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# A contest will contain n questions each of which is to be

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Manager
Joined: 07 Feb 2010
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A contest will contain n questions each of which is to be [#permalink]

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02 Nov 2010, 06:31
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35% (medium)

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69% (01:25) correct 31% (01:35) wrong based on 179 sessions

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A contest will contain 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 then 1/1000 then a person who randomly guesses the answer to each q's will be a winner?

A. 5
B. 10
C. 50
D. 100
E. 1000
[Reveal] Spoiler: OA

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Math Expert
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Re: a contest will contain n questions [#permalink]

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02 Nov 2010, 06:48
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anilnandyala wrote:
a contest will contain 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 probablity is less then 1/1000 then a person who randomly guesses the answer to each q's will be a winner?

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

The probability that a person will randomly guess all $$n$$ questions correctly is $$\frac{1}{2^n}$$, so we want the value of $$n_{min}$$ for which $$\frac{1}{2^n}<\frac{1}{1000}$$ --> $$2^n>1000$$ --> as $$n$$ is an integer $$n_{min}=10$$ ($$2^{10}=1024>1000$$).

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Manager
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Location: Boston
Re: a contest will contain n questions [#permalink]

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02 Nov 2010, 06:50
The probability of answering all the questions correctly is $$\frac{{1}}{{2^n}}$$. We want this probability to be less than $$\frac{1}{1,000}$$, so we need the smallest value of n that gives us $$2^n > 1,000$$. $$2^{10} = 1,024$$, so the answer is 10. B.

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Re: A contest will contain n questions each of which is to be [#permalink]

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20 Sep 2014, 09:36
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Re: A contest will contain n questions each of which is to be [#permalink]

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23 Dec 2015, 00:14
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).

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Re: A contest will contain n questions each of which is to be [#permalink]

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20 Sep 2017, 21:16
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).

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Re: A contest will contain n questions each of which is to be   [#permalink] 20 Sep 2017, 21:16
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