If n and k are positive integers, is n divisible by 6?
(1) n = k(k + 1)(k - 1)
(2) k – 1 is a multiple of 3.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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Divisible problem
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namitrajiv
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A it ,
n = (k-1)k(k+1)
implies product of 3 consecutive numbers , which will always be divisible by 6
n = (k-1)k(k+1)
implies product of 3 consecutive numbers , which will always be divisible by 6
IMO A.gmat009 wrote:If n and k are positive integers, is n divisible by 6?
(1) n = k(k + 1)(k - 1)
(2) k – 1 is a multiple of 3.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
in order for n to be divisible by 6, it needs prime factorization of 2 & 3. if you look at statement 1, it's 3 consecutive # that starts with number greater than 0 since it has to be positive. Therefore, for any given value of k, n is divisible by 6.
Statement B does not give us any information about n - not sufficient.
What's the OA?
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cubicle_bound_misfit
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thephoenix
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product of 3 consecutive no. will have a no. which is multiple of 3 and a no. which is multiple of 2duongthang wrote:how do you know that product of 3 consecutives is divided by 3.2
pls, prove.
n*(n+1)*(n+2)
if n is odd , then two case arises either it is div by 3 or not ; but in any case n+1 is div by 2
now when its div by 3 -------> the no. is div by 6
when it is not div by 3-------->then either n+1 or n+2 will be div by 3
and hence the product is div by 6
if n is even ---------> div by 2
either n+1 or n+2 will be div by 3
hence the product will be div by 6
one check with no's....
1*2*3
2*3*4
4*5*6
5*6*7
7*8*9
any combination u pick it will div by 6
HTH
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Brent@GMATPrepNow
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Target question: Is n divisible by 6?gmat009 wrote:If n and k are positive integers, is n divisible by 6?
(1) n = k(k + 1)(k - 1)
(2) k-1 is a multiple of 3.
Aside: For a number to be divisible by 6, it must be divisible by 2 AND by 3
Statement 1: n = k(k + 1)(k - 1)
First recognize that k-1, k and k+1 are 3 consecutive integers
There's a nice rule that says: If there are b consecutive integers, then exactly one of them is divisible by b
Since there are 3 consecutive integers, we know that one of them is divisible by 3.
We can also conclude that at least one of them is divisible by 2.
Given all of this, the product of the 3 integers (n) must be divisible by 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: k-1 is a multiple of 3
Since there's no information about n, there's no way to determine whether or not n is divisible by 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Brent@GMATPrepNow wrote:Target question: Is n divisible by 6?gmat009 wrote:If n and k are positive integers, is n divisible by 6?
(1) n = k(k + 1)(k - 1)
(2) k-1 is a multiple of 3.
Aside: For a number to be divisible by 6, it must be divisible by 2 AND by 3
Statement 1: n = k(k + 1)(k - 1)
First recognize that k-1, k and k+1 are 3 consecutive integers
There's a nice rule that says: If there are b consecutive integers, then exactly one of them is divisible by b
Since there are 3 consecutive integers, we know that one of them is divisible by 3.
We can also conclude that at least one of them is divisible by 2.
Given all of this, the product of the 3 integers (n) must be divisible by 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: k-1 is a multiple of 3
Since there's no information about n, there's no way to determine whether or not n is divisible by 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
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