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 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: 504
Yeah, that'll work. I wouldn't have thought to do it that way. How long did it take you?


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 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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 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: 2644
Nice discussion! Thank you all.

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 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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 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: 2644
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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 Post subject: Re: GMATPrep - Practice Test 2 - Problem #7
 Post Posted: Mon Jul 02, 2012 8:02 pm 
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Posts: 125
givemeanid wrote:
Harish Dorai wrote:
A certain jar contains only "b" black marbles, "w" white marbles and "r" red marbles. If one marble is to be chosen at random from the jar, is the probability that the marble chosen is red greater than the probability that the marble chosen will be white?

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

2) b - w > r


The question asks whether r/(b+w+r) > w/(b+w+r) or in other words is r > w?

1. r(b+r) > w(b+w)
br + r^2 > bw + w^2
br - bw > w^2 - r^2
b(r-w) > (w-r)(w+r)
r-w > (w-r)(w+r)/b ----> We know b is positive. So, we can divide both sides without changing the inequality
r-w > k(w-r) ----> Where k > 0 as b,r and w are all positive
This is true only when r > w.
If r < w, left side is -ve and right side is +ve and the inequality doesn't hold.
SUFFICIENT.

2. b - w > r
b > w + r
This doesn't tell us anything about relationship between w and r.
INSUFFICIENT.

Answer is A.



I agree. Even I got the same answer. But I did not understand givemeanid's solution to this problem. He mentions

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

after this point, this is how I understand it.

-w+r/b is positive as w,r,b are all positive. Agreed
-since this is a positive number, consider this to be a positive number k. Agree
- Now, as r-w >(w-r)*k
since RHS needs to be positive, LHS must be positive. hence r>w. but if so, w-r on the right hand side will be negative. so LHS and RHS do not match anyway.

Do I make any sense or am I misunderstanding the scenario here?


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 Post subject: Re: A certain jar contains only "b" black marbles
 Post Posted: Mon Jul 02, 2012 8:05 pm 
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Posts: 125
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.


Loved this one since this is exactly how I solved this problem :) :)


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 Post subject: Re: A certain jar contains only "b" black marbles
 Post Posted: Tue Jul 03, 2012 5:37 am 
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ManhattanGMAT Staff


Posts: 13427
jnelson0612 wrote:
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.


actually that works, but maybe not for the reason this poster originally thought.

namely, if you have
r/(b + w) > w/(b + r)
then you can put that into words as
red / everything else > white / everything else
if this is true, then, since both sides are talking about the same group of marbles, we must have red > white.

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 Post subject: Re: A certain jar contains only "b" black marbles
 Post Posted: Sat Sep 01, 2012 6:47 am 
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Posts: 175
Location: Bangalore
I solved it the following way .
Not sure if the approach is right but I do get teh ans.

r / (b + w) > w / (b + r)
since all of them have to be +ve as they are real marbles
=>

r(b+w) >w(b+r) .... (if a/b>0 => ab>0)
=>
simplifying this we get r>w..

Hope this approach correct.

but adding 1 would be a universal approach as this may not work if we dont know the signs


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 Post subject: Re: A certain jar contains only "b" black marbles
 Post Posted: Sun Sep 02, 2012 6:07 am 
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ManhattanGMAT Staff


Posts: 13427
sachin.w wrote:
I solved it the following way .
Not sure if the approach is right but I do get teh ans.

r / (b + w) > w / (b + r)
since all of them have to be +ve as they are real marbles
=>

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


whoa, no, you can't do that -- you can't just take the denominators and magick them into numerators.

try it with actual numbers and you'll see the problem. what you're saying is that you could take, e.g., 1/2 > 1/3 (a true statement) and transform it, as if by magic, into 1(2) > 1(3) (a false statement).

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Pueden hacerle preguntas a Ron en castellano
Potete fare domande a Ron in italiano
On peut poser des questions ã Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

Un bon vêtement, c'est un passeport pour le bonheur.
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