Math questions from mba.com and GMAT Prep software
mschwrtz
ManhattanGMAT Staff
 
Posts: 500
Joined: Tue Dec 14, 2004 1:03 pm
 

Re: A certain jar contains only "b" black marbles

by mschwrtz Tue Oct 19, 2010 3:19 pm

Yeah, that'll work. I wouldn't have thought to do it that way. How long did it take you?
vicksikand
Students
 
Posts: 38
Joined: Mon Oct 26, 2009 12:54 am
Location: Texas
 

Re: A certain jar contains only "b" black marbles

by vicksikand Sat Dec 11, 2010 11:02 am

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
jnelson0612
ManhattanGMAT Staff
 
Posts: 2668
Joined: Fri Feb 05, 2010 10:57 am
 

Re: A certain jar contains only "b" black marbles

by jnelson0612 Tue Dec 14, 2010 12:20 am

Nice discussion! Thank you all.
Jamie Nelson
ManhattanGMAT Instructor
rafael.odorizzi
Forum Guests
 
Posts: 1
Joined: Sun Feb 19, 2012 2:07 am
 

Re: A certain jar contains only "b" black marbles

by rafael.odorizzi Sun Feb 19, 2012 10:09 am

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 ?
jnelson0612
ManhattanGMAT Staff
 
Posts: 2668
Joined: Fri Feb 05, 2010 10:57 am
 

Re: A certain jar contains only "b" black marbles

by jnelson0612 Sun Feb 19, 2012 10:42 pm

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.
Jamie Nelson
ManhattanGMAT Instructor
krishnan.anju1987
Forum Guests
 
Posts: 125
Joined: Mon May 07, 2012 6:13 pm
 

Re: GMATPrep - Practice Test 2 - Problem #7

by krishnan.anju1987 Mon Jul 02, 2012 8:02 pm

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?
krishnan.anju1987
Forum Guests
 
Posts: 125
Joined: Mon May 07, 2012 6:13 pm
 

Re: A certain jar contains only "b" black marbles

by krishnan.anju1987 Mon Jul 02, 2012 8:05 pm

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 :) :)
RonPurewal
ManhattanGMAT Staff
 
Posts: 16149
Joined: Tue Aug 14, 2007 8:23 am
 

Re: A certain jar contains only "b" black marbles

by RonPurewal Tue Jul 03, 2012 5:37 am

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

Un bon vêtement, c'est un passeport pour le bonheur.
– Yves Saint-Laurent
sachin.w
Forum Guests
 
Posts: 173
Joined: Wed Aug 29, 2012 4:29 am
Location: Bangalore
 

Re: A certain jar contains only "b" black marbles

by sachin.w Sat Sep 01, 2012 6:47 am

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
RonPurewal
ManhattanGMAT Staff
 
Posts: 16149
Joined: Tue Aug 14, 2007 8:23 am
 

Re: A certain jar contains only "b" black marbles

by RonPurewal Sun Sep 02, 2012 6:07 am

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

Un bon vêtement, c'est un passeport pour le bonheur.
– Yves Saint-Laurent