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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42
GPA: 3.82
A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls  [#permalink]

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19 Feb 2019, 01:52
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Difficulty:

65% (hard)

Question Stats:

49% (01:28) correct 51% (01:50) wrong based on 57 sessions

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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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" GMAT Club Legend Joined: 18 Aug 2017 Posts: 5020 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls [#permalink] Show Tags 19 Feb 2019, 02:03 1 MathRevolution 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 total balls = 36 so as to have atleast 7 balls of same color ; we need to remove balls which are max in no of same color ; 11+5+9+3= 28 balls so now we are left with 7 balls of same color i.e blue and 1 of red.. Senior Manager Joined: 04 Aug 2010 Posts: 477 Schools: Dartmouth College A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls [#permalink] Show Tags 19 Feb 2019, 04:43 1 MathRevolution 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 . _________________ GMAT and GRE Tutor Over 1800 followers GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Senior Manager Joined: 12 Sep 2017 Posts: 302 Re: A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls [#permalink] Show Tags 19 Feb 2019, 19:11 Archit3110 wrote: MathRevolution 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 total balls = 36 so as to have atleast 7 balls of same color ; we need to remove balls which are max in no of same color ; 11+5+9+3= 28 balls so now we are left with 7 balls of same color i.e blue and 1 of red.. Archit3110 Could you please explain to me why do we have to keep the red one? Kind regards! Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8017 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls [#permalink] Show Tags 21 Feb 2019, 01:14 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls   [#permalink] 21 Feb 2019, 01:14
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