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# Given that n is an integer, is n 1 divisible by 3?

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Given that n is an integer, is n 1 divisible by 3? [#permalink]  18 May 2010, 04:36
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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
[Reveal] Spoiler: OA
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Re: is n — 1 divisible by 3? [#permalink]  18 May 2010, 04:59
dimitri92 wrote:
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,

St1 $$n^2 + n = n* (n +1)$$ is not divisible by 3

which means neither n nor n+1 is divisble by 3 hence n-1 will be divisble by 3

St2 - 3n +5 >= k +8 = > 3n >= K

Now n can be a divisble by 3 or not

for .e g take n = 3 and k = 2 then n is divisble by 3 but if n =4 and k = 2 then n is not.

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Re: is n — 1 divisible by 3? [#permalink]  18 May 2010, 06:48
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dimitri92 wrote:
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

IMO C.

n^2+n = n(n+1) is not divisible by 3 => n-1 is divisible by 3 IF N is no equal to 0,1,-1 else this wont hold true, thus not sufficient.

3n +5 >= k+8
=> 3n >= k+3 , take k = 3m as k is positive multiple of 3

=> 3n>=3m+3
=> n >= m+1 => n>1 Not sufficient.

But if we combine the both then n-1 is divisible by 3 when n>1
Thus C
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Re: is n — 1 divisible by 3? [#permalink]  18 May 2010, 06:55
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gurpreetsingh wrote:
dimitri92 wrote:
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

IMO C.

n^2+n = n(n+1) is not divisible by 3 => n-1 is divisible by 3 IF N is no equal to 0,1,-1 else this wont hold true, thus not sufficient.

3n +5 >= k+8
=> 3n >= k+3 , take k = 3m as k is positive multiple of 3

=> 3n>=3m+3
=> n >= m+1 => n>1 Not sufficient.

But if we combine the both then n-1 is divisible by 3 when n>1
Thus C

n^2+n = n(n+1) is not divisible by 3 => n-1 is divisible by 3 IF N is no equal to 0,1,-1 else this wont hold true, thus not sufficient.

I guess you overlooked some facts,

Let me try to explain them with examples,

Say, n=0 then n(n+1) = 0 -> which is divisble by 3 and hence the st 1 is not valid for this example
Now let n=1 then n(n+1) - > 2 which is not diviable by 3 but then n-1 = 0 which is divisble by 3
Now let n=-1 then n(n+1) = 0 which is again divisble y 3 and hence St 1 does not hold true for this example as well.

Cheers,
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Re: is n — 1 divisible by 3? [#permalink]  18 May 2010, 07:07
nitishmahajan wrote:
gurpreetsingh wrote:
dimitri92 wrote:
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

IMO C.

n^2+n = n(n+1) is not divisible by 3 => n-1 is divisible by 3 IF N is no equal to 0,1,-1 else this wont hold true, thus not sufficient.

3n +5 >= k+8
=> 3n >= k+3 , take k = 3m as k is positive multiple of 3

=> 3n>=3m+3
=> n >= m+1 => n>1 Not sufficient.

But if we combine the both then n-1 is divisible by 3 when n>1
Thus C

n^2+n = n(n+1) is not divisible by 3 => n-1 is divisible by 3 IF N is no equal to 0,1,-1 else this wont hold true, thus not sufficient.

I guess you overlooked some facts,

Let me try to explain them with examples,

Say, n=0 then n(n+1) = 0 -> which is divisble by 3 and hence the st 1 is not valid for this example
Now let n=1 then n(n+1) - > 2 which is not diviable by 3 but then n-1 = 0 which is divisble by 3
Now let n=-1 then n(n+1) = 0 which is again divisble y 3 and hence St 1 does not hold true for this example as well.

Cheers,

ok great catch ..but are you suggesting A or C then ?
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Re: is n — 1 divisible by 3? [#permalink]  18 May 2010, 07:08
yes right, got it Thanks

should be A
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Re: is n — 1 divisible by 3? [#permalink]  18 May 2010, 18:47
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1 - neither n or n+1 are divisible by 3. Thus, n-1 must be divisible by 3, since every 3rd integer is divisible by 3. SUFF

2 - 3n + 5 >= k + 8

3n - 3 >= k

3(n-1) >= k

Because we know k is divisible by 3, but not 9 (3x3), n-1 could or could not be divisible by 3. INS

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Re: is n — 1 divisible by 3? [#permalink]  18 May 2010, 21:39
I completely understand how statement 1 is sufficient, but am going to have to review statement 2 further to understand why it is not sufficient. I understand the simple math just not the explanation that follows.

Good question though. Had me thinking. Thank you very much.
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Re: is n — 1 divisible by 3? [#permalink]  19 Jul 2011, 02:30
its MGMAT

The OE for statement 1.

Since we are told in Statement (1) that the product n^2+n 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.

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Re: is n — 1 divisible by 3? [#permalink]  19 Jul 2011, 02:45
sudhir18n wrote:
its MGMAT

The OE for statement 1.

Since we are told in Statement (1) that the product n^2+n 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.

Neither.

Here is my logic:

We know this from the question stem:
n = Set of all integers = {..., -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, ... }

1) n^2 + n is not divisible by 3

We now know:
n = {... -11, -8, -5, -2, 1, 4, 7, 10, ...} <--- very clear pattern here

We are interested in n-1 (but only from the above set, which meet our condition imposed on 1)
n - 1 = {..., -12, -9, -6, -3, 0, 3, 6, 9, ... }

Let's check these against what ware testing for, are these divisible by three? Very clearly, yes.

1 is sufficient.
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Re: is n — 1 divisible by 3? [#permalink]  19 Jul 2011, 03:47

if n(n+1) is not divisible by 3 that itself means that n or n+1 cannot be 0.
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Re: is n — 1 divisible by 3? [#permalink]  19 Jul 2011, 04:48
sudhir18n wrote:
its MGMAT

The OE for statement 1.

Since we are told in Statement (1) that the product n^2+n 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.

Thanks Sudhir. Please notify MGMAT. Product of three consecutive integers must be divisible by 3 irrespective of 0, -ves or +ves.

(n-1)n(n+1) must be divisible by 3.
n(n+1): Not Divisible
(n-1): must be divisible
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Re: is n — 1 divisible by 3? [#permalink]  19 Jul 2011, 04:58
A is the answer, if we consider "0" is divisible by "3" otherwise C.
I would lean towards A
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Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink]  31 Mar 2013, 06:16
Can experts say the final word regarding option (1)? I wonder whether A is sufficient
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Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink]  31 Mar 2013, 06:55
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Expert's post
LalaB wrote:
Can experts say the final word regarding option (1)? I wonder whether A is sufficient

Given that n is an integer, is n — 1 divisible by 3?

(1) n^2 + n is not divisible by 3 --> n(n+1) is not divisible by 3 --> neither n nor n+1 is divisible by 3. Now, n-1, n and n+1 are three consecutive integers, thus one of them must be divisible by 3, so if n and n+1 are NOT, then n-1 must be. Sufficient.

(2) 3n +5 >= k+8 , where k is a positive multiple of 3. Not sufficient.

Hope it's clear.
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Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink]  02 Jun 2013, 12:25
Bunuel wrote:
LalaB wrote:
Can experts say the final word regarding option (1)? I wonder whether A is sufficient

Given that n is an integer, is n — 1 divisible by 3?

(1) n^2 + n is not divisible by 3 --> n(n+1) is not divisible by 3 --> neither n nor n+1 is divisible by 3. Now, n-1, n and n+1 are three consecutive integers, thus one of them must be divisible by 3, so if n and n+1 are NOT, then n-1 must be. Sufficient.

(2) 3n +5 >= k+8 , where k is a positive multiple of 3. Not sufficient.

Hope it's clear.

Can you kindly explain why B is not sufficient...
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Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink]  02 Jun 2013, 12:56
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Expert's post
karjan07 wrote:
Bunuel wrote:
LalaB wrote:
Can experts say the final word regarding option (1)? I wonder whether A is sufficient

Given that n is an integer, is n — 1 divisible by 3?

(1) n^2 + n is not divisible by 3 --> n(n+1) is not divisible by 3 --> neither n nor n+1 is divisible by 3. Now, n-1, n and n+1 are three consecutive integers, thus one of them must be divisible by 3, so if n and n+1 are NOT, then n-1 must be. Sufficient.

(2) 3n +5 >= k+8 , where k is a positive multiple of 3. Not sufficient.

Hope it's clear.

Can you kindly explain why B is not sufficient...

Sure.

(2) says that 3n +5 >= k+8 , where k is a positive multiple of 3 --> k=3x, for some positive integer x --> $$3n +5\geq{3x+8}$$ --> $$3n-3\geq{3x}$$ --> $$n-1\geq{x}$$. So, basically we just have that n-1 is greater or equal to some positive integer x, thus it may or may not be a multiple of 3.

Hope it's clear.
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Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink]  03 Sep 2013, 05:12
Quote:
(2) says that 3n +5 >= k+8 , where k is a positive multiple of 3 --> k=3x, for some positive integer x --> $$3n +5\geq{3x+8}$$ --> $$3n-3\geq{3x}$$ --> $$n-1\geq{x}$$. So, basically we just have that n-1 is greater or equal to some positive integer x, thus it may or may not be a multiple of 3.

Just to go a bit further on this, in what case would $$n-1$$ be divisible by $$3$$? Say if you ended up with $$n-1\geq{3x}$$ it would still be insufficient, is not it so? The fact that we have $$\geq$$ seems to necessarily mean that $$n-1$$ may not necessarily be divisible because we have so many options, or I am missing the point here?
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Re: Given that n is an integer, is n 1 divisible by 3? [#permalink]  30 Dec 2013, 09:10
dimitri92 wrote:
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

The product of three consecutive integers (n-1)(n)(n+1) must be divisible by 2

Statement 1

If n^2+n= n(n+1) is not divisible by three then (n-1) must be divisible by 3

Suff

Statement 2

If k is a multiple of three
Then we get that 3n >= k + 3
This only tell us that n >=1 but nothing else. Could be any number

Hope it helps
Cheers!
J

That means that n
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Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink]  26 Apr 2014, 03:25
Bunuel wrote:
LalaB wrote:
Can experts say the final word regarding option (1)? I wonder whether A is sufficient

Given that n is an integer, is n — 1 divisible by 3?

(1) n^2 + n is not divisible by 3 --> n(n+1) is not divisible by 3 --> neither n nor n+1 is divisible by 3. Now, n-1, n and n+1 are three consecutive integers, thus one of them must be divisible by 3, so if n and n+1 are NOT, then n-1 must be. Sufficient.

(2) 3n +5 >= k+8 , where k is a positive multiple of 3. Not sufficient.

Hope it's clear.

Hi Bunnel,

I choose ans as D. st1 is fine no issue.

my reasoning in st2

3n+5 >= k+8
3n+5 >= k+5+3
3n >= k+3
3n-3>k
3(n-1)>k

cant we say that n-1 is a multiple of 3?

Thanks.
Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 +   [#permalink] 26 Apr 2014, 03:25

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