Author 
Message 
sharmin.karim

Post subject: From a bag containing 12 identical blue balls, y identical Posted: Thu Oct 15, 2009 7:40 pm 


Course Students 

Posts: 18

From a bag containing 12 identical blue balls, y identical yellow balls, and no other balls, one ball will be removed at random. If the probability is less than 2/5 that the removed ball will be blue, what is the least number of yellow balls that must be in the bag?
A. 17 B. 18 C. 19 D. 20 E. 21





rags99

Post subject: Re: From a bag containing 12 identical blue balls, y identical Posted: Fri Oct 16, 2009 1:31 am 


Students 

Posts: 10

B : 18
P(blue) = 12 / (12+Y)
P(blue) < 2/5
so when you solve: 12 /12+Y = 2/5 y = 18 [editor: this is the solution to the equation, not the inequality. the first proper solution to the inequality is the first number greater than 18, which is 19. mind the problem you're solving!]
Any other solution.





tantrix

Post subject: Re: From a bag containing 12 identical blue balls, y identical Posted: Fri Oct 16, 2009 10:08 pm 


Students 

Posts: 1

rags99 wrote: B : 18
P(blue) = 12 / (12+Y)
P(blue) < 2/5
so when you solve: 12 /12+Y = 2/5 y = 18
Any other solution. Shouldn't the answer be 19? Since you solve for the inequality 12/(12+Y) < 2/5 you end up with y>18





RonPurewal

Post subject: Re: From a bag containing 12 identical blue balls, y identical Posted: Sat Oct 24, 2009 8:08 am 


ManhattanGMAT Staff 

Posts: 12800

tantrix wrote: rags99 wrote: B : 18
P(blue) = 12 / (12+Y)
P(blue) < 2/5
so when you solve: 12 /12+Y = 2/5 y = 18
Any other solution. Shouldn't the answer be 19? Since you solve for the inequality 12/(12+Y) < 2/5 you end up with y>18 correct. don't forget that you're dealing with an inequality!
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RonPurewal

Post subject: Re: From a bag containing 12 identical blue balls, y identical Posted: Sat Oct 24, 2009 8:10 am 


ManhattanGMAT Staff 

Posts: 12800

you can also solve this problem by plugging in the answer choices.
note that 2/5 is 40%.
start with (a), since you're looking for the smallest viable solution. (a) > this would be 12/29, which is greater than 40%. no go. (b) > this would be 12/30, which is exactly 40%. no go. (c) > this would be 12/31, which is less than 40%. correct answer.
_________________ Pueden hacerle preguntas a Ron en castellano Potete fare domande a Ron in italiano On peut poser des questions Ã£ Ron en franÃ§ais Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi
Un bon vÃªtement, c'est un passeport pour le bonheur. â€“ Yves SaintLaurent





asharma8080

Post subject: Re: From a bag containing 12 identical blue balls, y identical Posted: Sun May 19, 2013 9:30 pm 


Course Students 

Posts: 23

Thank you for the solution Ron. I tried the backsolving approach on this one worked fine however, how were you able to tell so quickly that 12/29 is > 40%, I want to be able to quickly tell this on the exam. My approach was to multiply 29 x 4 and that gave me 116 so that meant it is > 40%.
Thank you in advance.





RonPurewal

Post subject: Re: From a bag containing 12 identical blue balls, y identical Posted: Tue May 21, 2013 4:43 am 


ManhattanGMAT Staff 

Posts: 12800

asharma8080 wrote: Thank you for the solution Ron. I tried the backsolving approach on this one worked fine however, how were you able to tell so quickly that 12/29 is > 40%, I want to be able to quickly tell this on the exam. My approach was to multiply 29 x 4 and that gave me 116 so that meant it is > 40%.
Thank you in advance. 12/30 is 0.4, so 12/29 is more than 0.4.
_________________ Pueden hacerle preguntas a Ron en castellano Potete fare domande a Ron in italiano On peut poser des questions Ã£ Ron en franÃ§ais Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi
Un bon vÃªtement, c'est un passeport pour le bonheur. â€“ Yves SaintLaurent





