GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 16 Jul 2020, 06:07

### 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

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

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

Author Message
TAGS:

### Hide Tags

Director
Joined: 05 Feb 2006
Posts: 600
A contest will consist of n questions, each of which is to be answered  [#permalink]

### Show Tags

18 Nov 2006, 08:48
8
30
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:42) correct 34% (01:53) wrong based on 648 sessions

### HideShow timer Statistics

A contest will consist of n questions, each of which is to be answered wither "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 a winner?

A. 5
B. 10
C. 50
D. 100
E. 1000
Math Expert
Joined: 02 Sep 2009
Posts: 65384
Re: A contest will consist of n questions, each of which is to be answered  [#permalink]

### Show Tags

21 Feb 2012, 10:25
5
14
SimaQ wrote:
A contest will consist of n questions, each of which is to be answered wither "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 a 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 $$\frac{1}{2^n}<\frac{1}{1,000}$$ --> $$2^n>1,000$$ --> $$n_{min}=10$$.

_________________
##### General Discussion
Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 869
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Re: A contest will consist of n questions, each of which is to be answered  [#permalink]

### Show Tags

21 Feb 2012, 10:54
4
+1 B

The probability of answering right randomly is 1/2.

So, the probability of winning the contest is $$\frac{1}{2} * \frac{1}{2} *....\frac{1}{2} = \frac{1}{2^n}$$

$$2^9 = 512$$
2^(10) $$= 1024$$

So, n must be at least 10.

_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings
VP
Joined: 06 Sep 2013
Posts: 1491
Concentration: Finance
Re: A contest will consist of n questions, each of which is to be answered  [#permalink]

### Show Tags

10 Jan 2014, 09:54
1
SimaQ wrote:
A contest will consist of n questions, each of which is to be answered wither "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 a winner?

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

Min 'n' for 2^n >=1000

2^9 = 512

Then 2^10 >=1000 actually 1024

So B
Manager
Joined: 10 Mar 2013
Posts: 165
GMAT 1: 620 Q44 V31
GMAT 2: 690 Q47 V37
GMAT 3: 610 Q47 V28
GMAT 4: 700 Q50 V34
GMAT 5: 700 Q49 V36
GMAT 6: 690 Q48 V35
GMAT 7: 750 Q49 V42
GMAT 8: 730 Q50 V39
GPA: 3
Re: A contest will consist of n questions, each of which is to be answered  [#permalink]

### Show Tags

30 Oct 2014, 21:40
(1/2)^n < 1/1000
(1/2)^n < (1/2)^3*(1/5)^3
Because 1/5 ~ (1/2)^2
n > 3 + 3*2 = 9

B
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2799
Re: A contest will consist of n questions, each of which is to be answered  [#permalink]

### Show Tags

20 Jul 2017, 15:47
SimaQ wrote:
A contest will consist of n questions, each of which is to be answered wither "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 a winner?

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

Since the probability of correctly answering a question is ½, we need to determine the least value of n such that (1/2)^n < 1/1000. Since (1/2)^10 = 1/1024, the least value of n is 10.

_________________

# Jeffrey Miller | Head of GMAT Instruction | Jeff@TargetTestPrep.com

250 REVIEWS

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Manager
Joined: 22 Jun 2017
Posts: 239
Location: Argentina
Schools: HBS, Stanford, Wharton
GMAT 1: 630 Q43 V34
Re: A contest will consist of n questions, each of which is to be answered  [#permalink]

### Show Tags

30 May 2020, 16:43
A contest will consist of n questions, each of which is to be answered wither "True" or "False". This question is not correctly written Bunuel
_________________
The HARDER you work, the LUCKIER you get.
Re: A contest will consist of n questions, each of which is to be answered   [#permalink] 30 May 2020, 16:43