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If the sum of 5 consecutive integers is x, which of the

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If the sum of 5 consecutive integers is x, which of the [#permalink]

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If the sum of 5 consecutive integers is x, which of the following must be true?

I. x is an even number
II. x is an odd number
III. x is a multiple of 5

(A) I only

(B) II only

(C) III only

(D) I and III

(E) II and III
[Reveal] Spoiler: OA

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Last edited by Bunuel on 08 Mar 2013, 15:30, edited 1 time in total.
Edited the tags: not a 700-level question at all.
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Re: If the sum of 5 consecutive integers is x, which of the [#permalink]

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I. If you start off with an even number, the sum (x) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true.
II. Same as above. This need not be always true.
III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)
= 5p + 10 = 5 (p+2) => divisible by 5. There this must be true in all cases.

Therefore C is the answer.
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Re: If the sum of 5 consecutive integers is x, which of the [#permalink]

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New post 08 Mar 2013, 22:19
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OA: C
there can be two cases
1. first no is odd---then sun of 5 consecutive no is odd
2. first no is even---then sun of 5 consecutive no is even
so we can't conclude 1 and second statement.
Sum of five consecutive no is always divisible by 5 hence option C
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Re: If the sum of 5 consecutive integers is x, which of the [#permalink]

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megafan wrote:
If the sum of 5 consecutive integers is x, which of the following must be true?

I. x is an even number
II. x is an odd number
III. x is a multiple of 5

(A) I only

(B) II only

(C) III only

(D) I and III

(E) II and III


You can solve this question simply considering different sets of 5 consecutive integers.

I. x is an even number --> if the set is {-1, 0, 1, 2, 3}, then the sum is 5=odd. Thus this statement is not always true. Eliminate A and D.

II. x is an odd number --> if the set is {-2, -1, 0, 1, 2}, then the sum is 0=even. Thus this statement is not always true. Eliminate B and E.

Only option C remains.

Answer: C.
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Re: If the sum of 5 consecutive integers is x, which of the [#permalink]

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New post 22 Apr 2013, 21:52
Sum of every odd number of consecutive integers is always divisible by the odd number
Eg: sum of 5 odd number of integers= 1+2+3+4+5 = 15/5=3

The same does not hold true for even number of consecutive integers
Thus IMO C

Statements 1 and 2 are not true, since we dont know what exactly is the value of x
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If the sum of 5 consecutive integers is x, which of the [#permalink]

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New post 03 Jan 2015, 12:26
Assume the simplest series , I assumed following
a) 1,2,3,4,5

Sum=15 , Odd
b) 2,3,4,5,6
Sum=20, Even
c) 3,4,5,6,7
sum= 25, Odd

Took less than a minute to find such series will be multiple of 5.

Now see why ?

In another way this series can be re-written as (a-2),(a-1),a,(a+1),(a+2) , where a is an integer

Sum = 5a ...... Easy isnt it ? whatever may the value of 'a' be the sum of the given series will be a multiple of '5'
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Re: If the sum of 5 consecutive integers is x, which of the [#permalink]

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Re: If the sum of 5 consecutive integers is x, which of the [#permalink]

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New post 03 Feb 2017, 11:44
megafan wrote:
If the sum of 5 consecutive integers is x, which of the following must be true?

I. x is an even number
II. x is an odd number
III. x is a multiple of 5

(A) I only

(B) II only

(C) III only

(D) I and III

(E) II and III


We can let our integers be the following:

n, n + 1, n + 2, n + 3, n + 4

Summing them, we have:

n + n + 1 + n + 2 + n + 3 + n + 4 = 5n + 10

Since the sum is 5n + 10, we see that if n were an odd number, then 5n + 10 would be odd; however, if n were even, 5n + 10 would be even. Thus, I or II do not have to be true. However, regardless of the value of n, we see that 5n + 10 is divisible by 5:

(5n + 10)/5 = 5n/5 + 10/5 = n + 2

Thus, III must be true.

Answer: C
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Re: If the sum of 5 consecutive integers is x, which of the [#permalink]

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New post 03 Apr 2017, 06:04
The 5 nos. are:
a,(a+1),(a+2),(a+3),(a+4)
Add them, we get:
5a+10= 5(a+2)

- If a is even, the expression would be even. (5*even)
- If a is odd, the expression would be odd. (5*odd)
But whatever the final answer would be, it would be a multiple of 5 because 5 is a factor here.
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Re: If the sum of 5 consecutive integers is x, which of the   [#permalink] 03 Apr 2017, 06:04
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