Sep 18 12:00 PM EDT  01:00 PM EDT Mindful MBA series Part 1, Fall 2019. Becoming a More Mindful GMAT Taker. Tuesday, September 18th at 12 PM ET Sep 19 12:00 PM PDT  10:00 PM PDT On Demand $79, For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Sep 19 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. One hour of live, online instruction. Sep 19 10:00 PM PDT  11:00 PM PDT Join a FREE 1day Data Sufficiency & Critical Reasoning workshop and learn the best strategies to tackle the two trickiest question types in the GMAT! Sep 21 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Sep 21 08:00 PM PDT  09:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE Sep 23 08:00 AM PDT  09:00 AM PDT Join a free 1hour webinar and learn how to create the ultimate study plan, and be accepted to the upcoming Round 2 deadlines. Save your spot today! Monday, September 23rd at 8 AM PST
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 07 Feb 2010
Posts: 115

A certain jar contains only b black marbles, w white marbles
[#permalink]
Show Tags
16 Nov 2010, 06:43
Question Stats:
59% (02:12) correct 41% (02:25) wrong based on 731 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) bw > r
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 57996

Re: a certain jar contains
[#permalink]
Show Tags
16 Nov 2010, 06:52
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) bw > 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 \(R(B+R)>W(B+W)\) > \(RB+R^2>WB+W^2\) > \((R^2W^2)+(RBWB)>0\) > \((RW)(R+W)+B(RW)>0\) > \((RW)(R+W+B)>0\). As \(R+W+B>0\), the above inequality to hold true \(RW\) must also be more than zero, so \(RW>0\) > \(R>W\). (2) \(BW>R\), not sufficient to determine whether \(R>W\) or not. Answer: A.
_________________




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9633
Location: Pune, India

Re: a certain jar contains
[#permalink]
Show Tags
16 Nov 2010, 12:40
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) bw > 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. Answer (A).
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Senior Manager
Joined: 08 Nov 2010
Posts: 292
WE 1: Business Development

Re: a certain jar contains
[#permalink]
Show Tags
17 Nov 2010, 23:55
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: 66
Location: Vietnam
WE 1: 5.0

Re: a certain jar contains
[#permalink]
Show Tags
23 Nov 2010, 23:36
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) bw > 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. Answer: A. 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: 79
Location: Nepal
Concentration: Finance, Entrepreneurship
GPA: 3.83
WE: Accounting (Consulting)

A certain jar contains only b black marbles, w white marbles and
[#permalink]
Show Tags
22 May 2013, 07:40
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.



Intern
Joined: 24 Apr 2013
Posts: 44

Re: A certain jar contains only b black marbles, w white marbles
[#permalink]
Show Tags
22 May 2013, 14:41
chose B. I hate my life!



Manager
Joined: 05 Nov 2012
Posts: 140

A jar contains 8 red marbles and y white marbles. If Joan takes
[#permalink]
Show Tags
30 Dec 2013, 11:17
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



SVP
Joined: 06 Sep 2013
Posts: 1604
Concentration: Finance

Re: A certain jar contains only b black marbles, w white marbles
[#permalink]
Show Tags
10 Jan 2014, 06:31
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) bw > r Is r>w? r/(b+w)>w(b+r) rb + r^2 ? wb + w^2 (r+w)(rw) > b(wr) Now if rw>0 then wr < 0 and inequality holds true. Other way around if rw<0, LHS is negative and RHS is positive and inequality does NOT hold true So only valid scenario is rw>0 and thus r>w Sufficient (B) Not enough Info Answer is A Cheers J PS. Alternatively, first statement can be treated as rw / b+r>0 Well b+r is always positive, thus rw has to be positive too Then r>w



Manager
Status: suffer now and live forever as a champion!!!
Joined: 01 Sep 2013
Posts: 102
Location: India
Dheeraj: Madaraboina
GPA: 3.5
WE: Information Technology (Computer Software)

Re: A certain jar contains only b black marbles, w white marbles
[#permalink]
Show Tags
03 Jun 2014, 09:58
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: bw > r
We can consider two cases(numbers) for which the above statement is both true and false;
case1: b=10; w=2 ; r=7; 102>7; r>w(true)
Case2: b=10; w=5; r=4; 105>4; but here 4>5(false); Hence Insufficient.



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1843

A certain jar contains only b black marbles, w white marbles
[#permalink]
Show Tags
20 Jun 2015, 00:25
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



Retired Moderator
Joined: 29 Oct 2013
Posts: 257
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)

A certain jar contains only b black marbles, w white marbles
[#permalink]
Show Tags
15 Jan 2016, 08:35
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
_________________
Please contact me for super inexpensive quality private tutoring
My journey V46 and 750 > http://gmatclub.com/forum/myjourneyto46onverbal750overall171722.html#p1367876



Intern
Joined: 13 Aug 2016
Posts: 1

Re: A certain jar contains only b black marbles, w white marbles
[#permalink]
Show Tags
15 Nov 2016, 20:37
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) bw > 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: 84
Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47 GMAT 2: 710 Q47 V39
GPA: 3.57

Re: A certain jar contains only b black marbles, w white marbles
[#permalink]
Show Tags
21 Dec 2016, 04:49
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) bw > 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!



Manager
Joined: 10 Apr 2015
Posts: 178
GPA: 3.31

Re: A certain jar contains only b black marbles, w white marbles
[#permalink]
Show Tags
08 Apr 2017, 09:55
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) add wr in both side and it leads to solution. Yes. Suff. (2) bw > r b > w + r No info on w and r . NS. Ans A.
_________________
In case you find my posts helpful, give me Kudos. Thank you.



CEO
Joined: 12 Sep 2015
Posts: 3960
Location: Canada

Re: A certain jar contains only b black marbles, w white marbles
[#permalink]
Show Tags
24 Apr 2018, 11:12
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) bw > r Target question: Is the probability that the marble chosen will be red greater than the probability that the marble chosen will be white? We can rephrase the target question as... REPHRASED target question: Is r > w? Statement 1: r/(b + w) > w/(b + r) Let's let T = the TOTAL number of marbles in the jar. This means that b + w + r = T This also means that b + w = T  r And it means that b + r = T  w So, we can take statement 1, r/(b + w) > w/(b + r), and rewrite it as... r/(T  r) > w/(T  w) Multiply both sides by (T  r) to get: r > w(T  r)/(T  w) Multiply both sides by (T  w) to get: r(T  w) > w(T  r) Expand both sides: rT  rw > wT  rw Add rw to both sides: rT > wT Divide both sides by T to get: r > w Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT Statement 2: b  w > r Add w to both sides to get: b > w + r All this means is that there are more black marbles than there are white and red marbles combined. Given this information, there's no way to determine whether or not r is greater than w Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT Answer: A Cheers, Brent
_________________
Test confidently with gmatprepnow.com



Intern
Joined: 30 Nov 2017
Posts: 30

Re: A certain jar contains only b black marbles, w white marbles
[#permalink]
Show Tags
17 May 2018, 01:31
Can someone help me where I am going wrong?
r/(b+w) > w/(b+r)
Cross multiplying:
r(b+r) > w(b+w)
rb + r^2 > wb + w^2
rb  wb > w^2  r^2
b(rw) > (wr)(w+r)
b(wr) > (wr)(w+r)
(wr) gets cancelled on both sides.
b > w + r
(w+b) > r
r < (w+b)
Now what do I do?



Manager
Joined: 28 Jun 2018
Posts: 132
Location: Bouvet Island
GMAT 1: 490 Q39 V18 GMAT 2: 640 Q47 V30 GMAT 3: 670 Q50 V31 GMAT 4: 700 Q49 V36
GPA: 4

Re: A certain jar contains only b black marbles, w white marbles
[#permalink]
Show Tags
23 Jan 2019, 23:30
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) bw > r Hi chetan2u Is it really necessary to do the long simplifications for st 1 ? \(\frac{r}{(b+w)} > \frac{w}{(b+r)}\) Since we know "b" is just some constant, we can just start by taking the above as  \(\frac{r}{(w)} > \frac{w}{(r)}\) After which it simply is  \(r^2 > w^2\) or \(r > w\) Is this approach okay?



Math Expert
Joined: 02 Aug 2009
Posts: 7812

Re: A certain jar contains only b black marbles, w white marbles
[#permalink]
Show Tags
23 Jan 2019, 23:46
blitzkriegxX 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) bw > r Hi chetan2u Is it really necessary to do the long simplifications for st 1 ? \(\frac{r}{(b+w)} > \frac{w}{(b+r)}\) Since we know "b" is just some constant, we can just start by taking the above as  \(\frac{r}{(w)} > \frac{w}{(r)}\) After which it simply is  \(r^2 > w^2\) or \(r > w\) Is this approach okay? Yes, this is much simpler and better.. You can do this as all variables are positive and the question finally boils down to which is more r or w..
_________________



Manager
Status: wake up with a purpose
Joined: 24 Feb 2017
Posts: 103
Concentration: Accounting, Entrepreneurship

Re: A certain jar contains only b black marbles, w white marbles
[#permalink]
Show Tags
25 Aug 2019, 10:58
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) bw > 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 \(R(B+R)>W(B+W)\) > \(RB+R^2>WB+W^2\) > \((R^2W^2)+(RBWB)>0\) > \((RW)(R+W)+B(RW)>0\) > \((RW)(R+W+B)>0\). As \(R+W+B>0\), the above inequality to hold true \(RW\) must also be more than zero, so \(RW>0\) > \(R>W\).(2) \(BW>R\), not sufficient to determine whether \(R>W\) or not. Answer: A. I don't understand the highlighted part. Would you please explain it in simple words? BunuelPosted from my mobile device
_________________
If people are NOT laughing at your GOALS, your goals are SMALL.




Re: A certain jar contains only b black marbles, w white marbles
[#permalink]
25 Aug 2019, 10:58



Go to page
1 2
Next
[ 21 posts ]



