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Register now and save up to $200 Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code ## red ball_prep tagged by: Brent@GMATPrepNow This topic has 4 expert replies and 4 member replies mukherjee.tanuj3@gmail.co Master | Next Rank: 500 Posts Joined 11 Dec 2013 Posted: 218 messages Followed by: 4 members Thanked: 3 times #### red ball_prep Mon Apr 28, 2014 8:36 pm Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! perwinsharma Junior | Next Rank: 30 Posts Joined 22 Jun 2009 Posted: 21 messages Thanked: 3 times Test Date: 3 December 2010 GMAT Score: 770 Sat Jul 26, 2014 11:50 pm Here we know, that all the variables B, R, and W are positive. 1) R/(B + W) > W/(B + R) If we cross multiply RB + R^2 > WB + W^2 => (R^2 - W^2) + (RB - WB) > 0 => (R + W) (R - W) + B(R - W) > 0 => (R- W) (B + R + W) > 0 => We know that B + R + W > 0 as all the variables are positive => R - W has to be more than zero => R > W SUFFICIENT 2) B - W > R Doesn't give us any information. The answer is (A). Praveen Sharma Veritas Prep GURGAON _________________ Praveen Sharma Wizius Careers Gurgaon India https://www.facebook.com/wiziuscareergmat/ ### GMAT/MBA Expert GMATGuruNY GMAT Instructor Joined 25 May 2010 Posted: 13383 messages Followed by: 1781 members Thanked: 12903 times GMAT Score: 790 Sun Jul 27, 2014 2:32 am Quote: 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 Very little math is needed here. Just use common sense. Question stem, rephrased: Is R>W? Statement 1: r/(b+w) > w/(b+r) Put into words: The ratio of R to the OTHER marbles is greater than the ratio of W to the OTHER marbles. The statement above can be true only if THERE ARE MORE RED MARBLES THAN WHITE MARBLES. Thus, R>W. SUFFICIENT. Statement 2: b-w > r B > R+W. No way to determine whether R>W. INSUFFICIENT. The correct answer is A. _________________ Mitch Hunt GMAT Private Tutor GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "Thank" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Last edited by GMATGuruNY on Sun Jul 27, 2014 3:24 am; edited 1 time in total Thanked by: binit Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMATGuruNY GMAT Instructor Joined 25 May 2010 Posted: 13383 messages Followed by: 1781 members Thanked: 12903 times GMAT Score: 790 Sun Jul 27, 2014 2:45 am Another way to evaluate statement 1. Statement 1: r/(b+w) > w/(b+r) Test whether it's possible that R=W or that R<W. Case 1: R=W=1 Substituting R=1 and W=1 into r/(b+w) > w/(b+r), we get: 1/(b+1) > 1/(b+1) b+1 > b+1 0 > 0. Doesn't work. Case 1 illustrates that R=W is not viable. Case 2: R=1 and W=2 Substituting R=1 and W=2 into r/(b+w) > w/(b+r), we get: 1/(b+2) > 2/(b+1) b+1 > 2b + 4 -b > 3 b < -3. Not possible: b must be a positive value. Case 2 illustrates that R<W is not viable. Since it's not possible that R=W or that R<W, it must be true that R>W. SUFFICIENT. _________________ Mitch Hunt GMAT Private Tutor GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "Thank" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### Top Member GMATinsight Legendary Member Joined 10 May 2014 Posted: 998 messages Followed by: 21 members Thanked: 203 times Sun Jul 27, 2014 9:57 am Quote: 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 Probability of Red marble picked = r/(b+w+r) Probability of White marble picked = w/(b+w+r) Question : Is r/(b+w+r) > w/(b+w+r) Question Rephrased : Is r > w ? Statement 1) r/(b+w) > w/(b+r) i.e. r(b+r) > w(b+w) i.e. rb + r^2 > wb + w^2 i.e. rb - wb > w^2 - r^2 i.e. b(r - w) > (w - r)(w + r) i.e. 0 > (w - r)(w + r) - b(r - w) i.e. 0 > (w - r)(w + r) + b(w - r) i.e. 0 > (w - r)(w + r + b) BUT (w + r + b) is definitely Greater than Zero Therefore, (w-r) is certainly Negative i.e. w-r < 0 i.e. w < r SUFFICIENT Statement 2) b-w > r Due to b being present in the above expression, w and r can't be compared, therefore INSUFFICIENT Answer: Option A _________________ Prosper!!! Bhoopendra Singh & Sushma Jha "GMATinsight" Contact Us Testimonials To register for One-on-One FREE ONLINE DEMO Class Call/e-mail e-mail: info@GMATinsight.com Mobile: +91-9999687183 / +91-9891333772 Get in touch for SKYPE-Based Interactive Private Tutoring One-On-One Classes fee - US$40 per hour &
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Brent@GMATPrepNow GMAT Instructor
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Sun Jul 27, 2014 10:59 am
Quote:
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
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

Cheers,
Brent

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binit Master | Next Rank: 500 Posts
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Sun May 03, 2015 3:47 am
St 1: r/(b+w)> w/(b+r) add 1 to both sides and simplify
So, (r+b+w)/(b+w) > (w+b+r)/(b+r) both the numerators are equal now
or, 1/b+w > 1/b+r
or, b+w < b+r ,inequality will be reversed
or w < r. Sufficient.

St 2: b > w+r no idea about w and r, insufficient.

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Matt@VeritasPrep GMAT Instructor
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Sun May 03, 2015 11:52 pm
binit wrote:
or, 1/b+w > 1/b+r
or, b+w < b+r ,inequality will be reversed
Be careful, this is misleading. Since b, w, and r are all positive, you're just multiplying both sides by (b+w)(b+r) and arriving at b + r > b + w. This isn't a reversal, just a rearrangement. ((b + w) need not always be on the left hand side.)

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binit Master | Next Rank: 500 Posts
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Mon May 04, 2015 10:43 pm
Quote:
Since b, w, and r are all positive, you're just multiplying both sides by (b+w)(b+r) and arriving at b + r > b + w. This isn't a reversal, just a rearrangement.
Thanks Matt, for pointing that out. Yeah, "reversal" is not the right term here. I am poor at vocab What I had in mind was: since, 1/3 > 1/5, we can readily simplify it as: 3 < 5.

~Binit.

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