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have 23 balls of the same color

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have 23 balls of the same color

by sanju09 » Tue May 24, 2011 2:02 am
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


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OA D[/spoiler]
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by GMATGuruNY » Tue May 24, 2011 3:14 am
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.
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by nafiul9090 » Tue May 24, 2011 6:58 am
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
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by iongmat » Tue May 24, 2011 7:19 am
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.
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by GMATGuruNY » Tue May 24, 2011 8:04 am
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
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