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Director
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Is the average of X consecutive numbers odd? [#permalink]
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03 Aug 2004, 09:01
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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
Posts: 592

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+X1)]/2 = a + (x 1)/2
Ave depends on X.
If X is odd, x1 is even, x1/2 is whole => Ave is either odd or even.
If X is even, x1 is odd, x1/2 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 plugin 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
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Director
Joined: 08 Jul 2004
Posts: 596

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



Director
Joined: 08 Jul 2004
Posts: 596

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



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Re: DS Another consecutive number problem [#permalink]
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04 Aug 2004, 09:29
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
Location: Russian Federation
Concentration: Entrepreneurship, International Business
GMAT 3: 740 Q40 V50 GMAT 4: 700 Q48 V38 GMAT 5: 710 Q45 V41 GMAT 6: 680 Q47 V36 GMAT 9: 740 Q49 V42 GMAT 11: 500 Q47 V33 GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)

Re: DS Another consecutive number problem [#permalink]
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04 Aug 2004, 09:32
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.



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 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










