Each of the integers from 1 to 20 is written on the a separate index card and placed in a box. If the cards...

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Princeton Review

Each of the integers from 1 to 20 is written on the a separate index card and placed in a box. If the cards are drawn from the box at random without replacement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even?

A. 19
B. 12
C. 11
D. 10
E. 3

OA C

[Scott@TargetTestPrep]

Princeton Review

Each of the integers from 1 to 20 is written on the a separate index card and placed in a box. If the cards are drawn from the box at random without replacement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even?

A. 19
B. 12
C. 11
D. 10
E. 3

OA C

Solution:

We see that 10 cards have odd integers and the other 10 cards have even integers. If the first 10 cards drawn are all odd integers, then the product of these integers is still odd. Since the next card drawn must be an even integer, then the product of the 11 integers will of necessity be even, and so 11 cards must be drawn to ensure that the product of all the integers drawn is even.

Answer: C