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Is the average of X consecutive numbers odd?

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Director
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Is the average of X consecutive numbers odd? [#permalink] New post 03 Aug 2004, 08:01
00:00
A
B
C
D
E

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Hi all,

Is the average of X consecutive numbers odd?

(1) The first number in the series is odd.

(2) The sum of the numbers is odd.
Director
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 [#permalink] New post 03 Aug 2004, 21:40
E?
Let a be the first number.

(I) The first number in the series is odd.
X th number = a + x -1
Ave of X consecutive numbers = [a + (a+X-1)]/2 = a + (x -1)/2

Ave depends on X.
If X is odd, x-1 is even, x-1/2 is whole => Ave is either odd or even.
If X is even, x-1 is odd, x-1/2 always ends in .5 => Ave is not odd/even

(II) The sum of the numbers is odd.
Ave = Sum/X = Odd/X

Ave depends on X.
If X is odd, ave = odd/odd => Ave is odd.
If X is even, ave = odd/even => Ave is a decimal, not odd/even

Any other easy way? Even plug-in seems too clumsy.
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 [#permalink] New post 04 Aug 2004, 03:14
Yes, it is E.

(1) is insufficient.
(2) The sum of the numbers is odd ---> the number of odd integers is odd. There're 2 possibilities
- The number of odd and even numbers is odd ---> the average is odd
- The number of odd and even numbers is odd ---> the average is always .5 , not odd or even.
---> insufficient.

(1)&(2) ---> insufficient. The ans is E
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Director
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 [#permalink] New post 04 Aug 2004, 03:19
bigtooth81 wrote:
Yes, it is E.

(1) is insufficient.
(2) The sum of the numbers is odd ---> the number of odd integers is odd. There're 2 possibilities
- The number of odd and even numbers is odd ---> the average is odd
- The number of odd and even numbers is odd ---> the average is always .5 , not odd or even.
---> insufficient.

(1)&(2) ---> insufficient. The ans is E


No the anwer is B. Out of the 2 possibilites in 2nd condition, you are given the first one only where they add up to odd.
S
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 [#permalink] New post 04 Aug 2004, 03:28
saurya_s wrote:
bigtooth81 wrote:
Yes, it is E.

(1) is insufficient.
(2) The sum of the numbers is odd ---> the number of odd integers is odd. There're 2 possibilities
- The number of odd and even numbers is odd ---> the average is odd
- The number of odd and even numbers is odd ---> the average is always .5 , not odd or even.
---> insufficient.

(1)&(2) ---> insufficient. The ans is E


No the anwer is B. Out of the 2 possibilites in 2nd condition, you are given the first one only where they add up to odd.
S


Saurya_s. Please consider:
- 1,2,3,4 and 5. They add up to 15, odd and the average is 3, odd

- 1,2,3,4,5 and 6. They add up to 21, odd but the average here is 3.5, not odd or even.
So B is insufficient
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Director
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 [#permalink] New post 04 Aug 2004, 03:47
bigtooth81 wrote:
Yes, it is E.

(1) is insufficient.
(2) The sum of the numbers is odd ---> the number of odd integers is odd. There're 2 possibilities
- The number of odd and even numbers is odd ---> the average is odd
- The number of odd and even numbers is odd ---> the average is always .5 , not odd or even.
---> insufficient.

(1)&(2) ---> insufficient. The ans is E

Ok, you are right and thanks for the exxplaanation. U need to correct this line
- The number of odd and even numbers is odd to even.
Thanks a lot
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Re: DS Another consecutive number problem [#permalink] New post 04 Aug 2004, 08:29
saurya_s wrote:
Hi all,

Is the average of X consecutive numbers odd?

(1) The first number in the series is odd.

(2) The sum of the numbers is odd.


2 is clearly sufficient to answer YES.

1 is sufficient to answer NO (there are 2 cases - the average is not an integer or it is even. in both cases it is NOT odd).

D is the answer.
Joined: 31 Dec 1969
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Re: DS Another consecutive number problem [#permalink] New post 04 Aug 2004, 08:32
vergilius wrote:
saurya_s wrote:
Hi all,

Is the average of X consecutive numbers odd?

(1) The first number in the series is odd.

(2) The sum of the numbers is odd.


2 is clearly sufficient to answer YES.

1 is sufficient to answer NO (there are 2 cases - the average is not an integer or it is even. in both cases it is NOT odd).

D is the answer.


I apologize for my error: 2 is not sufficient to answer YES, since even if the sum is odd, the average may not be an integer...

Therefore, A is the answer.
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 [#permalink] New post 04 Aug 2004, 18:56
bigtooth81 wrote:
saurya_s wrote:
bigtooth81 wrote:
Yes, it is E.

(1) is insufficient.
(2) The sum of the numbers is odd ---> the number of odd integers is odd. There're 2 possibilities
- The number of odd and even numbers is odd ---> the average is odd
- The number of odd and even numbers is odd ---> the average is always .5 , not odd or even.
---> insufficient.

(1)&(2) ---> insufficient. The ans is E


No the anwer is B. Out of the 2 possibilites in 2nd condition, you are given the first one only where they add up to odd.
S


Saurya_s. Please consider:
- 1,2,3,4 and 5. They add up to 15, odd and the average is 3, odd

- 1,2,3,4,5 and 6. They add up to 21, odd but the average here is 3.5, not odd or even.
So B is insufficient



bigtooth:

in above example, you get ODD on the first one but not an integer on the second one. Since second option is not even an ineteger. Wouldn't B enough to answer the question?

I am confused :oops:
  [#permalink] 04 Aug 2004, 18:56
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Is the average of X consecutive numbers odd?

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