# Given that n is an integer, is n - 1 divisible by 3?
(1) (n^2+N ) is not divisible by 3
(2) 3N+5>= K+8 , where k is a positive 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.
pl explain your answer. thanks.
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clock60
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here i got A
(1) n(n+1) is not divisible by 3 thus n-1 is divisible by 3 as product of 3 consecutive integers is divisible by 3
(2) do not understand the st
3(n-1)>=k, where k is multiple if 3 say k=3m
3(n-1)>=3m
cancel 3
n-1>=m, or
n-m>=1
from here (n-1) can be divisible or can`t
what is the gist of 2st?
(1) n(n+1) is not divisible by 3 thus n-1 is divisible by 3 as product of 3 consecutive integers is divisible by 3
(2) do not understand the st
3(n-1)>=k, where k is multiple if 3 say k=3m
3(n-1)>=3m
cancel 3
n-1>=m, or
n-m>=1
from here (n-1) can be divisible or can`t
what is the gist of 2st?
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crackinggmat
- Senior | Next Rank: 100 Posts
- Posts: 79
- Joined: Thu Jun 03, 2010 11:58 am
- Thanked: 1 times
clearly A is sufficient...
lets see B .
3N+5 >= k + 8
LET K= 3M
3N + 5 >= 3M +8
3N >= 3M + 3
3N >= 3(M+1)
LHS AND RHS ARE BOTH MULTILES OF 3
IF M = 1 ...RHS WILL BE 6 ,IF N= 4 IT SATISFIES OUR LAST EQUATOIN AND (N -1 ) IS DIVISIBLE BY 3
BUT IF M=1 AND N =3 THAT ALSO SATISFY OUR LAST EQUATION ..BUT IN THAT CASE (N - 1 ) = 2 WHICH IS NOT DIVISIBLE BY 3....
HENCE B does not help....
lets see B .
3N+5 >= k + 8
LET K= 3M
3N + 5 >= 3M +8
3N >= 3M + 3
3N >= 3(M+1)
LHS AND RHS ARE BOTH MULTILES OF 3
IF M = 1 ...RHS WILL BE 6 ,IF N= 4 IT SATISFIES OUR LAST EQUATOIN AND (N -1 ) IS DIVISIBLE BY 3
BUT IF M=1 AND N =3 THAT ALSO SATISFY OUR LAST EQUATION ..BUT IN THAT CASE (N - 1 ) = 2 WHICH IS NOT DIVISIBLE BY 3....
HENCE B does not help....
hi all... here is explanation.... is this true...??pl explain..!!
Statement (1) gives us information about n^2+n , which can be rewritten as the product of two consecutive integers as follows: n^2+n = n(n+1)
Since the question asks us about n - 1, we can see that we are dealing with three consecutive integers: n - 1, n, and n + 1 .
By definition, the product of consecutive nonzero integers is divisible by the number of terms. Thus the product of three consecutive nonzero integers must be divisible by 3.
Since we are told in Statement (1) that the product is not divisible by 3, we know that neither n nor n + 1 is divisible by 3. Therefore it seems that n - 1 must be divisible by 3.
However, this only holds if the integers in the consecutive set are nonzero integers. Since Statement (1) does not tell us this, it is not sufficient.
Statement (2) can be rewritten as follows:
3n+5 >=K+8
3n>=k+3
n>=k/3 +1
Given that k is a positive multiple of 3, we know that n must be greater than or equal to 2. This tells us that the members of the consecutive set n - 1, n, n + 1 are nonzero integers.
By itself, this information does not give us any information about whether n - 1 is divisible by 3. Thus Statement (2) alone is not sufficient.
When both statements are taken together, we know that the members of the consecutive set n - 1, n, n + 1 are nonzero integers and that neither n nor n + 1 is divisible by 3. Therefore, n - 1 must be divisible by 3.
The correct answer is C: both statements together are sufficient but neither statement alone is sufficient to answer the question.
Statement (1) gives us information about n^2+n , which can be rewritten as the product of two consecutive integers as follows: n^2+n = n(n+1)
Since the question asks us about n - 1, we can see that we are dealing with three consecutive integers: n - 1, n, and n + 1 .
By definition, the product of consecutive nonzero integers is divisible by the number of terms. Thus the product of three consecutive nonzero integers must be divisible by 3.
Since we are told in Statement (1) that the product is not divisible by 3, we know that neither n nor n + 1 is divisible by 3. Therefore it seems that n - 1 must be divisible by 3.
However, this only holds if the integers in the consecutive set are nonzero integers. Since Statement (1) does not tell us this, it is not sufficient.
Statement (2) can be rewritten as follows:
3n+5 >=K+8
3n>=k+3
n>=k/3 +1
Given that k is a positive multiple of 3, we know that n must be greater than or equal to 2. This tells us that the members of the consecutive set n - 1, n, n + 1 are nonzero integers.
By itself, this information does not give us any information about whether n - 1 is divisible by 3. Thus Statement (2) alone is not sufficient.
When both statements are taken together, we know that the members of the consecutive set n - 1, n, n + 1 are nonzero integers and that neither n nor n + 1 is divisible by 3. Therefore, n - 1 must be divisible by 3.
The correct answer is C: both statements together are sufficient but neither statement alone is sufficient to answer the question.
