The problem intends to ask the following:
On a deck of 20 index cards, Jerome has written the integers 1 through 20, inclusive, with each integer on a separate card. Jerome is playing a game in which he places all of the cards in a bowl and draws them out one at a time. After each card is drawn, Jerome calculates the sum of the card values drawn the bowl. If the sum is odd, Jerome draws another card; if the sum is even, the game ends. At the end of the game, Jerome receives a score equal to the total number of cards drawn from the bowl. What is the maximum possible score that Joel could receive at the end of the game?
3
11
12
19
20
We want to MAXIMIZE the number of cards that could be drawn WITHOUT yielding an even sum.
The deck consists of 10 odd integers and 10 even integers.
If the 1st card is ODD, and the next 10 cards are all EVEN, then the sum following the drawing of each card will always be ODD:
1st card --> ODD.
2nd card --> ODD+EVEN = ODD.
3rd card --> ODD+EVEN+EVEN = ODD.
And so on, until all 10 even cards have been drawn:
11th card --> ODD + 10(EVEN) = ODD.
Thus, the greatest number of cards that could be drawn without yielding an even sum = 11.
But the next card drawn from the bowl must be ODD, with result that the sum will be EVEN, ending the game:
12th card --> ODD + 10(EVEN) + ODD = EVEN.
Thus, the greatest score that Jerome could receive at the end of the game = 12.
The correct answer is
C.
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