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

It is currently 18 Nov 2018, 12:48

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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

In a multiple choice test comprising 5 Questions, each with

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

Hide Tags

Senior Manager
Senior Manager
avatar
Joined: 15 Jun 2010
Posts: 307
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Reviews Badge
In a multiple choice test comprising 5 Questions, each with  [#permalink]

Show Tags

New post 07 Aug 2012, 05:58
3
5
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

63% (02:41) correct 37% (02:51) wrong based on 133 sessions

HideShow timer Statistics

In a multiple choice test comprising 5 Questions, each with 4 choices, what is the probability of a student getting 3 or more questions correct? Each question has only one correct answer and the student is equally likely to choose any of the four choices.

A) 24/256
B) 53/512
C) 105/512
D) 459/512
E) 47/256

_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50627
Re: In a multiple choice test comprising 5 Questions, each with  [#permalink]

Show Tags

New post 07 Aug 2012, 07:02
2
1
SOURH7WK wrote:
In a multiple choice test comprising 5 Questions, each with 4 choices, what is the probability of a student getting 3 or more questions correct? Each question has only one correct answer and the student is equally likely to choose any of the four choices.

A) 24/256
B) 53/512
C) 105/512
D) 459/512
E) 47/256


The probability of getting correct (C) answer is 1/4 and the the probability of getting wrong (W) answer is 3/4.

We need to find the probability of getting at 3, 4 or 5 correct answers:

The probability of getting 3 correct answers out of 5 is \(\frac{5!}{3!2!}*(\frac{1}{4})^3*(\frac{3}{4})^2\), we are multiplying by \(\frac{5!}{3!2!}\) since CCCWW scenario can occur in several ways: CCCWW, WWCCC, CWCWC, ... basically the number of permutations of 5 letters CCCWW, out of which 3 C's and 2 W's are identical (\(\frac{5!}{3!2!}\));

The probability of getting 4 correct answers out of 5 is \(\frac{5!}{4!}*(\frac{1}{4})^4*(\frac{3}{4})\);

The probability of getting 5 correct answers out of 5 is simply \((\frac{1}{4})^5\).

The overall probabity will be the sum of the above probabilities: \(\frac{5!}{3!2!}*(\frac{1}{4})^3*(\frac{3}{4})^2+\frac{5!}{4!}*(\frac{1}{4})^4*(\frac{3}{4})+(\frac{1}{4})^5=\frac{53}{512}\).

Answer: B.

P.S. Not a GMAT type of qustion.
_________________

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

Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 601
WE: Science (Education)
Re: In a multiple choice test comprising 5 Qs, each with 4 choic  [#permalink]

Show Tags

New post 07 Aug 2012, 07:06
SOURH7WK wrote:
In a multiple choice test comprising 5 Questions, each with 4 choices, what is the probability of a student getting 3 or more questions correct? Each question has only one correct answer and the student is equally likely to choose any of the four choices.

A) 24/256
B) 53/512
C) 105/512
D) 459/512
E) 47/256


We can compute either the probability of answering 3, 4, or 5 questions correctly, or subtract from 1 the probability of answering 0, 1, or 2 questions.
The probability of answering any question correctly is 1/4, and obviously, answering incorrectly is 3/4.

P(3 correct answers) =\(\frac{5*4}{2}(\frac{1}{4})^3(\frac{3}{4})^2=\frac{90}{4^5}\)
P(4 correct answers) =\(5(\frac{1}{4})^4(\frac{3}{4})=\frac{15}{4^5}\)
P(5 correct answers) =\((\frac{1}{4})^5=\frac{1}{4^5}\)
The sum of the above probabilities gives \(\frac{106}{4^5}=\frac{53}{512}\).

Answer B

Relevant topic for this question - Binomial probability distribution
Being a straightforward technical question, I question its importance for a real test.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Intern
avatar
Joined: 15 Apr 2012
Posts: 8
Re: In a multiple choice test comprising 5 Questions, each with  [#permalink]

Show Tags

New post 07 Aug 2012, 07:16
Here is my approach-
Probability for choosing correct answer is 1/4 and incorrect answer is 3/4
For 3 correct answers,
C(5,3)*(1/4)^3*(3/4)^2=90/(4^5)
For 4 correct answers,
C(5,4)*(1/4)^4*(3/4)^1=15/(4^5)
For 5 correct answers,
C(5,5)*(1/4)^5*(3/4)^0=1/(4^5)

So total probability
=106/1024

=53/512
Ans B
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2645
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: In a multiple choice test comprising 5 Questions, each with  [#permalink]

Show Tags

New post 18 Mar 2016, 18:59
SOURH7WK wrote:
In a multiple choice test comprising 5 Questions, each with 4 choices, what is the probability of a student getting 3 or more questions correct? Each question has only one correct answer and the student is equally likely to choose any of the four choices.

A) 24/256
B) 53/512
C) 105/512
D) 459/512
E) 47/256


we need to find the probability when:
3 questions are answered correctly, 2 incorrectly
4 correctly, 1 incorrectly
and 5 correctly.

1 case: (1/4)^3 * (3/4)^2 = 9/1024. since we have 5 questions, and we need to select 3 out of these, we can answer correctly 3 out of 5 in 5C3 ways. or total probability 90/1024
2 case: (1/4)^3 * (3/4) = 3/1024. we can answer 4 correctly in 5C4 ways. total probability 15/1024
3 case: (1/4)^5. we can answer all 5 correctly in 1 way. so 1/1024

total: 90+15+1/1024 = 106/1024 = 53/512

B
Intern
Intern
avatar
B
Joined: 08 Aug 2018
Posts: 33
WE: Engineering (Energy and Utilities)
CAT Tests
Re: In a multiple choice test comprising 5 Questions, each with  [#permalink]

Show Tags

New post 31 Oct 2018, 06:26
Bunuel wrote:
SOURH7WK wrote:
In a multiple choice test comprising 5 Questions, each with 4 choices, what is the probability of a student getting 3 or more questions correct? Each question has only one correct answer and the student is equally likely to choose any of the four choices.

A) 24/256
B) 53/512
C) 105/512
D) 459/512
E) 47/256


The probability of getting correct (C) answer is 1/4 and the the probability of getting wrong (W) answer is 3/4.

We need to find the probability of getting at 3, 4 or 5 correct answers:

The probability of getting 3 correct answers out of 5 is \(\frac{5!}{3!2!}*(\frac{1}{4})^3*(\frac{3}{4})^2\), we are multiplying by \(\frac{5!}{3!2!}\) since CCCWW scenario can occur in several ways: CCCWW, WWCCC, CWCWC, ... basically the number of permutations of 5 letters CCCWW, out of which 3 C's and 2 W's are identical (\(\frac{5!}{3!2!}\));

The probability of getting 4 correct answers out of 5 is \(\frac{5!}{4!}*(\frac{1}{4})^4*(\frac{3}{4})\);

The probability of getting 5 correct answers out of 5 is simply \((\frac{1}{4})^5\).

The overall probabity will be the sum of the above probabilities: \(\frac{5!}{3!2!}*(\frac{1}{4})^3*(\frac{3}{4})^2+\frac{5!}{4!}*(\frac{1}{4})^4*(\frac{3}{4})+(\frac{1}{4})^5=\frac{53}{512}\).

Answer: B.

P.S. Not a GMAT type of qustion.


Hi,

Can we not solve the question by calculating the probability of minimum 2 wrongs out of 5 questions?
P (at least of 3 correct) = 1 - P(minimum 2 wrongs)
GMAT Club Bot
Re: In a multiple choice test comprising 5 Questions, each with &nbs [#permalink] 31 Oct 2018, 06:26
Display posts from previous: Sort by

In a multiple choice test comprising 5 Questions, each with

  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®.