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Math Expert V
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Posts: 58257
There is a total of 120 marbles in a box, each of which is red, green,  [#permalink]

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Difficulty:   5% (low)

Question Stats: 95% (01:08) correct 5% (02:41) wrong based on 214 sessions

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There is a total of 120 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/4 and the probability that it will be green is 1/3. What is the probability that the marble will be either red or blue ?

(A) 1/6
(B) 1/4
(C) 2/7
(D) 1/3
(E) 5/12

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Re: There is a total of 120 marbles in a box, each of which is red, green,  [#permalink]

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Total marbles in the box=120
white marbles=120/4=30
green marbles=120/3=40
w+g=70
red+blue=50
p(red or blue)=50/120=5/12
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There is a total of 120 marbles in a box, each of which is red, green,  [#permalink]

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1
Probability( white )= 1/4
Probability(green) = 1/3
Probability (red or blue marbles) = 1 - (1/4 + 1/3)
= 1 - 7/12 = 5/12

Alternatively we can can calculate the number of balls and then calculate the probability . This will take a little more time .
Total number of marbles in box = 120
Prob( white )= 1/4
=> 1/4 = number of white marbles/120
=> number of white marbles = 30

Prob(green) = 1/3
Number of green marbles = 40

Number of red or blue marbles = 120 - 70 = 50

Probablity of drawing red or blue marbles = 50/120 = 5/12

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Re: There is a total of 120 marbles in a box, each of which is red, green,  [#permalink]

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P(Red or blue)= 1 - (1/4 + 1/3) = 5/12

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: There is a total of 120 marbles in a box, each of which is red, green,  [#permalink]

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Hi All,

With this question, you can 'convert' the data and use the structure of the answer choices to your advantage:

First off, in almost all cases, when the answers to a GMAT Quant question are numbers, they will be arranged from least to greatest. This will allow you to take advantage of approximation, rounding, etc., so that you can quickly eliminate answers that are "too big" or "too small"

In this prompt, we're dealing with some simple fractions (1/4 and 1/3), which you should be able to convert to decimal (you should have them memorized):

1/4 are white = .25 are white
1/3 are green = .33 are green (approximately)

.25 + .33 = .58 total of white and green (approximately)

The question asks for the probability of red or blue, so we have…

1 - .58 = .42 total of red and blue (approximately)

The answers here are arranged from least (1/6 = .1666) to greatest (5/12 = let's not mess with this just yet)

Answer D = 1/3 = .33, which is TOO LOW (we're looking for approximately .42). This means that A, B and C are also TOO LOW. There's only one answer left that would make any sense...

GMAT assassins aren't born, they're made,
Rich
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Re: There is a total of 120 marbles in a box, each of which is red, green,  [#permalink]

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Top Contributor
Bunuel wrote:
There is a total of 120 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/4 and the probability that it will be green is 1/3. What is the probability that the marble will be either red or blue ?

(A) 1/6
(B) 1/4
(C) 2/7
(D) 1/3
(E) 5/12

...the probability that it [the marble] will be white is 1/4
So, 1/4 of the 120 marbles are white.
In other words, there are 30 white marbles.

...the probability that it [the marble] will be green is 1/3
So, 1/3 of the 120 marbles are green .
In other words, there are 40 green marbles.

Altogether, there are 70 marbles that are EITHER white or green.
This means that the remaining 50 marbles are EITHER red or blue.

So, P(selected marble is EITHER red or blue) = 50/120
= 5/12

Cheers,
Brent
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Re: There is a total of 120 marbles in a box, each of which is red, green,  [#permalink]

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Bunuel wrote:
There is a total of 120 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/4 and the probability that it will be green is 1/3. What is the probability that the marble will be either red or blue ?

(A) 1/6
(B) 1/4
(C) 2/7
(D) 1/3
(E) 5/12

We see that there are 120 x 1/4 = 30 white marbles and 120 x 1/3 = 40 white marbles, so there must be 120 - 70 = 50 blue or red marbles.

So the probability of selecting either a red or blue marble is 50/120 = 5/12.

Alternate solution:

Since P(red) + P(green) + P(blue) + P(white) = 1 and P(green) = 1/3 and P(white) = 1/4, we have:

P(red) + 1/3 + P(blue) + 1/4 = 1

P(red) + P(blue) = 1 - 1/3 - 1/4

P(red or blue) = 5/12

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