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

It is currently 23 May 2019, 11:20

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 contest will consist of n questions, each of which is to

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
VP
VP
avatar
Joined: 21 Jul 2006
Posts: 1363
A contest will consist of n questions, each of which is to  [#permalink]

Show Tags

New post 21 Nov 2007, 16:13
1
16
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

73% (01:00) correct 27% (01:28) wrong based on 550 sessions

HideShow timer Statistics

A contest will consist of n questions, each of which is to be answered either "True" or "False." Anyone who answers all n questions correctly will be a winner. What is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be winner?

a) 5
b) 10
c) 50
d) 100
e) 1000

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-contest-will-consist-of-n-questions-each-of-which-is-to-38710.html
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 769
GMAT ToolKit User
  [#permalink]

Show Tags

New post 21 Nov 2007, 19:20
8
Each question has the probability of being correct equal to " 1/2 ".

So the question is basically asking us:

(1/2)^n <1> 1000

n = 10 gives us 1024, which is greater than 1000.

Thus answer should be n = 10. The choice "b".
Manager
Manager
avatar
Joined: 03 Sep 2006
Posts: 231
  [#permalink]

Show Tags

New post 21 Nov 2007, 19:39
1
15 sec. question.
The same approach as abhishakes2001
Senior Manager
Senior Manager
avatar
Joined: 02 Dec 2007
Posts: 382
Re: Probability  [#permalink]

Show Tags

New post 23 Sep 2008, 11:36
tarek99 wrote:
A contest will consist of n questions, each of which is to be answered either "True" or "False." Anyone who answers all n questions correctly will be a winner. What is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be winner?

a) 5
b) 10
c) 50
d) 100
e) 1000


B

2^(-n) > 10^-3 => 2^-3 *5^-3 => 2^-3*(4)^-3 => 2^-9

so n > -9
Manager
Manager
avatar
Joined: 18 Jun 2007
Posts: 247
Re: Probability  [#permalink]

Show Tags

New post 23 Sep 2008, 12:59
interesting tarek, this is GMAT Prep 2 question.
I got this question as 37th question me too got it wrong but then Probability has never been my strong point but still it is interesting cause got this '15 sec'. question on 37th number though I scored 760 in Prep2.
Director
Director
User avatar
Joined: 25 Oct 2008
Posts: 500
Location: Kolkata,India
Re: Probability  [#permalink]

Show Tags

New post 24 Jul 2009, 18:53
1
i was looking for a way out without calculating 2^10 :(
_________________
http://gmatclub.com/forum/countdown-beginshas-ended-85483-40.html#p649902
Manager
Manager
User avatar
Joined: 22 Jul 2009
Posts: 161
Re: Probability  [#permalink]

Show Tags

New post 29 Aug 2009, 16:03
2
tejal777 wrote:
i was looking for a way out without calculating 2^10 :(


Manually. Get 2. 2^2=4. Multiply that 8 times

Shortcut: remember that 2^5=32. Then multiply 5 times.
32x2=64=2^6
64x2=128=2^7
128x2=256=2^8
256x2=512=2^9
512x2=1024=2^10
_________________
Please kudos if my post helps.
Manager
Manager
User avatar
Joined: 14 Aug 2009
Posts: 115
Re: Probability  [#permalink]

Show Tags

New post 30 Aug 2009, 07:13
2
2^10 in computer science is K.
for instance, 1MB=1024KB=2^10KB

a very useful number which should be kept in mind.
_________________
Kudos me if my reply helps!
Manager
Manager
avatar
Joined: 27 Oct 2008
Posts: 167
Re: Probability  [#permalink]

Show Tags

New post 27 Sep 2009, 02:12
(1/2)^10 < 1/1000

Hence 10 questions is the minimum
Manager
Manager
User avatar
Joined: 02 Jan 2010
Posts: 103
Re: Probability  [#permalink]

Show Tags

New post 08 Sep 2010, 03:20
wow nice one!!!!abhishakes2001 nailed it :)
_________________
Regards
Ganesh
Class of 2012
Great Lakes Institute of Management
http://greatlakes.edu.in
Manager
Manager
avatar
Joined: 08 Sep 2010
Posts: 121
Re: Probability  [#permalink]

Show Tags

New post 17 Jun 2011, 19:54
agree with 10...maybe a 40 sec question
_________________
My will shall shape the future. Whether I fail or succeed shall be no man's doing but my own.

If you like my explanations award kudos.
Intern
Intern
avatar
Joined: 23 May 2011
Posts: 7
Re: Probability  [#permalink]

Show Tags

New post 17 Jun 2011, 21:29
1
P(T)=1/2
P(F)=1/2

P(n)= Favourable/ Total
= 1/ 2^n

For 1/2^n <1/1000

least value of n is 10.

Hope this helps.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55266
Re: A contest will consist of n questions, each of which is to  [#permalink]

Show Tags

New post 11 Sep 2013, 11:16
7
1
A contest will consist of n questions, each of which is to be answered either "True" or "False." Anyone who answers all n questions correctly will be a winner. What is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be winner?

A. 5
B. 10
C. 50
D. 100
E. 1000

The probability to randomly guess the answer for 1 question is 1/2, for 2 questions 1/2*1/2=1/2^2, similarly for n questions the probability is 1/2^n.

We need to find the least value of \(n\) for which \(\frac{1}{2^n}<\frac{1}{1,000}\) --> \(2^n>1,000\) --> \(n_{min}=10\).

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-contest-will-consist-of-n-questions-each-of-which-is-to-38710.html
_________________
MBA Section Director
User avatar
V
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 6207
City: Pune
GMAT ToolKit User
Re: A contest will consist of n questions, each of which is to  [#permalink]

Show Tags

New post 15 Sep 2013, 06:39
tarek99 wrote:
A contest will consist of n questions, each of which is to be answered either "True" or "False." Anyone who answers all n questions correctly will be a winner. What is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be winner?
a) 5
b) 10
c) 50
d) 100
e) 1000


Answer Choice B

In all there are n questions, and each question can be answered 2 ways (i.e. True or False). So we will get \(2^n\) different sequences of answers. Of which one sequence is TTTTTTTT......n times (i.e. All correct Answers)

We are told that The person who get all the answers correct that means who get the sequence mentioned above (TTTTT.... n times) will be a winner.

A person can choose any sequence from \(2^n\) sequences. He has to choose TTTT.... n times in order to win the game.

So Probability that a person will win the game is \(\frac{1}{2^n}\)

What is the least value of n for which the probability is less than 1/1000 -------> \(\frac{1}{2^n} < \frac{1}{1000}\) -----------------------> Here we can cross multiply the inequality since we know that \(2^n\) will always be positive (We know that n can neither be zero nor be Negative)

So We have that \(2^n > 1000\) --------> Using n=10 we get \(1024 > 1000\) Sufficient.
_________________
Starts from Feb 4th: MBA Video Series, Video answers to specific components and questions about the MBA application.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 11005
Re: A contest will consist of n questions, each of which is to  [#permalink]

Show Tags

New post 25 Aug 2018, 06:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: A contest will consist of n questions, each of which is to   [#permalink] 25 Aug 2018, 06:03
Display posts from previous: Sort by

A contest will consist of n questions, each of which is to

  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®.