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

It is currently 22 Sep 2018, 22:11

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
A jar contains only black marbles and white marbles. If two thirds of  [#permalink]

Show Tags

New post 21 Apr 2015, 05:59
2
7
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

65% (01:53) correct 35% (06:49) wrong based on 216 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.

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
Retired Moderator
User avatar
Joined: 06 Jul 2014
Posts: 1244
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT ToolKit User Premium Member
A jar contains only black marbles and white marbles. If two thirds of  [#permalink]

Show Tags

New post 21 Apr 2015, 08:01
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.

Answer is D
_________________

Simple way to always control time during the quant part.
How to solve main idea questions without full understanding of RC.
660 (Q48, V33) - unpleasant surprise
740 (Q50, V40, IR3) - anti-debrief ;)

General Discussion
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2683
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: A jar contains only black marbles and white marbles. If two thirds of  [#permalink]

Show Tags

New post 10 Mar 2016, 19:31
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.
Senior Manager
Senior Manager
User avatar
P
Joined: 14 Dec 2017
Posts: 477
Re: A jar contains only black marbles and white marbles. If two thirds of  [#permalink]

Show Tags

New post 03 Jul 2018, 10:06
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.



Answer D.



Thanks,
GyM
_________________

New to GMAT Club - https://gmatclub.com/forum/new-to-gmat-club-need-help-271131.html#p2098335

Intern
Intern
User avatar
B
Joined: 17 May 2018
Posts: 32
A jar contains only black marbles and white marbles. If two thirds of  [#permalink]

Show Tags

New post 10 Jul 2018, 08:47
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!

GMAT Club Bot
A jar contains only black marbles and white marbles. If two thirds of &nbs [#permalink] 10 Jul 2018, 08:47
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.