Combinatorics

[abhirup1711]

In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 green balls. How many balls must be taken out in order to make sure we took out 8 of the same color?

a) 8
b) 23
c) 29
d) 32
e) 53

[Brent@GMATPrepNow]

In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 green balls. How many balls must be taken out in order to make sure we took out 8 of the same color?

a) 8
b) 23
c) 29
d) 32
e) 53

First, what is the MAXIMUM number of balls we can remove WITHOUT getting 8 of the same color?
Well, we can remove 7 white balls, 7 red balls, 7 blue balls and 7 green balls, for a total of 28 balls.
At this point, the next ball we remove will ensure that there are 8 balls of the same color.
Answer = [spoiler]28 = C[/spoiler]

Cheers,
Brent

[GMATGuruNY]

In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 green balls. How many balls must be taken out in order to make sure we took out 8 of the same color?

a) 8
b) 23
c) 29
d) 32
e) 53

In order to GUARANTEE that we get 8 of the same color, we must consider the WORST-CASE SCENARIO.

Here, the worst-case scenario is to choose 7 of each color:
7+7+7+7 = 28.

Thus, it is possible to select 28 marbles and NOT get 8 of the same color.
To GUARANTEE that we get 8 of one of the colors, we must choose ONE MORE BALL:
28+1 = 29.

The correct answer is C.