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# (D/S) N is divisible by 6

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Manager
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(D/S) N is divisible by 6 [#permalink]

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13 Nov 2007, 08:12
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Q. Positive Integer N is divisible by 6?

1) 2N is divisible by 3
2) N^2+1 is a prime number

C or E?

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VP
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Re: (D/S) N is divisible by 6 [#permalink]

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13 Nov 2007, 08:20
pretttyune wrote:

Q. Positive Integer N is divisible by 6?

1) 2N is divisible by 3
2) N^2+1 is a prime number

C or E?

Lemmi give it a shoot.

1. 2n is divisible by 3. then n can be 3 or 6. thus insuff.

2. n^2+1 is a prime number. then n can be 2 or 3, 4 or 6 so insuff.

combined n can be 3 or 6 so insuff.

E.

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Manager
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Re: (D/S) N is divisible by 6 [#permalink]

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13 Nov 2007, 09:02
Ravshonbek wrote:
pretttyune wrote:

Q. Positive Integer N is divisible by 6?

1) 2N is divisible by 3
2) N^2+1 is a prime number

C or E?

Lemmi give it a shoot.

1. 2n is divisible by 3. then n can be 3 or 6. thus insuff.

2. n^2+1 is a prime number. then n can be 2 or 3, 4 or 6 so insuff.

combined n can be 3 or 6 so insuff.

E.

E right?! I thought so, but the answer, though it is not the official answer bc I've got this question on the web community, was C.. so, the answer on that site was wrong, wasn't it?

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Intern
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13 Nov 2007, 09:36
I believe the answer is C.

A. If 2N/3 is an integer, then N can be 3, 6, 9 etc. (Insuff.)
B. If N^2 + 1 is prime, then N can be 2, 4 or 6 (i.e. 5, 17 or 37 so Insuff).

Together, N cannot be 2, since 2(2)/3 is not an integer. Also, 2(4)/3 is not an integer. However, 2(6)/3 is an integer, and (6)/(6) is an integer, so C.

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Director
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13 Nov 2007, 11:30
Statement 1
-----------------
2N/3 is an integer means 2N is divisible by 3 --> N is divisible by 3 --> N is a mutiple of 3
Possible values for N : 3,6,9,12,15,18,21,24,27,30,33,35 ...

Statement 2
----------------
Possible values for N : 2,4,6,10, 24 ...

Statements 1+2
------------------
More than one possible integer overlap.

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SVP
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13 Nov 2007, 14:12
. Positive Integer N is divisible by 6?

1) 2N is divisible by 3
2) N^2+1 is a prime number

is N = 3*2 x?

From one:

2n = 3k ie n = 3/2k ie : if k = 6 thus n=9 , if k = 4 thus n = 6 ..insuff

n^2+1 = prime , ie n = 1 if prime = 2 or 4 if prime = 17 or 6 if prime is 37........insuff

both:

n^2+1 = 9/4k^2 + 1 =prime

prime here is always odd because k is a +ve intiger

prime - 1 = even intiger = 9/4k^2

thus k^2 must be in the form 2^2 p^2 , thus 9/4 k^2 = 9*p^2 and p is even or odd...............insuff

i know it is a bit lenghty and might look confusing , apologies

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Director
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13 Nov 2007, 19:44
Agree with mistahfold explanation. Think it is C.

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Senior Manager
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Re: (D/S) N is divisible by 6 [#permalink]

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14 Nov 2007, 06:55
pretttyune wrote:

Q. Positive Integer N is divisible by 6?

1) 2N is divisible by 3
2) N^2+1 is a prime number

C or E?

From 1

n = 3,6,9,12,15,18,21,24............

From 2

n = 1,2,4,6,10,

I find only one common value..........so ans is (C).

What's the source of this question??

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Senior Manager
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Re: (D/S) N is divisible by 6 [#permalink]

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14 Nov 2007, 06:56
pretttyune wrote:
E right?! I thought so, but the answer, though it is not the official answer bc I've got this question on the web community, was C.. so, the answer on that site was wrong, wasn't it?

Which web community are you referring to???

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Manager
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14 Nov 2007, 08:16
I make it C as well.

Statement 1 – can be – 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 – Note all the even numbers are a multiple of 6

Statement 2 – can be – 1, 2, 4, … and ONLY even numbers thereafter (as all odd numbers squared are odd, and the +1 will mean the result is even – and 2 is the only even prime)

Thus, the only numbers that fit both are multiples of 6.

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SVP
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15 Nov 2007, 10:21
Still beleive it is E, if anyone can help me point out where my logic is wrong , i will appreciate

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GMAT Instructor
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Re: (D/S) N is divisible by 6 [#permalink]

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15 Nov 2007, 10:43
pretttyune wrote:

Q. Positive Integer N is divisible by 6?

1) 2N is divisible by 3
2) N^2+1 is a prime number

C or E?

(1) N is a multiple of 3, but can be odd or even
NOT SUFF
(2) Note that 2 is the only even prime. Thus N is either 1 or a positive even number.
NOT SUFF
(T) As 1 is not a multiple of 3, (2) tells us that N is even. (1) tells us N is a multiple of 3.
SUFF

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Re: (D/S) N is divisible by 6 [#permalink]

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15 Nov 2007, 11:57
kevincan wrote:
pretttyune wrote:

Q. Positive Integer N is divisible by 6?

1) 2N is divisible by 3
2) N^2+1 is a prime number

C or E?

(1) N is a multiple of 3, but can be odd or even
NOT SUFF
(2) Note that 2 is the only even prime. Thus N is either 1 or a positive even number.
NOT SUFF
(T) As 1 is not a multiple of 3, (2) tells us that N is even. (1) tells us N is a multiple of 3.
SUFF

C.
1) n could be 3 or multiple of 3. if n is 3 or an odd multiple of 3, not possible. if n is an even multiple of 3, yes.
2) n could be 1 or 2, 4, 6, 10, or some other even integers (because the same doesnot apply with 8).

Togather, n has to be an even multiple of 3, which is obviously a multiple of 6. suff...

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CEO
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Re: (D/S) N is divisible by 6 [#permalink]

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15 Nov 2007, 21:39
pretttyune wrote:

Q. Positive Integer N is divisible by 6?

1) 2N is divisible by 3
2) N^2+1 is a prime number

C or E?

1: 2N is divisible by 3. This means that N is divisible by 3. Stem says N is an integer so no mixed fractions are possible. Ex/ 9/2

N can be 3 or 6. insuff

2: N^2+1 is a prime number well N can be 1^2+1--> 2 or 6^2+1 --> 37

Insuff.

1 and 2: We already have one case to prove YES for 1 and 2. N =6

2(6)/3 OK 6^2+1= prime.

Now notice whenever N is odd N^2+1 is even (O+O=E) so in order for N^2 +1 to be prime we are going to have make N even. (E+O=O)

Attempting several values we cannot get a prime number out of N^2+1 under the condition that N is divisible by 3 and NOT divisible by 6.

Ex: 24*24=576+1=577 which is prime. However 24 is divisible by 6 so the answer again is YES.

C

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Manager
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15 Nov 2007, 22:50
Q. Positive Integer N is divisible by 6?

1) 2N is divisible by 3
2) N^2+1 is a prime number

1. For 2N to be divisble by 3 , N has to be divisible by 3. So N is 3 and multiples of 3
2. Since it is a prime. N^2 is even
So N is even ; hence N is divisible by 2

If put together ; N is divisible by 2 as well as 3; hence by 6.

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Manager
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16 Nov 2007, 04:49
Mishari wrote:
Statement 1
-----------------
2N/3 is an integer means 2N is divisible by 3 --> N is divisible by 3 --> N is a mutiple of 3
Possible values for N : 3,6,9,12,15,18,21,24,27,30,33,35 ...

Statement 2
----------------
Possible values for N : 2,4,6,10, 24 ...

Statements 1+2
------------------
More than one possible integer overlap.

Agreed that there are more than 2 values (6,24..) which satisy 1) & 2) taken together however it does help us answer the question stem without any ambiguity. And the answer to question stem is YES, since 6 & 24 both show that 2N/3 is divisible by 3.

Ans should be C.

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16 Nov 2007, 04:49
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