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

This topic has expert replies
User avatar
Master | Next Rank: 500 Posts
Posts: 212
Joined: Mon Dec 06, 2010 12:52 am
Location: India
Thanked: 5 times
Followed by:1 members
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

Please explain

Regards
Sachin
Never surrender

GMAT/MBA Expert

User avatar
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 » Wed Aug 06, 2014 7:37 am
sachin_yadav 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 = [spoiler]5/12[/spoiler]

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

GMAT/MBA Expert

User avatar
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 » Wed Aug 06, 2014 7:42 am
sachin_yadav 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
Alternatively, we can use the COMPLEMENT.
That is, P(Event A happening) = 1 - P(Event A not happening)

So, P(selected marble is EITHER red or blue) = 1 - P(selected marble is NEITHER red nor blue)
= 1 - P(selected marble is either white or green)
= 1 - [P(marble is white) + P(marble is green)]
= 1 - [1/4 + 1/3]
= 1 - [3/12 + 4/12]
= 1 - 7/12
= [spoiler]5/12[/spoiler]

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Wed Aug 06, 2014 12:02 pm
sachin_yadav 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
Since the problem asks for a FRACTION, the total number of marbles can be ANY VALUE.
Let the total number of marbles = the LCM of 3 and 4 = 12.

If one marble is drawn from the box at random, the probability that it will be white is 1/4.
Thus:
W = (1/4)(12) = 3.
If one marble is drawn from the box at random, the probability that it will be green is 1/3.
Thus:
G = (1/3)(12) = 4.
Implication:
Of the 12 marbles, the number that are R or B = 12-3-4 = 5.

Since 5 of the 12 marbles are R or B, we get:
P(R or B) = 5/12.

The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

by GMATinsight » Wed Aug 06, 2014 9:23 pm
sachin_yadav 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

OA E

Please explain

Regards
Sachin
Total Probability = 1
i.e. 1 = Either White + or Green + or Red + or Blue
i.e. 1 = (1/4) + (1/3) + (Probability of Red or Blue)
i.e. (Probability of Red or Blue) = 1 - ((1/4)+(1/3) = 5/12

Answer: Option E
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour

User avatar
Master | Next Rank: 500 Posts
Posts: 212
Joined: Mon Dec 06, 2010 12:52 am
Location: India
Thanked: 5 times
Followed by:1 members

by sachin_yadav » Sat Aug 09, 2014 6:28 am
Thank you for your replies. Appreciate it :D

Regards
Sachin
Never surrender

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Sat Aug 09, 2014 12:03 pm
Hi sachin_yadav,

Each of the methods outlined in this post can help you to get to the correct answer. Here's one more that is based on converting the data and using 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.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image