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# n questions can either be true or false. If you answer all n correct

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Manager
Joined: 05 Jan 2011
Posts: 167
n questions can either be true or false. If you answer all n correct [#permalink]

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22 Mar 2011, 23:44
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Difficulty:

45% (medium)

Question Stats:

68% (00:58) correct 32% (01:24) wrong based on 173 sessions

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n questions can either be true or false. If you answer all n correct you win. What is the least value of n for which the probability is less than 1/1000 for you to win by guessing randomly?

A. 5
B. 10
C. 50
D. 100
E. 1000
[Reveal] Spoiler: OA
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1945
Re: n questions can either be true or false. If you answer all n correct [#permalink]

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23 Mar 2011, 00:11
5
KUDOS
Onell wrote:
n questions can either be true or false. If you answer all n correct you win. What is the least value of n for which the probability is less than 1/1000 for you to win by guessing randomly?
5
10
50
100
1000

1 question; probability of winning = 1/2
2 question; probability of winning = (1/2)^2
3 question; probability of winning = (1/2)^3
.
.
.
n question; probability of winning = (1/2)^n

$$(\frac{1}{2})^n<\frac{1}{1000}$$

Or find n for which;
$$2^n>1000$$
$$2^{10}=1024>1000$$

n=10

Ans: "B"
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Re: n questions can either be true or false. If you answer all n correct [#permalink]

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19 Oct 2014, 00:16
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Re: n questions can either be true or false. If you answer all n correct [#permalink]

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06 Jan 2016, 14:31
Hello from the GMAT Club BumpBot!

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Re: n questions can either be true or false. If you answer all n correct [#permalink]

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10 Mar 2017, 10:29
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: n questions can either be true or false. If you answer all n correct   [#permalink] 10 Mar 2017, 10:29
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