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# A certain jar contains only b black marbles, w white marbles

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Manager
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A certain jar contains only b black marbles, w white marbles [#permalink]

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26 Dec 2007, 20:07
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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 will be red greater then the probability that the marble chosen will be white?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-jar-contains-only-b-black-marbles-w-white-marbles-104924.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Sep 2013, 11:57, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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Director
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26 Dec 2007, 21:02
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Simplify the question: are there more red marbles or white marbles?

1. boils down to r/w > w/r (since b is found in both denominators) telling us there are more red marbles than white marbles.

SUFFICIENT

2. b-w > r tells us there are more black than white, but that's all. Doesn't tell us anything about the relationship between red and white.

INSUFFICIENT

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25 Aug 2008, 11:13
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jimjohn 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 will be red greater than the probability that the marble chosen will be white?

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

2) b-w > r

1) r / (b+w) > w / (b+r)
r(b+r) > w(b+w) ... this is possible only if r>w.
suffcieint

2) b-w > r
w >r or w<r
INSUFFCIENT.

A
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16 Oct 2008, 00:13
eschn3am wrote:
Simplify the question: are there more red marbles or white marbles?

1. boils down to r/w > w/r (since b is found in both denominators) telling us there are more red marbles than white marbles.

SUFFICIENT

2. b-w > r tells us there are more black than white, but that's all. Doesn't tell us anything about the relationship between red and white.

INSUFFICIENT

can someone explain how did it happen?

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16 Oct 2008, 01:33
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kazakhb wrote:
eschn3am wrote:
Simplify the question: are there more red marbles or white marbles?

1. boils down to r/w > w/r (since b is found in both denominators) telling us there are more red marbles than white marbles.

SUFFICIENT

2. b-w > r tells us there are more black than white, but that's all. Doesn't tell us anything about the relationship between red and white.

INSUFFICIENT

can someone explain how did it happen?

Look at stmt1: r/(b+w) > w/(b+r)
Since, b is common in both denominators, remove it. Hence, r/w > w/r.

Alternatively, (my approcah):
1 + r/(b+w) > 1 + w/(b+r)
or, (b+w+r)/(b+w) > (b+w+r)/(b+r)
or, 1/(b+w) > 1/(b+r)
or b+w < b+r
or w < r.

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Manager
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16 Oct 2008, 08:07
picking #'s works very nice here as well.

A is suff,

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Manager
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27 Sep 2009, 11:44
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 will be red greater than the probability that the marble chosen will be white?

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

2) b-w > r

Soln. From statements what we need to find is
i.e if P(choosing one red) > P(choosing one white)
i.e if r / (b+w+r) > w / (b+w+r)
or in its simplest form after cancelling out the denominators,
if r > w

Statement 1 alone is sufficient.
Given that
=> r / (b+w) > w / (b+r)
=> (b+r)/w > (b+w)/r
adding 1 to both sides and taking common denominator
=> (b+r+w)/w > (b+w+r)/r
cancelling numerators and taking r and w to numerators
=> r > w

Statement 2 alone is not sufficient
Given that
=> b-w > r
from this we cannot find if r > w or r < w
Hence not sufficient

Thus ans is A

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Senior Manager
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15 Feb 2010, 16:16
jimjohn 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 will be red greater than the probability that the marble chosen will be white?

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

2) b-w > r

Ques:
Is r /(b+w+r) > w /(b+w+r) ?
or rb + rw + r^2 > wb + w^2 + rw?
or rb + r^2 > wb + w^2 ?

S1: r / (b+w) > w / (b+r)
rb + r^2 > wb + w^2... Hence SuFF..

S2: b-w>r
b > r + w..... this doesnt give r > w or not..... hence INSUFF.

Therefore A.
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15 Feb 2010, 16:39
jimjohn 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 will be red greater than the probability that the marble chosen will be white?

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

2) b-w > r

(i) is sufficient because it gives us r<w. Thus we know the answer.
From (ii) we can'tsay whether w>r or r>w.
Therefore "A"

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Manager
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17 Feb 2010, 14:53
Damn I'm so bad at DS and inequalities.... scthakur's solution was the easiest for me to understand. Do you guys actually see the answer intuitively without going all the way to the end?

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Manager
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08 Oct 2010, 16:18
A

is p(r) > p(w) => is r > w?

1)
r w
------ > -------
b + w b + r

b is a positive constant... hence, r > w

=> SUFF

2)
does not say anything about the relationship between w and r
=> NOT SUFF
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28 Sep 2013, 08:25
elmagnifico wrote:
picking #'s works very nice here as well.

A is suff,

I can not really see how to pick smart numbers here.
Can someone explain the process of picking the numbers?

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29 Sep 2013, 11:58
ronr34 wrote:
elmagnifico wrote:
picking #'s works very nice here as well.

A is suff,

I can not really see how to pick smart numbers here.
Can someone explain the process of picking the numbers?

Agree that not the best question for number picking.

For alternative solutions check here: a-certain-jar-contains-only-b-black-marbles-w-white-marbles-104924.html

Hope it helps.
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Re: DS - Probability   [#permalink] 29 Sep 2013, 11:58
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