Is the Positive Integer n Divisible by 8? (1) n is Divisible by the Product of Three GMAT Data Sufficiency

Question: Is the positive integer n divisible by 8?

(1) n is divisible by the product of three consecutive integers.
(2) n is divisible by the product of two consecutive even integers.

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:
(1) n is divisible by the product of three consecutive integers.

If these three consecutive integers are 1, 2, and 3, then the product is 6 and the answer is NO;
If these three consecutive integers are 2, 3, and 4, then the product is 24 and the answer is YES.

Not sufficient.

(2) n is divisible by the product of two consecutive even integers.
Out of any two consecutive EVEN integers, one will be disabled by 4. So, the product will be divisible by
2∗4=8
2∗4=8.

Sufficient.

Approach Solution 2:
Statement 1 :

N is divisible by the product of three consecutive integers.

Let the set of integers be : {1,2,3} product = 6.
Now 12 is divisible by 6 but not by 8.
24 is divisible by 6 and by 8 as well.

Thus the statement is not sufficient.

Statement 2 :

N is divisible by the product of two consecutive even integers.
for two consecutive even integers : the product will be of the form : 2^t * 2^(t+1)
Minimum t=1, Thus minimum value of index on 2 =3 . Thus product is always of the form = 8k.

Hence N is divisible.

Approach Solution 3:
For n to be divisible by 8, n should contain min. power of 2 as 3.

Statement 1

Case A: 3 consecutive integers can be 2 Odd & 1 Even....if this is the case then n is may be or may be not divisible by 8 as the even integer has to be multiple of 8.
Case B: 3 consecutive integers can be 1 Odd & 2 Even....if this is the case then n is may be divisible by 8 as the min. even integers can be 2 & 4.

Insufficient info.

Statement 2

Min. even integers can be 2 & 4, hence n will be divisible by 8.

Sufficient info.

“Is the positive integer n divisible by 8? (1) n is divisible by the product of three”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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Is the Positive Integer n Divisible by 8? (1) n is Divisible by the Product of Three GMAT Data Sufficiency

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