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A certain jar contains only "b" black marbles

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mschwrtz
 Post subject: Re: A certain jar contains only "b" black marbles
 Post Posted: Tue Oct 19, 2010 3:19 pm 
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ManhattanGMAT Staff


Posts: 506
Yeah, that'll work. I wouldn't have thought to do it that way. How long did it take you?
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vicksikand
 Post subject: Re: A certain jar contains only "b" black marbles
 Post Posted: Sat Dec 11, 2010 11:02 am 
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Students


Posts: 38
Location: Texas
sudeepkapoor wrote:
Taking statement (1)

r/(b+w) > w/(b+r) :

taking reciprocal ,

(b+w)/r < (b+r)/w

[take the example of 1/2 and 1/3 ; 1/2 > 1/3 but if one takes the reciprocal , 2<3 ]

now, add 1 to both sides,
(b+w)/r +1 < (b+r)/w +1 [inequality holds good when a positive constant is added]

This implies , (b+w+r)/r < (b+r+w)/w

Again take the reciprocal and the sign changes

r/(b+w+r) > w/(b+r+w)

also we know that :

P(red)=r/(b+w+r)
P(white)=w/(b+w+r)


therefore P(red) > P(white)

Therefore statement 1 is sufficient

Statement (2) does not give any relation between red and white marbles and is obviously not sufficient ;

Answer is A.


I used a similar technique:
r/(b+w) +1 > w/(b+r) +1
(r+b+w)/(b+w) > (r+b+w)/(b+r)
Take reciprocal
b/(r+b+w) + w/(r+b+w) < b/(r+b+w) + r/(r+b+w)
or P(w) < P(r)

2 is insufficient
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jnelson0612
 Post subject: Re: A certain jar contains only "b" black marbles
 Post Posted: Tue Dec 14, 2010 12:20 am 
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ManhattanGMAT Staff


Posts: 1857
Nice discussion! Thank you all.

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Jamie Nelson
ManhattanGMAT Instructor
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rafael.odorizzi
 Post subject: Re: A certain jar contains only "b" black marbles
 Post Posted: Sun Feb 19, 2012 10:09 am 
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I used this argument to accept st1, is it correct ?

r / (b + w) > w / (b + r)

r / w > w / r, therefore, r > w

Is it possible to assume that ?
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jnelson0612
 Post subject: Re: A certain jar contains only "b" black marbles
 Post Posted: Sun Feb 19, 2012 10:42 pm 
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ManhattanGMAT Staff


Posts: 1857
rafael.odorizzi wrote:
I used this argument to accept st1, is it correct ?

r / (b + w) > w / (b + r)

r / w > w / r, therefore, r > w

Is it possible to assume that ?


I would feel very nervous dismissing the effect of b. If b were being multiplied to w and r, and you knew that all the numbers were positive integers (which we do know in this problem), you could safely disregard the b in the denominator. However, this seems a bit fast and loose to me. I'd prefer that you do the algebra here (which isn't complicated) to make sure that you are completely safe.

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Jamie Nelson
ManhattanGMAT Instructor
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