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How many positive integers in a set?

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by Bens4vcobra » Fri Jul 08, 2011 7:33 am
Set S consists of 20 different positive integers. How many of the intergers in S are odd?

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

The answer is A but it seems like you have to assume all integers of S aren't even. No other constraints are given to justify this assumption in my opinion. If the set isn't consecutive, then you could easily have 20 even integers in the set. Where is the contraint that they all don't have to be odd? Couldn't they all be even?
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by mirantdon » Fri Jul 08, 2011 11:54 am
Imo A.

The only other way for it not to be even would be if there was a Zero in the set S .
But even 0 is an even number . Hence we can say that for those numbers that are not odd in a
given set S with postive integers . the rest of the numbers are even .

Also for option B, multiple of 4 is not sufficient if there were numbers which were multiples of 2 . Hence this statement is insufficient
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by Tani » Fri Jul 08, 2011 2:00 pm
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.
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by rishijhawar » Sun Jul 10, 2011 2:43 am
Bens4vcobra, would appreciate if you can use Spoiler :)
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