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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 [#permalink]

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12 Apr 2016, 02:19
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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
[Reveal] Spoiler: OA

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Re: If n + 12 is a positive odd integer, which of the following must be [#permalink]

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12 Apr 2016, 10:27
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Bunuel wrote:
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

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
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Re: If n + 12 is a positive odd integer, which of the following must be [#permalink]

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13 Apr 2016, 00:50
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Bunuel wrote:
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

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
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Re: If n + 12 is a positive odd integer, which of the following must be [#permalink]

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10 Dec 2016, 09:48
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

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Re: If n + 12 is a positive odd integer, which of the following must be [#permalink]

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10 Dec 2016, 11:22
Bunuel wrote:
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

n + Even = Odd

So, n = Odd

Quote:
The sum of the next four integers

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

Hence, the sum must be Even and will be divisible by 2 , answer will be (E)
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If n + 12 is a positive odd integer, which of the following must be [#permalink]

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13 Apr 2017, 05:00
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
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Last edited by RR88 on 17 Apr 2017, 02:14, edited 1 time in total.

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

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16 Apr 2017, 13:36
Bunuel wrote:
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

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.

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Re: If n + 12 is a positive odd integer, which of the following must be [#permalink]

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25 Jul 2017, 16:45
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?

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Re: If n + 12 is a positive odd integer, which of the following must be [#permalink]

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25 Jul 2017, 17:32
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.

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Re: If n + 12 is a positive odd integer, which of the following must be   [#permalink] 25 Jul 2017, 17:32
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