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.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. 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.

Suggested GMAT Data Sufficiency Samples

• A rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively GMAT Data Sufficiency
• What is the circumference of circle C ? (1) The radius of circle C is 2π GMAT Data Sufficiency
• Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is 5 units GMAT Data Sufficiency
• If each side of parallelogram P has length 1, what is the area of P? GMAT Data Sufficiency
• Is the positive integer n a multiple of 24? GMAT Data Sufficiency
• Did Insurance Company K have More than $300 Million in Total Net Profits Last Year? GMAT Data Sufficiency
• Is 1/(a - b) > b - a ? GMAT Data Sufficiency
• Is |x-10| > |x-30| GMAT Data Sufficiency
• If J≠0, What Is The Value Of J? GMAT Data Sufficiency
• P and Q are prime numbers less than 70. What is the units digit of P*Q? GMAT Data Sufficiency 
• Max purchased a guitar for a total of $624,which consisted of the price of the guitar and the sales tax. GMAT Data Sufficiency 
• In the figure shown, point O is the center of the semicircle and points B, C, D lie on the semicircle GMAT Data Sufficiency 
• Is 500 the average (arithmetic mean) score on the GMAT? GMAT Data Sufficiency 
• If 4x = 5y = 10z, what is the value of x + y + z ? (1) x - y = 6 (2) y + z = 36 GMAT Data Sufficiency 
• If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies GMAT Data Sufficiency
• From a Group of M Employees, N Will be Selected, at RandomGMAT Data Sufficiency-
• Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)? GMAT Data Sufficiency
• Figure ABCD is a rectangle with sides of length x centimeters and width y centimeters, and a diagonal of length z centimeters. GMAT Data Sufficiency 
• Can the Positive Integer p be Expressed as the Product of Two Integers GMAT Data Sufficiency 
• A School Administrator will Assign each Student in a Group GMAT Data Sufficiency 
• What is the total value of Company H's stock? GMAT Data Sufficiency
• Is PQ > 1? GMAT Data Sufficiency
• How Many of the Students in a Certain Class are Taking Both a History and a Science Course? GMAT Data Sufficiency
• The Set S of Numbers has the following Properties GMAT Data Sufficiency
• A Contractor Combined x Tons of a Gravel Mixture that Contained 10 percent Gravel G GMAT Data Sufficiency
• If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies GMAT Data Sufficiency
• From a Group of M Employees, N Will be Selected, at Random, GMAT Data Sufficiency
• Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)? GMAT Data Sufficiency
• Juan Bought Some Paperback Books That Cost $8 GMAT Data Sufficiency
• The symbol ∆ Denotes One of The Four Arithmetic Operations GMAT DATA Sufficiency
• X is Older Than Y, Z Is Younger Than W And V is Older Than Y. Is Z Younger Than X? GMAT Data Sufficiency
• 2x+3y GMAT Critical Reasoning
• The Selling Price of an Article is Equal to the Cost of the Article GMAT Critical Reasoning
• If Vertices of a Triangle have Coordinates (-2,2) (3,2) GMAT Data Sufficiency
• If Set S Consists of Even Number of Integer, Is the Median GMAT Data Sufficiency
• What Is The Value Of N GMAT Data Sufficiency
• What is the value of x^2 + 1/x^2 ? GMAT Data Sufficiency
• Is the range of a combined set (S,T) bigger than the sum of the ranges of sets S and T? GMAT Data Sufficiency
• How many integers in a group of 5 consecutive positive integers are divisible by 4? GMAT Data Sufficiency
• Is the standard deviation of set S greater than the standard deviation of set T? GMAT Data Sufficiency
• Is a^7∗b^2∗c^3>0? (1) bc < 0 (2)ac > 0 GMAT Data Sufficiency
• If n is a non-negative integer, is 10^n+8 divisible by 18? GMAT Data Sufficiency
• Is the Range of Set S Greater than its Mean? GMAT Data Sufficiency
• Equilateral triangle BDF Is Inscribed in Equilateral Triangle ACE GMAT Data Sufficiency
• What is the value of x if x^3 < x^2? GMAT Data Sufficiency
• If x ≠0, then what is the value of (|x|)x? GMAT Data Sufficiency
• What is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair? GMAT Data Sufficiency
• Does The Equation y = (x – p)(x – q) Intercept The x-axis At GMAT Data Sufficiency
• S is a Set of n Consecutive Positive Integers. Is the Mean of the Set GMAT Data Sufficiency
• What is x? (1) |x| < 2 (2) |x| = 3x – 2 GMAT Data Sufficiency