have 23 balls of the same color

sanju09 wrote:In a jar there are 21 white balls, 24 green balls and 32 blue balls. How many balls must be taken out in order to make sure we have 23 balls of the same color?
(A) 23
(B) 46
(C) 57
(D) 66
(E) 67


[spoiler]Source: Eric’s collection on BTG


OA D[/spoiler]

Worst case scenario:
First 21 selected are all white.
Next 44 selected are 22 green, 22 blue.
Total selected so far = 21+22+22 = 65.
To get either 23 green or 23 blue, 1 more marble must be selected:
65+1 = 66.

The correct answer is D.

GMATGuruNY wrote:

sanju09 wrote:In a jar there are 21 white balls, 24 green balls and 32 blue balls. How many balls must be taken out in order to make sure we have 23 balls of the same color?
(A) 23
(B) 46
(C) 57
(D) 66
(E) 67


[spoiler]Source: Eric’s collection on BTG


OA D[/spoiler]

Worst case scenario:
First 21 selected are all white.
Next 44 selected are 22 green, 22 blue.
Total selected so far = 21+22+22 = 65.
To get either 23 green or 23 blue, 1 more marble must be selected:
65+1 = 66.

The correct answer is D.

hi mitch

could you please explain further. i didnt get that.

regards nafi

Another way to look at it is that the following pattern is repeated 21 times:

(WGB)
(WGB)
(WGB)
(WGB)
..
..
..
..
..
..
21 times. - Total 63 balls

After this, White balls are over (there are only 21 white balls). So, now we start alternating between green and blue balls.

64th: G (22nd Green ball)
65th: B (22nd Blue ball)
66th: Whether we pick Green ball or blue ball is immaterial, since it will make sure that either 23 Green balls or 23 Blue balls are picked.

Hence 66.

nafiul9090 wrote:

GMATGuruNY wrote:

sanju09 wrote:In a jar there are 21 white balls, 24 green balls and 32 blue balls. How many balls must be taken out in order to make sure we have 23 balls of the same color?
(A) 23
(B) 46
(C) 57
(D) 66
(E) 67


[spoiler]Source: Eric’s collection on BTG


OA D[/spoiler]

Worst case scenario:
First 21 selected are all white.
Next 44 selected are 22 green, 22 blue.
Total selected so far = 21+22+22 = 65.
To get either 23 green or 23 blue, 1 more marble must be selected:
65+1 = 66.

The correct answer is D.

hi mitch

could you please explain further. i didnt get that.

regards nafi

We need to determine the minimum number of marbles that must be selected in order to guarantee getting 23 of the same color.
Thus, we need to determine the maximum number that can be selected without getting 23 of the same color.

If 21 white, 22 green, and 22 blue are selected, then altogether 21+22+22=65 marbles will be chosen with getting 23 of the same color.
This is the worst-case scenario: the maximum number that can be selected without getting 23 of the same color.

The next marble selected must be green or blue, bringing the total of one of these colors to 23.
This marble increases the total number selected to 65+1=66.
Thus, to guarantee getting 23 of the same color, 66 marbles must be chosen.