A box contains 1 red ball, 3 green balls, 5 yellow balls, 7

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Tue Feb 19, 2019 12:37 am

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[GMAT math practice question]

A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls, 9 white balls, and 11 black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 7 balls of the same color are drawn?

A. 7
B. 14
C. 15
D. 27
E. 28

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

7 balls of the same color

by GMATGuruNY » Tue Feb 19, 2019 3:29 am

Max@Math Revolution wrote:[GMAT math practice question]

A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls, 9 white balls, and 11 black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 7 balls of the same color are drawn?

A. 7
B. 14
C. 15
D. 27
E. 28

Determine the WORST-CASE-SCENARIO -- for each color of ball, the MAXIMUM number that can be removed WITHOUT removing 7 of the same color:
1 red
3 green
5 yellow
6 blue
6 white
6 black
Sum = 1+3+5+6+6+6 = 27.

Implication:
It is possible to remove 27 balls without selecting 7 of the same color.
Thus, to GUARANTEE that 7 of the same color are removed, we must remove ONE MORE ball:
27+1 = 28.

The correct answer is E.

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Wed Feb 20, 2019 11:54 pm

=>

The maximum number of draws without 7 balls of a single color is 1 + 3 + 5 + 6 + 6 + 6 = 27, obtained by drawing 1 red ball, 3 green balls, 5 yellow balls, 6 blue balls, 6 white balls and 6 black balls. If we draw one more ball, then we must have 7 balls of one color.
Thus, we need to draw 28 balls to ensure that 7 balls of the same color are drawn.

Therefore, E is the answer.
Answer: E

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by Scott@TargetTestPrep » Thu Feb 21, 2019 4:53 pm

Max@Math Revolution wrote:[GMAT math practice question]

A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls, 9 white balls, and 11 black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 7 balls of the same color are drawn?

A. 7
B. 14
C. 15
D. 27
E. 28

We can pull 1 red, 3 green, 5 yellow, 6 white, 6 blue, and 6 black balls, for a total of 27 balls. If we pull one more ball, we will be assured that there are at least 7 balls of the same color selected (since it has to be a blue or white or black ball).

Answer: E

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