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# 20 cards are numbered 1-20 and drawn randomly from a hat and

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Intern
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20 cards are numbered 1-20 and drawn randomly from a hat and [#permalink]  10 Feb 2007, 14:32
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20 cards are numbered 1-20 and drawn randomly from a hat and not replaced. How many have to be drawn in order to ensure that the sum of all the cards drawn is even?

3
10
11
12
19
Intern
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I guess this is as much a probability as it is a number property problem. Anyway, I say 11.
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Senior Manager
Joined: 04 Jan 2006
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trivikram wrote:
11

1 Even + 10 Odd

This is still odd. I think you have to draw another card (odd card) to get

1 Even + 10 Odd + another one odd = Even number

12 is the answer for me.
VP
Joined: 28 Mar 2006
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devilmirror wrote:
trivikram wrote:
11

1 Even + 10 Odd

This is still odd. I think you have to draw another card (odd card) to get

1 Even + 10 Odd + another one odd = Even number

12 is the answer for me.

1 Even + 2*(5 Odd) = Even Number

Also we used all the 10 odd numbers so you dont have another odd number to add
Senior Manager
Joined: 04 Jan 2006
Posts: 280
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trivikram wrote:
devilmirror wrote:
trivikram wrote:
11

1 Even + 10 Odd

This is still odd. I think you have to draw another card (odd card) to get

1 Even + 10 Odd + another one odd = Even number

12 is the answer for me.

1 Even + 2*(5 Odd) = Even Number

Also we used all the 10 odd numbers so you dont have another odd number to add

Silly me.
Senior Manager
Joined: 19 Jul 2006
Posts: 361
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devilmirror wrote:
trivikram wrote:
devilmirror wrote:
trivikram wrote:
11

1 Even + 10 Odd

This is still odd. I think you have to draw another card (odd card) to get

1 Even + 10 Odd + another one odd = Even number

12 is the answer for me.

1 Even + 2*(5 Odd) = Even Number

Also we used all the 10 odd numbers so you dont have another odd number to add

Silly me.

Now i like to change my Answer to 12 .. I think devilmirror was correct

What happens if say in Eleven draws get 10 even numbers and 1 odd ..
then 10 even numbers + 1 odd = odd
VP
Joined: 28 Mar 2006
Posts: 1384
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Kudos [?]: 20 [0], given: 0

AK wrote:
devilmirror wrote:
trivikram wrote:
devilmirror wrote:
trivikram wrote:
11

1 Even + 10 Odd

This is still odd. I think you have to draw another card (odd card) to get

1 Even + 10 Odd + another one odd = Even number

12 is the answer for me.

1 Even + 2*(5 Odd) = Even Number

Also we used all the 10 odd numbers so you dont have another odd number to add

Silly me.

Now i like to change my Answer to 12 .. I think devilmirror was correct

What happens if say in Eleven draws get 10 even numbers and 1 odd ..
then 10 even numbers + 1 odd = odd

Wonderful...Atleast 1 guy was thinking out of box ...it should be 12
Intern
Joined: 20 Jan 2007
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If you take 12 cards and say you take:

2 4 6 8 10 12 14 = 56
1 3 5 7 9 = 25

I would say it is E: 19
Senior Manager
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even 19 is not enough....
you can still get 9 odd and 10 even...

however, i think the question is not wroded carefully...

when you say you draw n cards... do you mean that the n cards drawn have an even sum, or do you mean that UNTIL the Nth card drawn you get at an even sum on the way (i.e. maybe the (n-1) first cards or (n-2) first cards have even sum)...

if you simply draw n cards and expect to get an even sum - then you must draw ALL 20 cards.below that you can always come with a combination of odd number of odd cards and whatever number of even cards to complete it.
Intern
Joined: 20 Jan 2007
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hobbit wrote:
even 19 is not enough....
you can still get 9 odd and 10 even...

however, i think the question is not wroded carefully...

when you say you draw n cards... do you mean that the n cards drawn have an even sum, or do you mean that UNTIL the Nth card drawn you get at an even sum on the way (i.e. maybe the (n-1) first cards or (n-2) first cards have even sum)...

if you simply draw n cards and expect to get an even sum - then you must draw ALL 20 cards.below that you can always come with a combination of odd number of odd cards and whatever number of even cards to complete it.

You are correct, hobbit. I thought of it while having lunch. You must have all the cards (that is 20) drawn to get an even sum.
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