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WHat do you think the answer is? Explanation please..

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?

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.

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.

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?

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.

WHat do you think the answer is? Explanation please..

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

WHat do you think the answer is? Explanation please..

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...

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.
Answer C.

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.

ANSWER: E

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.