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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 tagged by: Max@Math Revolution ##### This topic has 3 expert replies and 0 member replies ### GMAT/MBA Expert ## A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [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 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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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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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.

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Only $149 for 3 month Online Course Free Resources-30 day online access & Diagnostic Test Unlimited Access to over 120 free video lessons-try it yourself Email to : info@mathrevolution.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 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 _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • FREE GMAT Exam Know how you'd score today for$0

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