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# From PR'05. Jerome wrote each of the integers 1 through

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From PR'05. Jerome wrote each of the integers 1 through [#permalink]

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10 Sep 2005, 20:49
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From PR'05.

Jerome wrote each of the integers 1 through 20 inclusive, on separate index cards. He placed the cards in a box, then drew cards one at a time randomly from the box without returning the cards he had already drawn to the box. In order to ensure that the sum of all the cards he drew was even, how many cards did Jerome have to draw?
A) 19
B) 12
C) 11
D) 10
E) 3
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10 Sep 2005, 21:57
I don't think the question is very well worded.
I think it must mean the maximum number he might have to draw.

All that matters is whether a number is Odd or Even, and whether the number of Odd numbers so far is even.
It's like picking socks out of a drawer.

The worst thing that could happen is that the first number is odd, then the next numbers are all even and then the next number must be odd.

So on that interpretation of the question the answer is 12.
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10 Sep 2005, 22:48
I would also go for 12

worst scenario would be : O+E+E+......until no more even
As we have 10 even numbers + the 1st number which is odd, we would need to pick at least 12 cards to ensure the final sum would be even
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11 Sep 2005, 06:54
B) 12 is the right answer.
I agree the wording was a mess for what was otherwise a simple problem.
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11 Sep 2005, 09:55
To ensure that the sum of all the cards he drew was even
19 cards have to be drawn
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11 Sep 2005, 10:54
Joy123,

OA is B)12
The explanations offered by the members in the above posts explain the answer.
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