A certain jar contains only b black marbles

[rakeshd347]

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

[theCodeToGMAT]

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]

[[email protected]]

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

GMAT assassins aren't born, they're made,
Rich

[vipulgoyal]

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

[theCodeToGMAT]

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

[Mission2012]

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

[theCodeToGMAT]

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

[lunarpower]

what is the source of this question

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

[GMATGuruNY]

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.