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.
D. …Each statement
Hey VPat ,
Can u tell me why it is D ?
Statement 2 does not do anything good as far as I notice
I chose A
A
C
A
E
A
A
c
I don´t understand the second statment … can anyone explain it???
Anyway … i think that the right answer is A
I guess C is the correct answer. If we go with answer A the expression is not correct for k=1.
I think “C” is the correct answer.
C
C.
Answer cannot be anything but “E”
Answer is A definately
As n = k(k + 1)(k – 1) or n = (k – 1)k(k + 1)
so we’ve 3 consecutive integers.
this implies we must have 1 of these integers as a multiple of 3.
and also atleast 1 of these should be even so div by 2
as n is div by 2 &3 so always divisible by 6.
GMAT Team. pls recheck your soln.
The ans is A.
For N to be div. by 6 it has to be div. by 2 and 3
For any +ve int K,
If K is even, then K+1 & K-1 will be odd and either of them will be div by 3. so N will be div by 6
If K is odd, K+1 and K-1 will be even and either one will be div by six.
take any 3 cons. integers randomly and you have the ans.
cond> B is insuff. as it does not tell us anything about N
The answer of TakeGMAT Team is right!
ANSWER C
Rephrasing the 1st statement, n=(k-1)k(k+1). From the question, it is clear that ‘k’ is a positive integer. Hence, minimum value of k is 1. If k = 1, then n = 0. And if k > 1, then a consecutive series is formed for ‘n’, which will be a multiple of 2, 3 and 6. So this statement alone is not enough.
From 2nd statement, it is clear that all ‘k’ values will not be a multiple of 6 unless it is a multiple of 2 also. So this statement alone is not enough.
hey srinivas,
if K=1, n would be zero. and the question says n is a positive integer. zero is signless. so that would make gmat team’s ans wrong.
(A) is the one.
I think it is A. Since statement 2 alone doesn’t suffice the requirement.
But i have a dilemma. From statement 1, when k=1, n=0 and product is 0, which is still divisible by 6. But do we need to take into consideration that n becomes 0 and not a positive integer? GMAT team, please clarify.
A
the answer is obviously A
Srinivasan, i’m sorry to say this but u really need to work on ur maths bro..
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.
Statement 1: Since n and k are positive integer, k can take a value of 1, therefore, n = 1 (1+1) (1-1) = 0 which is not true since n has to be a positive integer as well.
Statement 2: We only know k>1 and is a multiple of 3 but there is no relationship between n and k, but we do know that k>1, therefore n will now be greater than 1 and divisible by 6 (since ‘k’ is a multiple of 3).
So answer is C