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# Set S consists of 20 different positive integers. How many

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Intern
Joined: 16 Sep 2006
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Set S consists of 20 different positive integers. How many [#permalink]

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10 Oct 2006, 09:04
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Set S consists of 20 different positive integers. How many of the integers in S are odd?

(1) 10 of the integers in S are even
(2) 10 of the integers in S are multiples of 4

[Reveal] Spoiler:
I chose D, in that each stmt. is sufficient but the answer is A. Can someone explain why stmt. 2 is not sufficient? All multiples of 4 are even (such as 4, 8, 12, 16, 20, 24, 28, 32....), so if we have 10, the other ten integers must be odd...am I missing something?

Any help is appreciated, thx!
[Reveal] Spoiler: OA
Director
Joined: 23 Jun 2005
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Re: Set S consists of 20 different positive integers. How many [#permalink]

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10 Oct 2006, 09:07
Clear A

Statement 1:
10 are odd and all are positive integers.
SUFF

Statement 2:
10 are multiples of 4. There could be others that are even but not multiples of 4. eg. 6

INSUFF
Manager
Joined: 31 Aug 2006
Posts: 210
Re: Set S consists of 20 different positive integers. How many [#permalink]

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10 Oct 2006, 10:02
anandsebastin - Can you pls. explain how did u conclude from (1) that "10 are odd and all are positive integers."

I was thinking on the lines that all 20 can be also even ?Hence we cannot say for sure from (1) that "10 are odd and all are positive integers." Am I missing something ?
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Joined: 05 Jul 2006
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Re: Set S consists of 20 different positive integers. How many [#permalink]

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10 Oct 2006, 10:10
Set S consists of 20 different positive integers. How many of the integers in S are odd?

1) 10 of the integers in S are even
2) 10 of the integers in S are multiples of 4

all intigers are either even or odd ( as long as they are positive)

FROM ONE .....SUFF

FROM TWO
10 OF THE INTIGERS ARE MULTIPLES OF 4 ( EVEN) AND WE HAVE NO CLUE ABOUT THE OTHERS

WHERE SOME MIGHT BE EVEN BUT NOT MULTIPLES OF 4 (EG: 2,0)

Intern
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Re: Set S consists of 20 different positive integers. How many [#permalink]

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10 Sep 2010, 10:40
Please help explain how statement 1 is sufficient. I had this question on GMAT Prep and answered as E. Statement 1 does not emphasize that ONLY 10 Integers are even
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Re: Set S consists of 20 different positive integers. How many [#permalink]

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10 Sep 2010, 10:46
cmugeria wrote:
Please help explain how statement 1 is sufficient. I had this question on GMAT Prep and answered as E. Statement 1 does not emphasize that ONLY 10 Integers are even

dont forget - whatever data is given , IS true -
in A - 10 are even, that means others are odd - Suff

B - insuff
Ans is A
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Re: Set S consists of 20 different positive integers. How many [#permalink]

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10 Sep 2010, 11:01
cmugeria wrote:
Please help explain how statement 1 is sufficient. I had this question on GMAT Prep and answered as E. Statement 1 does not emphasize that ONLY 10 Integers are even

In this case saying that "10 of the integers in S are even" means that EXACTLY 10 are even, as if there were more than 10 even numbers in the set, say 15, then it would make no sense to say that there are 10 even numbers.

So as there are 20 integers and out of them 10 are even then the rest must be odd.

On the other hand statement (2) just tells us that there are at least 10 even numbers in the set, so number of odd numbers in the set could vary from 0 (if all numbers are even) to 10 (if these 10 multiples of 4 are the only even numbers in the set).

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Re: Set S consists of 20 different positive integers. How many [#permalink]

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12 Feb 2017, 00:41
We are told the numbers are positive integers so that leaves out zero.

All positive integers are either odd or even. If 10 of 20 are odd, the rest are even. (Assuming the statement means exactly 10 are even. If it means at least ten are even we don't have an answer.)

B doesn't work because we could have even numbers (e.g.2, 6, 10) that are not multiples of 4 so that there might be more than 10 even integers. Insufficient.

Hence A.
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Re: Set S consists of 20 different positive integers. How many   [#permalink] 12 Feb 2017, 00:41
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