GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Dec 2018, 02:56

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### 10 Keys to nail DS and CR questions

December 17, 2018

December 17, 2018

06:00 PM PST

07:00 PM PST

Join our live webinar and learn how to approach Data Sufficiency and Critical Reasoning problems, how to identify the best way to solve each question and what most people do wrong.
• ### R1 Admission Decisions: Estimated Decision Timelines and Chat Links for Major BSchools

December 17, 2018

December 17, 2018

10:00 PM PST

11:00 PM PST

From Dec 5th onward, American programs will start releasing R1 decisions. Chat Rooms: We have also assigned chat rooms for every school so that applicants can stay in touch and exchange information/update during decision period.

# A jar contains only black marbles and white marbles. If two thirds of

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51259
A jar contains only black marbles and white marbles. If two thirds of  [#permalink]

### Show Tags

21 Apr 2015, 04:59
2
8
00:00

Difficulty:

55% (hard)

Question Stats:

65% (02:29) correct 35% (02:10) wrong based on 222 sessions

### HideShow timer Statistics

A jar contains only black marbles and white marbles. If two thirds of the marbles are black, how many white marbles are in the jar?

(1) If two marbles were to be drawn, simultaneously and at random, from the jar, there is a 5/12 probability that both would be black.

(2) If one white marble were removed from the jar, there would be a 1/4 probability that the next randomly-drawn marble would be white.

Kudos for a correct solution.

_________________
Retired Moderator
Joined: 06 Jul 2014
Posts: 1235
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
A jar contains only black marbles and white marbles. If two thirds of  [#permalink]

### Show Tags

21 Apr 2015, 07:01
4
2
Bunuel wrote:
A jar contains only black marbles and white marbles. If two thirds of the marbles are black, how many white marbles are in the jar?

(1) If two marbles were to be drawn, simultaneously and at random, from the jar, there is a 5/12 probability that both would be black.

(2) If one white marble were removed from the jar, there would be a 1/4 probability that the next randomly-drawn marble would be white.

Kudos for a correct solution.

1) probability of first blacck marble equal $$\frac{2}{3}$$. if we multiply this probability on probability second black marble, we receive common probability $$\frac{5}{12}$$
Let's x be second probability
$$\frac{2}{3} * x = \frac{5}{12}$$
$$x = \frac{5}{8}$$ and this probability after we remove one marble, so initially we have 9 marbles in total and $$\frac{1}{3}$$ of them white: 3 white marbles
Sufficient

2) let's x be total marbles
$$\frac{1}{3}x-1 = \frac{1}{4}(x-1)$$
$$x = 9$$ marbles in total and $$\frac{1}{3}$$ of them white: 3 white marbles
Sufficient.

_________________
##### General Discussion
Board of Directors
Joined: 17 Jul 2014
Posts: 2618
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: A jar contains only black marbles and white marbles. If two thirds of  [#permalink]

### Show Tags

10 Mar 2016, 18:31
1
suppose we have X white, and 2X black
total 3X

now..
1 - probability that 2 black is:
2/3 * Y(variable) = 5/12
y=5/12*3/2
y=5/8
since y must be: (x-1)/(3x-1)
it must be true that there are 9 marbles, out of which 6 black and 2 white. sufficient

2. to draw a second white is 1/4
it must be true that x-1/3x-1 = 1/4
4x-1 = 3x-1
x=3.

sufficient.
Director
Joined: 14 Dec 2017
Posts: 518
Location: India
Re: A jar contains only black marbles and white marbles. If two thirds of  [#permalink]

### Show Tags

03 Jul 2018, 09:06
Bunuel wrote:
A jar contains only black marbles and white marbles. If two thirds of the marbles are black, how many white marbles are in the jar?

(1) If two marbles were to be drawn, simultaneously and at random, from the jar, there is a 5/12 probability that both would be black.

(2) If one white marble were removed from the jar, there would be a 1/4 probability that the next randomly-drawn marble would be white.

Kudos for a correct solution.

Let $$X$$ be the total # of marbles. hence we have $$\frac{2X}{3}$$ black marbles & $$\frac{X}{3}$$ white marbles.

The question prompt now translates to finding X.

Statement 1: When two marbles are drawn, the probability of both to be black = $$\frac{5}{12}$$

Hence, $${(2X/3)}/X$$ * $$((2X/3) - 1)/(X-1)$$ = $$\frac{5}{12}$$

We can solve this for X. Hence Statement 1 alone is sufficient.

Statement 2: A white ball is drawn & then a white ball is drawn, the probability of drawing a second white ball is $$\frac{1}{4}$$

Hence we, $$((X/3) - 1)/(X - 1) = 1/4$$

We can solve this for X. Hence statement 2 alone is sufficient.

Thanks,
GyM
_________________
Intern
Joined: 17 May 2018
Posts: 43
A jar contains only black marbles and white marbles. If two thirds of  [#permalink]

### Show Tags

10 Jul 2018, 07:47
1) We can say that we have one part of white balls per two parts of black balls. We want to find how much is one part.

The probability of having 2 black balls is:
$$\frac{5}{12}$$=$$\frac{2p}{3p}$$.$$\frac{(2p-1)}{(3p-1)}$$

We can cancel out the p in the first fraction $$\frac{2p}{3p}$$ so we can find p with the resulting equation. (p=3)

Sufficient.

2) We know that initially the probability of having a white ball is 1:3. To find the probability of having the second white ball, we need to subtract one to each. Let's write down our hypothesis of the initial amount of white balls vs total that meet the 1:3 probability. Then let's write down how it would look like after we removed one white ball and see if the resulting probability is 1:4:

1:3 => this would make it impossible to have a second white ball
2:6 => 1:5 ; not what we want
3:9 => 2:8 which is equivalent to 1:4; what we want

We needed to have 3 out of 9 white balls initially to meet this condition.

Sufficient.
_________________

¿Tienes que presentar el GMAT y no sabes por dónde empezar?
¡Visita GMAT para Principiantes y recibe el curso completo gratis!

A jar contains only black marbles and white marbles. If two thirds of &nbs [#permalink] 10 Jul 2018, 07:47
Display posts from previous: Sort by