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

BTGmoderatorDC wrote: ↑

Sat Apr 18, 2020 8:14 pm

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

Source: Princeton Review

From 1 to 20, there are 10 even and 10 odd integers. Since Odd*Odd = Odd and Odd*Even = Even, we must have at one even no. in the product; however, since we wish to be ENSURED that the product of all the integers drawn is even, we must draw all Odd integers and then any of the even integers would do.

So, we must draw at the max 10 + 1 = 11 integers

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorDC wrote: ↑

Sat Apr 18, 2020 8:14 pm

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

Source: Princeton Review

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