple of 3.
Hence the term n is a multiple of 6.
Hence, the statement alone is sufficient.

“If k is a positive integer and n = k(k + 7), is n divisible by 6?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide 2021". GMAT Data Sufficiency questions constitute a problem statement that is followed by two factual statements. The GMAT Quant section has a total of 31 questions among which the GMAT data sufficiency comprises 15 questions.

Suggested GMAT Data Sufficiency Questions

SHARE ON FACEBOOK SHARE ON TWITTER

If k is a Positive Integer and n = k(k + 7), is n Divisible by 6? GMAT Data Sufficiency

Fees Structure

Comments

SUBSCRIBE TO OUR NEWS LETTER