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Jerome wrote each of the integers 1 through 20, inclusive,

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Jerome wrote each of the integers 1 through 20, inclusive,  [#permalink]

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New post Updated on: 11 Oct 2007, 23:43
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Jerome wrote each of the integers 1 through 20, inclusive, on a separate index card. 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 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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Originally posted by mohansb on 11 Oct 2007, 23:26.
Last edited by mohansb on 11 Oct 2007, 23:43, edited 1 time in total.
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New post 11 Oct 2007, 23:30
Total 20 cards.

So the minimum to draw to ensure the sum is even is the first cards is even, the second cards is odd, and then all the remaining evens are drawn before drawing another odd. Total needed to draw = 12
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New post 11 Oct 2007, 23:32
answer shld b 12 -
first one = odd
next ten = even
next odd
1+10+1=12
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Re: Probabilty  [#permalink]

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New post 11 Oct 2007, 23:35
mohansb wrote:
Jerome wrote each of the integers 1 through 20, inclusive, on a separate index card. 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 cards he drew was even, how many cards did Jerome have to draw?
    a. 19
    b. 12
    c. 11
    d. 10
    e. 11


lol...why are C and E 11?
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Re: Probabilty  [#permalink]

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New post 11 Oct 2007, 23:39
mohansb wrote:
Jerome wrote each of the integers 1 through 20, inclusive, on a separate index card. 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 cards he drew was even, how many cards did Jerome have to draw?
    a. 19
    b. 12
    c. 11
    d. 10
    e. 11


what is from the 12 cards he drew...

3 were odd and 9 was even?

the the sum would be odd
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Re: Probabilty  [#permalink]

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New post 11 Oct 2007, 23:45
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beckee529 wrote:
mohansb wrote:
Jerome wrote each of the integers 1 through 20, inclusive, on a separate index card. 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 cards he drew was even, how many cards did Jerome have to draw?
    a. 19
    b. 12
    c. 11
    d. 10
    e. 11


what is from the 12 cards he drew...

3 were odd and 9 was even?

the the sum would be odd


the winning cases are:

Drawing the cards in this order
1) even
2) odd
3) odd
4) odd
5) odd
6) odd
7) odd
8) odd
9) odd
10) odd
11) odd
12) even

or in this order:
1) odd
2) even
3) even
4) even
5) even
6) even
7) even
8) even
9) even
10) even
11) even
12) odd

In both cases, you draw 2 odds and 10 evens. For this type of question, we want to consider the worst case situation. In this question, worst case would be you draw an even first, and then you run into an unlucky streak and end up with 10 odds next.
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New post 11 Oct 2007, 23:49
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Why can't it be 3, if he draws 2 odd and 1 even then its even right? I am still not clear on this.
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New post 11 Oct 2007, 23:57
mohansb wrote:
Why can't it be 3, if he draws 2 odd and 1 even then its even right? I am still not clear on this.


It can be 3. But the question is going for gaurantee. What must you do, so that you are gauranteed an even sum.

You can get an even if you draw two evens. But can you gaurantee that you will definitely draw 2 evens on your first two attempts? Same thing. You can get an even if you draw odd, then even, then even or odd. But can you gaurantee that you will draw odd-even-odd in this order on your first three attempts?

So what must I do to gaurantee eleven. Well, if you drew 12 cards, you will definitely get an even.
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Re: Probabilty  [#permalink]

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New post 12 Oct 2007, 03:00
mohansb wrote:
Jerome wrote each of the integers 1 through 20, inclusive, on a separate index card. 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 cards he drew was even, how many cards did Jerome have to draw?
    a. 19
    b. 12
    c. 11
    d. 10
    e. 3


I think the question is oddly worded.

I was confused at what exactly the question was asking, and thought the answer should be 20, to guarantee that when you have finished drawing, you have a even sum.

12 guarantees that at some point during the drawing, you will have an even sum. But in the case you draw 9 even cards, and 3 odd cards, you will end up with an odd sum.
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Re: Jerome wrote each of the integers 1 through 20, inclusive,  [#permalink]

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Re: Jerome wrote each of the integers 1 through 20, inclusive,   [#permalink] 14 Jul 2017, 12:09
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