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# Is the average of X consecutive numbers odd?

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Director
Joined: 08 Jul 2004
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Is the average of X consecutive numbers odd? [#permalink]  03 Aug 2004, 08:01
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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
Joined: 20 Jul 2004
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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.
Senior Manager
Affiliations: CFA Level 2
Joined: 05 May 2004
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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
_________________

"Life is like a box of chocolates, you never know what you'r gonna get"

Director
Joined: 08 Jul 2004
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Kudos [?]: 82 [0], given: 0

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
Senior Manager
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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

- 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
_________________

"Life is like a box of chocolates, you never know what you'r gonna get"

Director
Joined: 08 Jul 2004
Posts: 604
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Kudos [?]: 82 [0], given: 0

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
S
Joined: 31 Dec 1969
Location: India
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Kudos [?]: 89 [0], given: 87161

Re: DS Another consecutive number problem [#permalink]  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).

Joined: 31 Dec 1969
Location: India
Concentration: General Management, Strategy
GMAT 1: 710 Q49 V0
GMAT 2: 740 Q40 V50
GMAT 3: 700 Q48 V38
GPA: 3.6
Followers: 0

Kudos [?]: 89 [0], given: 87161

Re: DS Another consecutive number problem [#permalink]  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).

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...

Manager
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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

- 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
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