A certain jar contains only b black marbles

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rakeshd347: Master | Next Rank: 500 Posts; Posts: 391; Joined: Sat Mar 02, 2013 5:13 amFollowed by: 4 members; Thanked: 50 times

by rakeshd347 » Sat Oct 05, 2013 5:55 pm

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

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Source: Beat The GMAT — Data Sufficiency | Sat Oct 05, 2013 5:55 pm

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sat Oct 05, 2013 6:30 pm

To find: R>W
Statement 1:
r/(b+w) > w/(b+r)
Add "1" both sides
(r + b + w)/(b+w) > (r + b + w)/(b+r)
b + w < b + r
w<r
SUFFICIENT

Statement 2:
b-w>r
b+r>w
INSUFFICIENT

Answer [spoiler]{A}[/spoiler]

Last edited by theCodeToGMAT on Mon Oct 07, 2013 3:04 am, edited 1 time in total.

R A H U L

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Oct 06, 2013 12:34 am

Hi rakeshd347,

For this DS question, you can use a combination of Number Properties and TESTing Values to find the correct answer.

We're told of 3 types of marbles (B, W and R). We're asked if the probability of pulling an R is > the probability of pulling a W. This is a Yes/No question.

Fact 1: R/(B+W) > W/(B+R)

You'll notice that the "B" is in the denominator of BOTH fractions, so we can focus on the R and W. You can TEST Values to find the pattern or use a Number Property.

If you TEST Values:
R = 3
W = 2
B = 1
The answer to the question is YES.

With a bit of effort, you'll find that R CANNOT EQUAL W (if it did, then the two fractions in Fact 1 would be equal).
Also, IF the W was bigger than the R, the first fraction WOULDN'T be greater than the second fraction.
These two Number Properties ELIMINATE the possibility that R = W and ELIMINATE the possibility that R < W.
Fact 1 is ALWAYS going to give you a YES answer.
Fact 1 is SUFFICIENT

Fact 2: B - W > R

Try TESTing Values
B = 3
W = 1
R = 1
The answer to the question is NO

B = 4
W = 1
R = 2
The answer to the question is YES
Fact 2 is INSUFFICIENT

Final Answer:A

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Rich

Contact Rich at [email protected]

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Mon Oct 07, 2013 2:58 am

Hi Rahul,

b + w > b + r
w>r
SUFFICIENT

i think here above you did some typo error
correction
b + w < b + r
w < r
SUFFICIENT

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Mon Oct 07, 2013 3:03 am

vipulgoyal wrote:Hi Rahul,

b + w > b + r
w>r
SUFFICIENT

i think here above you did some typo error
correction
b + w < b + r
w < r
SUFFICIENT

Yes, typo... its tough to do maths on MS Notepad

.. issue fixed

R A H U L

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Mission2012: Master | Next Rank: 500 Posts; Posts: 184; Joined: Sun Aug 19, 2012 10:04 pmFollowed by: 2 members; Thanked: 10 times

by Mission2012 » Mon Oct 07, 2013 5:02 am

rakeshd347 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

@ Rahul - Awesome solution

@ Rakesh - what is the source of this question

If you find my post useful -> please click on "Thanks"

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Mon Oct 07, 2013 5:32 am

Mission2012 wrote:
rakeshd347 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
@ Rahul - Awesome solution

@ Rakesh - what is the source of this question

Thanks

R A H U L

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lunarpower: GMAT Instructor; Posts: 3380; Joined: Mon Mar 03, 2008 1:20 amFollowed by: 1535 members; Thanked: 2256 times; GMAT Score:800

by lunarpower » Tue Oct 08, 2013 3:28 am

what is the source of this question

This problem has been in the GMAT PREP software for several years.

Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions Ã Ron en franÃ§ais
Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi

--

Quand on se sent bien dans un vÃªtement, tout peut arriver. Un bon vÃªtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Oct 08, 2013 5:10 am

rakeshd347 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

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.
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.

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