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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 3 red balls, 4 green balls, 5 yellow balls, 6 tagged by: Max@Math Revolution ##### This topic has 3 expert replies and 1 member reply ### GMAT/MBA Expert ## A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue balls and 7 white balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 5 balls of a single color will be drawn? A. 10 B. 12 C. 15 D. 18 E. 21 _________________ 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 3 red balls, 4 green balls, 5 yellow balls, 6 blue balls and 7 white balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 5 balls of a single color will be drawn?

A. 10
B. 12
C. 15
D. 18
E. 21
Determine the WORST-CASE-SCENARIO -- for each color of ball, the MAXIMUM number that can be removed WITHOUT removing 5 of the same color:
3 red
4 green
4 yellow
4 blue
4 white
Sum = 3+4+4+4+4 = 19

Implication:
It is possible to remove 19 balls without selecting 5 of the same color.
Thus, to GUARANTEE that 5 of the same color are removed, we must remove ONE MORE ball:
19+1 = 20

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

A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue balls and 7 white balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 5 balls of a single color will be drawn?

A. 10
B. 12
C. 15
D. 18
E. 21
We could have 3 red balls, 4 green balls, 4 yellow balls, 4 blue balls, and 4 white balls drawn, that is, a total of 19 balls drawn, without 5 balls of a single color drawn. However, the next ball drawn will be yellow, blue or white, and we will have 5 balls of a single color drawn. Therefore, we need to draw 20 balls to guarantee that at least 5 balls of a single color will be drawn.

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=>

The maximum number of draws we can make without drawing 5 balls of a single color is 3 + 4 + 4 + 4 + 4 = 14. This occurs when we draw 3 red balls, 4 green balls, 4 yellow balls, 4 blue balls and 4 white balls. If we draw one more ball, then we will have drawn 5 balls of a single color.

Thus, to guarantee that we have drawn at least 5 balls of a single color, we must draw 14+1 = 15 balls.

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Math Revolution
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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 Master | Next Rank: 500 Posts Joined 15 Oct 2009 Posted: 329 messages Upvotes: 27 [quote="Max@Math Revolution"]=> The maximum number of draws we can make without drawing 5 balls of a single color is 3 + 4 + 4 + 4 + 4 = 14. This occurs when we draw 3 red balls, 4 green balls, 4 yellow balls, 4 blue balls and 4 white balls. If we draw one more ball, then we will have drawn 5 balls of a single color. Thus, to guarantee that we have drawn at least 5 balls of a single color, we must draw 14+1 = 15 balls. Therefore, C is the answer. Answer: C The highlighted calculation adds up to 19 not 14 • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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