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# Is the sum of five consecutive integers odd? (1) The first number is o

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Is the sum of five consecutive integers odd? (1) The first number is o  [#permalink]

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19 Dec 2018, 12:31
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25% (medium)

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76% (01:13) correct 24% (01:07) wrong based on 46 sessions

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Is the sum of five consecutive integers odd?

(1) The first number is odd.

(2) The average (arithmetic mean) of the five numbers is odd.

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Re: Is the sum of five consecutive integers odd? (1) The first number is o  [#permalink]

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19 Dec 2018, 12:42
Is the sum of five consecutive integers odd?

(1) The first number is odd.

(2) The average (arithmetic mean) of the five numbers is odd.

Note: we have 5 consecutive integers. we have to find out whether their sum is 5 or not.

Statement 1:

First integer is odd.

3 +4 +5+6+7 = 25

1 + 2+3+4+5 = 15.

odd all time.

Statement 2:

Average is given. we know we have 5 integers. So, 3rd one is given. if we multiply by 5 , we will get an odd integer.

Sufficient.

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Re: Is the sum of five consecutive integers odd? (1) The first number is o  [#permalink]

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19 Dec 2018, 15:01
1. first no. is odd
2n-1+ 2n + 2n+1 + 2n+2 + 2n+3 = even + odd = odd

2. The average (arithmetic mean) of the five numbers is odd.
[(n-2)+(n-1)+(n)+(n+1)+(n+2)]/5 = 5n/5 =n= odd
therefore, sum has to be odd
Both are sufficient, D
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Re: Is the sum of five consecutive integers odd? (1) The first number is o   [#permalink] 19 Dec 2018, 15:01
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