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

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26 Dec 2007, 20:07

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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?

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

1) r / (b+w) > w / (b+r) r(b+r) > w(b+w) ... this is possible only if r>w. suffcieint

2) b-w > r w >r or w<r INSUFFCIENT.

A
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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

Soln. From statements what we need to find is i.e if P(choosing one red) > P(choosing one white) i.e if r / (b+w+r) > w / (b+w+r) or in its simplest form after cancelling out the denominators, if r > w

Statement 1 alone is sufficient. Given that => r / (b+w) > w / (b+r) => (b+r)/w > (b+w)/r adding 1 to both sides and taking common denominator => (b+r+w)/w > (b+w+r)/r cancelling numerators and taking r and w to numerators => r > w

Statement 2 alone is not sufficient Given that => b-w > r from this we cannot find if r > w or r < w Hence not sufficient

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

Ques: Is r /(b+w+r) > w /(b+w+r) ? or rb + rw + r^2 > wb + w^2 + rw? or rb + r^2 > wb + w^2 ?

S1: r / (b+w) > w / (b+r) rb + r^2 > wb + w^2... Hence SuFF..

S2: b-w>r b > r + w..... this doesnt give r > w or not..... hence INSUFF.

Therefore A.
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|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

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

(i) is sufficient because it gives us r<w. Thus we know the answer. From (ii) we can'tsay whether w>r or r>w. Therefore "A"

Damn I'm so bad at DS and inequalities.... scthakur's solution was the easiest for me to understand. Do you guys actually see the answer intuitively without going all the way to the end?