how many cards do you have to draw to ensure an even sum?

[msweeney]

From PR page 434 #4

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 the cards he drew was even, how many cards did jerome have to draw?

a 19
b 12
c 11
d 10
e 3


The answer b 12, which i get if jerome drew all 10 of the even cards (even sum) plus 2 odd cards (even sum) = odd sum.

but what if the first 3 cards he drew were all odd? if the answer is 12, then you would have 3 cards that equal an odd number, and maybe 9 even cards equaling an even number, but the 12 cards together would lead to an odd sum.

that doesn't sound like 12 "ensures" an even sum.

am i missing something?

[RonPurewal]

From PR page 434 #4

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 the cards he drew was even, how many cards did jerome have to draw?

a 19
b 12
c 11
d 10
e 3


The answer b 12, which i get if jerome drew all 10 of the even cards (even sum) plus 2 odd cards (even sum) = odd sum.

but what if the first 3 cards he drew were all odd? if the answer is 12, then you would have 3 cards that equal an odd number, and maybe 9 even cards equaling an even number, but the 12 cards together would lead to an odd sum.

that doesn't sound like 12 "ensures" an even sum.

am i missing something?

yeah, that question seems flawed -- the way i read it, you'd have to draw all twenty cards.

unfortunately, though, we no longer discuss problems from sources other than GMAC and MGMAT on this forum.
details here:
why-can-t-i-post-in-the-general-math-folder-anymore-t10130.html

we do have instructors with a presence on various other forums, though, such as beatthegmat (where i post) and a couple of others.