GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Mar 2019, 20:15

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7091
GMAT 1: 760 Q51 V42
GPA: 3.82
A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls  [#permalink]

### Show Tags

19 Feb 2019, 01:52
00:00

Difficulty:

75% (hard)

Question Stats:

43% (01:40) correct 58% (01:56) wrong based on 40 sessions

### HideShow timer Statistics

[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

_________________

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 $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" SVP Joined: 18 Aug 2017 Posts: 2370 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.. _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. Senior Manager Joined: 04 Aug 2010 Posts: 383 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 Click here to learn more 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. Manager Joined: 12 Sep 2017 Posts: 180 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: 7091 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$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"

Re: A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls   [#permalink] 21 Feb 2019, 01:14
Display posts from previous: Sort by