If n + 12 is a positive odd integer, which of the following must be

Question

If n + 12 is a positive odd integer, which of the following must be true about the sum of the next four integers?

A. It is a multiple of 3 
B. It is a multiple of 4 
C. It is a prime number 
D. It is a multiple of 5 
E. It is a multiple of 2

chetan2u · Answer

Hi,
Irrespective of n+12 as ODD or EVEN, any four consecutive integers sum will be EVEN, so it will be div by 2
E

OptimusPrepJanielle · Answer

n+12 is a positive odd integer. This means n will be an odd integer
The next 4 integers would be: n + 12, n + 13, n + 14, n + 15
Sum = 4n + 54
This sum will always be even.
Option E

stonecold · Answer

Here is my solution to this one ->
As n+12 is odd => n will be odd
The sum of next four integers will be even+odd+even+odd => Even.
Hence the sum will be a multiple of 2

Abhishek009 · Answer

n + Even = Odd

So, n = Odd

Now, we have : ODD + EVEN + ODD + EVEN = EVEN

Hence, the sum must be Even and will be divisible by 2 , answer will be (E)

RR88 · Answer

Option E

A sum of Even number of consecutive integers, such that the number of integers (K) is a multiple of 4, is always Even and hence, a multiple of 2.

E.g. 
K = 4, 1+2+3+4 = 10 = Multiple of 2/Even
K = 6, 1+2+3+4+5+6 = 21 = Not a multiple of 2/Odd
K = 8, 1+2+3+4+5+6+7+8 = 36 = Multiple of 2/Even

gmatexam439 · Answer

Hello Bunuel, I don't really get the OA. According to my calculation it should always be divisible by 4 and of course 2.

My Explanation:
For n+12 to be a positive odd integer n should be =-11 (min) or -9 or -7 or so on.....  Since we are not given any thing about n being a +ve or -ve integer, we can't ignore negative values for n ]
Therefore the minimum value of n+12 = 1 and will increase in the order of 3, followed by 5 followed by 7 and so on....

Hence, 1+3+5+7=16
or, 3+5+7+9=24
or, 5+7+9+11=32
As we see the number is increasing by 8 always therefore it MUST be divisible by 4 always.

Hence we can't say what the correct answer is B or E.

Please correct my understanding.

Blackbox · Answer

Seriously! So, my understanding of this question seems to be f'd up! 
 
If n + 12 is a positive odd integer, which of the following must be true about the sum of the next four integers?

Aren't they asking for the   next   four integers? As in, the four starting with n+12+1 ...?

n+12+1+n+12+2+n+12+3+n+12+4 = 4n+48+10 = 4n+58 = 2(2n+29). And hence E?

john80rivera · Answer

n + 12 = odd
Therefore, n = odd

I got really confused with the wording of the question, however I assumed that the next four integers would be:
odd + even + odd + even (2 odds create an even, 2 even are even), therefore the next four are even and a multiple of 2.

Answer E.

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If n + 12 is a positive odd integer, which of the following must be

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If n + 12 is a positive odd integer, which of the following must be

Prep Toolkit

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