A certain jar contains only b black marbles, w white marbles : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 22:37

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

Hide Tags

Manager
Joined: 07 Feb 2010
Posts: 159
Followers: 2

Kudos [?]: 552 [2] , given: 101

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

Show Tags

16 Nov 2010, 05:43
2
KUDOS
11
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

59% (02:22) correct 41% (01:35) wrong based on 617 sessions

HideShow timer Statistics

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
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36568
Followers: 7081

Kudos [?]: 93224 [14] , given: 10553

Re: a certain jar contains [#permalink]

Show Tags

16 Nov 2010, 05:52
14
KUDOS
Expert's post
9
This post was
BOOKMARKED
anilnandyala 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 then the probability that the marble chosen will be white?

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

The question is $$\frac{R}{R+B+W}>\frac{W}{R+B+W}$$ true? Or is $$R>W$$ true?

(1) $$\frac{R}{B+W} > \frac{W}{B+R}$$ --> $$\frac{R}{B+W} +1> \frac{W}{B+R}+1$$ --> $$\frac{R+B+W}{B+W}> \frac{W+B+R}{B+R}$$ --> $$\frac{1}{B+W}> \frac{1}{B+R}$$ --> $$B+R>B+W$$ --> $$R>W$$. Sufficient.

OR:
Given: $$\frac{R}{B+W} > \frac{W}{B+R}$$ -->

Cross multiply, we can safely do this as $$B+W$$ and $$B+R$$ are more than zero.

We'll get $$R(B+R)>W(B+W)$$ --> $$RB+R^2>WB+W^2$$ --> $$(R^2-W^2)+(RB-WB)>0$$ --> $$(R-W)(R+W)+B(R-W)>0$$ --> $$(R-W)(R+W+B)>0$$.

As $$R+W+B>0$$, the above inequality to hold true $$R-W$$ must also be more than zero, so $$R-W>0$$ --> $$R>W$$.

(2) $$B-W>R$$, not sufficient to determine whether $$R>W$$ or not.

_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7125
Location: Pune, India
Followers: 2136

Kudos [?]: 13657 [7] , given: 222

Re: a certain jar contains [#permalink]

Show Tags

16 Nov 2010, 11:40
7
KUDOS
Expert's post
2
This post was
BOOKMARKED
anilnandyala wrote:
a certain jar contains only b black marbles, w white marbles & r red marbles. if one marble is to be chosen random from jar is the probability that the marble chosen will be red greater then the probability the marble chosen is white?
a) r/(b+w) > w/(b+r)
b) b-w > r

The probability that red marble is chosen will be greater than the probability that white marble is chosen if there are more red marbles than white marbles.
So the queestion is just: Is r > w

Statement 1: r/(b + w) > w/(b + r)
Cross multiply to get r(b + r) > w(b + w) .... [(b + w) and (b + r) are definitely positive so cross multiplying is not a problem.]
Now, if r > w, (b + r) has to be greater than (b + w)
If r were less than w, then (b + r) < (b + w) and the left side would have been smaller than the right side.
So this implies that r must be greater than w. Sufficient.

Statement 2: b > r + w
But we cant compare r and w so not sufficient.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Senior Manager
Joined: 08 Nov 2010
Posts: 417
Followers: 7

Kudos [?]: 105 [0], given: 161

Re: a certain jar contains [#permalink]

Show Tags

17 Nov 2010, 22:55
VeritasPrepKarishma and Bunuel - thanks a lot for ur explanations.

+1 from me... again.

keep up the good job.
_________________
Manager
Status: what we want to do, do it as soon as possible
Joined: 24 May 2010
Posts: 114
Location: Vietnam
WE 1: 5.0
Followers: 2

Kudos [?]: 61 [0], given: 315

Re: a certain jar contains [#permalink]

Show Tags

23 Nov 2010, 22:36
Bunuel wrote:
anilnandyala wrote:
a certain jar contains only b black marbles, w white marbles & r red marbles. if one marble is to be chosen random from jar is the probability that the marble chosen will be red greater then the probability the marble chosen is white?
a) r/(b+w) > w/(b+r)
b) b-w > r

(1) $$\frac{R}{B+W} > \frac{W}{B+R}$$ --> $$\frac{R}{B+W} +1> \frac{W}{B+R}+1$$ --> $$\frac{R+B+W}{B+W}> \frac{W+B+R}{B+R}$$ --> $$\frac{1}{B+W}> \frac{1}{B+R}$$ --> $$B+R>B+W$$ --> $$R>W$$. Sufficient.

OR:
Given: $$\frac{R}{B+W} > \frac{W}{B+R}$$ -->

Cross multiply, we can safely do this as $$B+W$$ and $$B+R$$ are more then zero.

awesome explanation. I have translated the question to is r>w but did not know how to solve the (1). Now get it clear
_________________

Consider giving me kudos if you find my explanations helpful so i can learn how to express ideas to people more understandable.

Manager
Status: Working hard to score better on GMAT
Joined: 02 Oct 2012
Posts: 90
Location: Nepal
Concentration: Finance, Entrepreneurship
GPA: 3.83
WE: Accounting (Consulting)
Followers: 0

Kudos [?]: 151 [0], given: 23

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

Show Tags

22 May 2013, 06:40
lets rephrase the question first.
It says IS r/(w+r+b)> w(r+w+b)
Cross multiply because we know all the variables are positive. It becomes
Is br+r^2> bw+w^2 ?

Statement 1: when cross multiplying we ger br+ r^2 >bw+ w^2........Thus sufficient

Statement 2: clearly insufficient.

Do not forget to press on Kudos button if it helps....
_________________

Do not forget to hit the Kudos button on your left if you find my post helpful.

Manager
Joined: 24 Apr 2013
Posts: 54
Schools: Duke '16
Followers: 0

Kudos [?]: 10 [1] , given: 76

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

Show Tags

22 May 2013, 13:41
1
KUDOS
chose B. I hate my life!
Manager
Joined: 05 Nov 2012
Posts: 171
Followers: 1

Kudos [?]: 33 [0], given: 57

A jar contains 8 red marbles and y white marbles. If Joan takes [#permalink]

Show Tags

30 Dec 2013, 10:17
Given 8 red marbles and y white marbles.
Number of ways you can pick any two marbles is $$(8+Y)C2$$.
Ways of picking 2 red marbles is 8*7 (first time you can pick out of 8 red marbles and second time you can pick one of the remaining 7 marbles).
Ways of picking 1 marble of each color. This can happen in 2 ways. 1 way) First pick white and second pick red [y*8 ways] or 2 way) first pick red and second pick white [8*y ways]. So total number of ways to pick two different colors will be $$y*8 + 8*y$$ = $$2*8y$$

A jar contains 8 red marbles and y white marbles. If Joan takes 2 random marbles from the jar, is it more likely that she will have 2 red marbles than that she will have one marble of each color?

Question is asking for - is probability of picking 2 red marbles > probability of picking different color marbles, is $$\frac{8*7}{(8+Y)C2} > \frac{2*8y}{(8+Y)C2}$$
Therefore, $$y<7/2=3.5$$

(1) y ≤ 8 y can be less than or greater than 3.5 - NS
(2) y ≥ 4 y is always greater than 3.5 - S

So B
Current Student
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 62

Kudos [?]: 594 [1] , given: 355

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

Show Tags

10 Jan 2014, 05:31
1
KUDOS
anilnandyala 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 then the probability that the marble chosen will be white?

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

Is r>w?

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

rb + r^2 ? wb + w^2

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

Now if r-w>0 then w-r < 0 and inequality holds true.
Other way around if r-w<0, LHS is negative and RHS is positive and inequality does NOT hold true

So only valid scenario is r-w>0 and thus r>w

Sufficient

(B) Not enough Info

Cheers
J

PS. Alternatively, first statement can be treated as

r-w / b+r>0

Well b+r is always positive, thus r-w has to be positive too
Then r>w
Manager
Status: suffer now and live forever as a champion!!!
Joined: 01 Sep 2013
Posts: 149
Location: India
GPA: 3.5
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 57 [0], given: 75

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

Show Tags

03 Jun 2014, 08:58
let's rephrase the question as "Is no of red marbles > no of white marbles ?"

Stmt1: r/(b+w) > w/(b+r)

There are two possibilities arising from the above statement .

A fraction r/(b+w) is greater than other fraction w/(b+r), if and only if the following 2 conditions are satisfied.
a) r>w or b) (b+r) >( b+w)
case1 : numerator 'r' is larger than numerator 'w';
case2 : denominator (b+r) > denominator (b+w) ;
in either case we get r>w ;
hence sufficient;

Stmt2: b-w > r

We can consider two cases(numbers) for which the above statement is both true and false;

case1: b=10; w=2 ; r=7;
10-2>7;
r>w(true)

Case2: b=10; w=5; r=4;
10-5>4;
but here 4>5(false);
Hence Insufficient.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13459
Followers: 575

Kudos [?]: 163 [0], given: 0

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

Show Tags

19 Jun 2015, 22:04
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1183
Followers: 421

Kudos [?]: 1505 [4] , given: 4

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

Show Tags

19 Jun 2015, 23:25
4
KUDOS
Expert's post
4
This post was
BOOKMARKED
I like this problem because there are at least five different ways to solve it. I'll mention a more conceptual solution since no one has mentioned it yet, but there are some great solutions above as well:

If you know the concept of "odds" that is used in daily life, you can answer this question very quickly. "Odds" are just ratios of good outcomes to bad outcomes, while probabilities are ratios of good outcomes to total outcomes (good+bad). So when we say the odds that something will happen are 2 to 1, that means there's a 2/3 probability it will happen, and a 1/3 probability it will not.

In this question, the fraction r/(b+w) is just the ratio of red marbles to other marbles, so it just represents the odds of picking a red marble. Similarly the fraction w/(b+r) is the ratio of white marbles to other marbles, so it represents the odds of picking a white marble. And if the odds of getting red are better than the odds of getting white, the probability of getting red must be higher than the probability of getting white, so S1 is sufficient.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Senior Manager
Joined: 29 Oct 2013
Posts: 297
Concentration: Finance
GMAT 1: 750 Q V46
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Followers: 14

Kudos [?]: 377 [0], given: 197

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

Show Tags

15 Jan 2016, 07:35
IanStewart wrote:
I like this problem because there are at least five different ways to solve it. I'll mention a more conceptual solution since no one has mentioned it yet, but there are some great solutions above as well:

If you know the concept of "odds" that is used in daily life, you can answer this question very quickly. "Odds" are just ratios of good outcomes to bad outcomes, while probabilities are ratios of good outcomes to total outcomes (good+bad). So when we say the odds that something will happen are 2 to 1, that means there's a 2/3 probability it will happen, and a 1/3 probability it will not.

In this question, the fraction r/(b+w) is just the ratio of red marbles to other marbles, so it just represents the odds of picking a red marble. Similarly the fraction w/(b+r) is the ratio of white marbles to other marbles, so it represents the odds of picking a white marble. And if the odds of getting red are better than the odds of getting white, the probability of getting red must be higher than the probability of getting white, so S1 is sufficient.

This is exactly how I solved it. I just didnt realize I was using the concept of odds And glad to see you are still active here on the gmatclub IanStewart! Thanks
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Intern
Joined: 12 Aug 2016
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 53

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

Show Tags

15 Nov 2016, 19:37
Bunuel wrote:
anilnandyala 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 then the probability that the marble chosen will be white?

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

The question is $$\frac{R}{R+B+W}>\frac{W}{R+B+W}$$ true? Or is $$R>W$$ true?

(1) $$\frac{R}{B+W} > \frac{W}{B+R}$$ --> $$\frac{R}{B+W} +1> \frac{W}{B+R}+1$$ --> $$\frac{R+B+W}{B+W}> \frac{W+B+R}{B+R}$$ --> $$\frac{1}{B+W}> \frac{1}{B+R}$$ --> $$B+R>B+W$$ --> $$R>W$$. Sufficient.

I know this is a very old post. Apologies. But why did you add 1 on both sides?
Manager
Joined: 22 Feb 2016
Posts: 112
Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47
GMAT 2: 710 Q47 V39
GPA: 3.57
Followers: 1

Kudos [?]: 7 [0], given: 208

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

Show Tags

21 Dec 2016, 03:49
shahidhussaink wrote:
Bunuel wrote:
anilnandyala 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 then the probability that the marble chosen will be white?

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

The question is $$\frac{R}{R+B+W}>\frac{W}{R+B+W}$$ true? Or is $$R>W$$ true?

(1) $$\frac{R}{B+W} > \frac{W}{B+R}$$ --> $$\frac{R}{B+W} +1> \frac{W}{B+R}+1$$ --> $$\frac{R+B+W}{B+W}> \frac{W+B+R}{B+R}$$ --> $$\frac{1}{B+W}> \frac{1}{B+R}$$ --> $$B+R>B+W$$ --> $$R>W$$. Sufficient.

I know this is a very old post. Apologies. But why did you add 1 on both sides?

Let us not add 1 on both sides and do something totally berserk. Bear with me GMAT has driven me half nuts

ok we need to find if R>W
Statement 2 is invalid it gives us nothing about R and W it just says B is more than R and W taken together. Forget that distraction.

Now coming hereto statement1
it says

R/W+b>W/B+R
Now according to the rules of ratio we can add or substract a constant from both numerator and denominator
Hence

R+W+B/2(W+B)> R+W+B/2(B+R)

We simply added the denominator to both the numerator and denominator. With me till here?

Ok

Now simplify

1/w+b>1/B+R

fine ? now we can cross multiple. They are balls so cannot be negative.
B+R> B+W
B cancels out
R>W Proved!
Re: A certain jar contains only b black marbles, w white marbles   [#permalink] 21 Dec 2016, 03:49
Similar topics Replies Last post
Similar
Topics:
5 A bag contains black and white marbles. How many white marbles are the 6 23 Jul 2015, 23:57
7 A jar contains only black marbles and white marbles. If two thirds of 2 21 Apr 2015, 04:59
83 A jar contains 8 red marbles and y white marbles. If Joan 21 26 Sep 2010, 11:55
30 In the jar there are white and black marbles (W>0 and B>0). 16 09 Oct 2009, 14:08
6 A certain jar contains only b black marbles, w white marbles 12 26 Dec 2007, 19:07
Display posts from previous: Sort by