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Can anyone please explain the solution to this problem? The PR explanation is not clear to me.

Jerome wrote each of the integers 1 through 20 inclusive on a separate index card. He placed the cards in a box, then drew one card at a time randomly from the box, without returning the cards he had already drawn. 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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X&Y please note , again, that
1+3+5+6+7+8+9+2+4+10+12+14=odd the sum of the first 5 is EVEN, so your example is irrelevant .
The logic is simple
A sum is even if E+E=E or O+O=E, now E+O= O so in order to ensure that the sum of the numbers drawn is even, one must take 12 cards. Why?
Because, the worst scenario is if he takes first card O and then 10 E the sum will be odd. When all evens are depleted he will draw O and the sum is E

X&Y please note , again, that 1+3+5+6+7+8+9+2+4+10+12+14=odd the sum of the first 5 is EVEN, so your example is irrelevant . The logic is simple A sum is even if E+E=E or O+O=E, now E+O= O so in order to ensure that the sum of the numbers drawn is even, one must take 12 cards. Why? Because, the worst scenario is if he takes first card O and then 10 E the sum will be odd. When all evens are depleted he will draw O and the sum is E

You mean to say after drwaing 12 cards, he can be sure that the sum is EVEN. I am not able to understand.
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a. 19 - can draw 10 odd and 9 even..sum is even. can draw 10 even and 9 odd, sum is odd X
b. 12 can draw 5 even and 7 odd, sum is odd. can draw 6 odd and 6 even, sum is even X
c. 11 can draw 5 even and 6 odd, sum is even. can draw 5 odd and 6 even sum is odd
d. 10 can draw all even sum is even, can draw 9 even and one odd sum is odd
e. 3 can draw all even sum is even, can draw all odd sum is odd.

I am kind of new here, and probablty wrong.
So we have 20 cards. We took some of them and we have number 11 total.
It means that we drew card with #2,#3 and #6 on it. So we have 11.
And answer is E.

Again, new in GMAT, so making mistakes on every step:(

I think the only part I didn't agree with was "why the need to draw odd first". It really doesn't matter - the point is to arrive at the most #: Draw all even possible = 10. Draw one more, this one has to be odd since all even already drawn. now the sum is E+O = odd and we are at a tally of 10+1 = 11 cards. Draw another one (odd of course since no even left) = 11+1 = 12 cards and sum is O + O = E.
_________________

I think the only part I didn't agree with was "why the need to draw odd first". It really doesn't matter - the point is to arrive at the most #: Draw all even possible = 10. Draw one more, this one has to be odd since all even already drawn. now the sum is E+O = odd and we are at a tally of 10+1 = 11 cards. Draw another one (odd of course since no even left) = 11+1 = 12 cards and sum is O + O = E.

I guess the reason for drawing the first one as odd is, if you draw the first one as even, the sum is already even, you don't need to draw another card. Does it sound plausible ?
I think, the solution has to be 12 - draw the first one as odd, draw 10 even and then one more odd.

Re: PR â€“ Math Bin 4 â€“ # 4 - pg 380 [#permalink]

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04 Dec 2006, 14:51

saumster wrote:

Can anyone please explain the solution to this problem? The PR explanation is not clear to me.

Jerome wrote each of the integers 1 through 20 inclusive on a separate index card. He placed the cards in a box, then drew one card at a time randomly from the box, without returning the cards he had already drawn. 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

I think the question is asking "after drawing how many cards can you be sure that the sum will be an even number?"

So best case is you only need to draw 1 card = 2 or 4 or 6 etc
Worst case is that you draw one odd card and then 10 even, and so require one more card to make the sume odd = 12 cards

In examples used where you draw 1+2+3+4 etc, you would reach an even number at 1+2+3 = 6.

Re: PR â€“ Math Bin 4 â€“ # 4 - pg 380 [#permalink]

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09 Jan 2011, 23:41

After being confused for a while, the solution seems clear to me.

The answer is B - 12 Keeping in mind that Jerome can stop in the middle when ever he has the sum as even .

Consider he starts with even , he stops . He has the sum as even . Consider he starts with ODD, he can not stop. At this point, he either has the bad luck of drawing all even numbers there of . He would now draw the 12th card , which would be ODD ,

O+(EVEN Series)+O = E .

Do note, IMO the question should not have been "how many cards did Jerome have to draw" but rather should be "how many maximum number of cards might Jerome have to draw" .

After being confused for a while, the solution seems clear to me.

The answer is B - 12 Keeping in mind that Jerome can stop in the middle when ever he has the sum as even .

Consider he starts with even , he stops . He has the sum as even . Consider he starts with ODD, he can not stop. At this point, he either has the bad luck of drawing all even numbers there of . He would now draw the 12th card , which would be ODD ,

O+(EVEN Series)+O = E .

Do note, IMO the question should not have been "how many cards did Jerome have to draw" but rather should be "how many maximum number of cards might Jerome have to draw" .

Jerome wrote each of the integers 1 through 20, inclusive, on a separate index card. He placed the cards in a box, then drew one card at a time randomly from the box, without replacing the cards he had already drawn. 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. 13 D. 10 E. 3

This is not a good question. The answer depends on how you interpret it.

The given solution suggests that they meant the maximum number of picks needed to ensure that on the way you had an even sum. In this case worst case scenario would be to draw odd number first, and then keep drawing all 10 even numbers. After 11 draws you'd still have an odd sum and need to draw 12th card, which will be an odd to get the even sum.

But if you interpret it as at which drawing the sum will definitely be even then the answer would be 20. As only on 20th draw I can say for sure that the sum is even.

I wouldn't worry about this question at all.
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