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

It is currently 20 Feb 2019, 11:44

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
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Prep Hour

     February 20, 2019

     February 20, 2019

     08:00 PM EST

     09:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST
  • Online GMAT boot camp for FREE

     February 21, 2019

     February 21, 2019

     10:00 PM PST

     11:00 PM PST

    Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

A jar contains 16 red balls and 8 white balls. If 3 balls are selected

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

Hide Tags

 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6967
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
A jar contains 16 red balls and 8 white balls. If 3 balls are selected  [#permalink]

Show Tags

New post 29 Aug 2018, 23:53
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (01:55) correct 33% (01:59) wrong based on 108 sessions

HideShow timer Statistics

[Math Revolution GMAT math practice question]

A jar contains 16 red balls and 8 white balls. If 3 balls are selected at random from the jar, what is the approximate probability that all balls selected are white?

A. 0.02
B. 0.03
C. 0.04
D. 0.05
E. 0.06

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Intern
avatar
S
Joined: 09 Apr 2017
Posts: 25
Location: Nepal
Concentration: Finance, Entrepreneurship
WE: Information Technology (Computer Software)
Reviews Badge
A jar contains 16 red balls and 8 white balls. If 3 balls are selected  [#permalink]

Show Tags

New post 30 Aug 2018, 00:12
MathRevolution wrote:
[Math Revolution GMAT math practice question]

A jar contains 16 red balls and 8 white balls. If 3 balls are selected at random from the jar, what is the approximate probability that all balls selected are white?

A. 0.02
B. 0.03
C. 0.04
D. 0.05
E. 0.06


3 balls selected without replacement.
P(WWW) = 8/24 * 7/23 *6/22 = 7/253 = 0.027
Senior Manager
Senior Manager
avatar
S
Joined: 04 Aug 2010
Posts: 351
Schools: Dartmouth College
Re: A jar contains 16 red balls and 8 white balls. If 3 balls are selected  [#permalink]

Show Tags

New post 30 Aug 2018, 02:21
MathRevolution wrote:
[Math Revolution GMAT math practice question]

A jar contains 16 red balls and 8 white balls. If 3 balls are selected at random from the jar, what is the approximate probability that all balls selected are white?

A. 0.02
B. 0.03
C. 0.04
D. 0.05
E. 0.06


P(1st marble is white) = \(\frac{8}{24}\) (Of the 24 marbles, 8 are white.)
P(2nd marble is white) = \(\frac{7}{23}\) (Of the 23 remaining marbles, 7 are white.)
P(3rd marble is white) = \(\frac{6}{22}\) (Of the 22 remaining marbles, 6 are white.)
To combine these probabilities, we multiply:
\(\frac{8}{24} * \frac{7}{23} * \frac{6}{22} = \frac{1}{3} * \frac{7}{23} * \frac{3}{11} = \frac{7}{23*11} = \frac{7}{253} ≈ \frac{7}{250} = \frac{28}{1000} = 0.028 ≈ 0.03\)


_________________

GMAT and GRE Tutor
Over 1800 followers
Click here to learn more
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 759
A jar contains 16 red balls and 8 white balls. If 3 balls are selected  [#permalink]

Show Tags

New post 30 Aug 2018, 03:25
MathRevolution wrote:
[Math Revolution GMAT math practice question]

A jar contains 16 red balls and 8 white balls. If 3 balls are selected at random from the jar, what is the approximate probability that all balls selected are white?

A. 0.02
B. 0.03
C. 0.04
D. 0.05
E. 0.06

\({\text{Jar}}\,\,\left\{ \begin{gathered}
16\,r \hfill \\
8\,w \hfill \\
\end{gathered} \right.\,\,\,\,\, \Rightarrow \,\,\,3\,\,{\text{simultaneous}}\,\,{\text{extractions}}\)

\({\text{? = P}}\left( {{\text{all}}\,\,w} \right)\)

\({\text{total}} = C\left( {16 + 8,3} \right) = C\left( {24,3} \right)\,\,\,\,{\text{equiprobable}}\)

\({\text{favorable}} = C\left( {8,3} \right)\)

\(? = \frac{{C\left( {8,3} \right)}}{{C\left( {24,3} \right)}} = \cdots = \frac{7}{{253}}\)
\({\left( ? \right)^{ - 1}} = \frac{{210 + 42 + 1}}{7} = \boxed{36\frac{1}{7}}\)

\({\left( A \right)^{ - 1}} = {\left( {\frac{2}{{100}}} \right)^{ - 1}} = 50\)
\({\left( B \right)^{ - 1}} = {\left( {\frac{3}{{100}}} \right)^{ - 1}} = \frac{{99 + 1}}{3} = \boxed{33\frac{1}{3}}\)

From the fact that 33 1/3 is less than 36 1/7 , we are sure the other alternative choices (all of them are in increasing order) are not closer to our FOCUS.
(In other words, the reciprocals of (C), (D) and (E) are certainly less than 33 1/3 , hence the closest to 36 1/7 is 33 1/3.)

The above follows the notations and rationale taught in the GMATH method.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3440
Location: Canada
A jar contains 16 red balls and 8 white balls. If 3 balls are selected  [#permalink]

Show Tags

New post Updated on: 30 Aug 2018, 09:35
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

A jar contains 16 red balls and 8 white balls. If 3 balls are selected at random from the jar, what is the approximate probability that all balls selected are white?

A. 0.02
B. 0.03
C. 0.04
D. 0.05
E. 0.06


There are 24 balls in the jar (before any are removed)

P(all 3 balls are white) = P(1st ball is white AND 2nd ball is white AND 3rd ball is white)
= P(1st ball is white) x P(2nd ball is white) x P(3rd ball is white)
= 8/24 x 7/23 x 6/22
= 1/3 x 7/23 x 3/11
= 7/253

ASIDE: rather than perform long division, we can take 7/253 and create an equivalent fraction by multiplying top and bottom by 4 to get...
7/253 = (7)(4)/(253)(4)
≈ 28/1000
≈ 0.028
≈ 0.03

Aside: I'm not suggesting that it would be wrong to use long division to convert 7/253 to a decimal. That's a perfectly valid approach. However, if you're looking for an alternative approach, then we can also apply the above approach.

Answer: B

RELATED VIDEO FROM OUR COURSE

_________________

Test confidently with gmatprepnow.com
Image


Originally posted by GMATPrepNow on 30 Aug 2018, 06:47.
Last edited by GMATPrepNow on 30 Aug 2018, 09:35, edited 1 time in total.
GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 759
Re: A jar contains 16 red balls and 8 white balls. If 3 balls are selected  [#permalink]

Show Tags

New post 30 Aug 2018, 07:31
GMATPrepNow wrote:
ASIDE: rather than perform long division, we can take 7/253 and create an equivalent fraction by multiplying top and bottom by 4 to get...
7/253 = (7)(4)/(253)(4)
≈ 28/1000
≈ 0.028
≈ 0.03


Long division is something that must be avoided. That´s why GMATH´s approach deals with what we call "breaking numbers".

It is not comfortable to do (say) 253/7 by long division - and we did not - this can be done WITHOUT APPROXIMATIONS easily, as we did and the way we repeat below:

253 = 210 + 42 + 1 , this choice is "smart" because 210 and 42 are not only divisible by 7 (obviously), but also because their quotients are trivial (30 and 6)...

Therefore 253/7 = 210/7 + 42/7 + 1/7 = 36 + 1/7 , without FULL PRECISION!

One last detail:

When we approximate (say) 7/253 by 7/250 , we must be cautious because approximations in denominators may have "small errors" that propagate according to the "magnitude" (absolute value) of the numerator... that´s why we believe the approach we have taken is safer, although in this case the approximation 7/253 by 7/250 was sufficiently good for the alternative choices purposes.


The above follows the notations and rationale taught in the GMATH method.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6967
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: A jar contains 16 red balls and 8 white balls. If 3 balls are selected  [#permalink]

Show Tags

New post 02 Sep 2018, 17:50
=>

There are 24C3 ways of choosing \(3\) balls from the \(24\) in the jar, and 8C3 ways of choosing \(3\) balls from the \(8\) white balls. Therefore, the probability of choosing \(3\) white balls from the jar is:
8C3 / 24C3 = \({ (\frac{8*7*6)}{(1*2*3)} } / {\frac{(24*23*22)}{(1*2*3)} } = \frac{(8*7*6)}{(24*23*22)} = \frac{7}{( 23* 11 )} ≒ \frac{1}{(3*11)} ≒ 0.03\)

Therefore, the answer is B.
Answer: B
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7334
Premium Member Reviews Badge
A jar contains 16 red balls and 8 white balls. If 3 balls are selected  [#permalink]

Show Tags

New post 02 Sep 2018, 19:08
MathRevolution wrote:
[Math Revolution GMAT math practice question]

A jar contains 16 red balls and 8 white balls. If 3 balls are selected at random from the jar, what is the approximate probability that all balls selected are white?

A. 0.02
B. 0.03
C. 0.04
D. 0.05
E. 0.06



Now picking up three balls in 24 balls is a very basic question in GMAT and is equal to \(\frac{8C3}{24C3}\)..
This as shown above equals \(\frac{8*7*6}{24*23*22}\)=\(\frac{7}{253}\)..
Of course the biggest question is how do you simplify 7/253..
All methods shown above are correct..

1) 7/253 can be easily written as 7*4/250*4=28/1000=0.028 As also shown by GMATPrepNow
A decrease of 3 in 253 is perfectly fine . Of course don't decrease by 3 if the denominator is small, say make 13 as 10 in denominator as it will have a huge effect.

2) you can get the denominator to slightly friendly terms when compared to numerator 7.
253 lies between 210 and 280, so answer should be between 7/210 and 7/280.
7/210=1/30=0.033 and 7/280=1/40=0.025
So all values between 210 and 280 will be approximated to 0.03
Thus our answer is 0.03

You have to look at the way that suits you and can vary from person to person
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827
Re: A jar contains 16 red balls and 8 white balls. If 3 balls are selected  [#permalink]

Show Tags

New post 04 Sep 2018, 03:49
MathRevolution wrote:
[Math Revolution GMAT math practice question]

A jar contains 16 red balls and 8 white balls. If 3 balls are selected at random from the jar, what is the approximate probability that all balls selected are white?

A. 0.02
B. 0.03
C. 0.04
D. 0.05
E. 0.06


The probability of selecting 3 white balls is:

8/24 x 7/23 x 6/22 = 1/3 x 7/23 x 3/11 = 7/23 x 1/11 = 7/253 = 0.0277 ≈ 0.03

Alternate Solution:

The total number of ways that we can draw 3 balls from 24 balls is 24C3 = 24!/(3! x 21!) = 24 x 23 x 22 / 3 x 2 x 1 = 8 x 23 x 11 = 2024.

The number of ways we can pick 3 white balls out of 8 white balls is 8C3 = 8!/(3! x 5!) = 8 x 7 x 6 / 3 x 2 x 1 = 4 x 7 x 2 = 56. The total number of ways we can pick 0 red balls out of 16 red balls is 1.

Thus, the number of ways to pick 3 white balls out of 3 picks, when there are 8 white balls and 16 red balls is by getting 3 white balls and no red balls, out of a total of 24 balls to choose from: (8C3 x 16C0) / 24C3 = 56 x 1 / 2024 = 0.0277 ≈ 0.03

Answer: B
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

GMAT Club Bot
Re: A jar contains 16 red balls and 8 white balls. If 3 balls are selected   [#permalink] 04 Sep 2018, 03:49
Display posts from previous: Sort by

A jar contains 16 red balls and 8 white balls. If 3 balls are selected

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


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®.