There is a total of 120 marbles in a box, each of which is

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

There is a total of 120 marbles in a box, each of which is

by AAPL » Sat Jan 12, 2019 5:24 am

GMAT Paper Tests

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

OA E

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Source: Beat The GMAT — Problem Solving | Sat Jan 12, 2019 5:24 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sat Jan 12, 2019 6:02 am

AAPL wrote:GMAT Paper Tests

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

OA E

...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

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

by fskilnik@GMATH » Sun Jan 13, 2019 5:50 am

AAPL wrote:GMAT Paper Tests

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

$$? = {{\# \left( {{\rm{red}}\,\,{\rm{or}}\,\,{\rm{blue}}} \right)} \over {\,120\,\,{\rm{equiprobables}}\,}}$$
$$\# \left( {{\rm{red}}\,\,{\rm{or}}\,\,{\rm{blue}}} \right)\,\,\, = \,\,\,120\,\, - \,\,\# \left( {{\rm{white}}\,\,{\rm{or}}\,\,{\rm{green}}} \right) = 120 - \left[ {{1 \over 4}\left( {120} \right) + {1 \over 3}\left( {120} \right)} \right] = 50$$
$$? = {5 \over {12}}$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Jan 14, 2019 5:54 pm

AAPL wrote:GMAT Paper Tests

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

Answer: E

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