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

 It is currently 21 Jan 2019, 16:21

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

January 21, 2019

January 21, 2019

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.
• ### The winners of the GMAT game show

January 22, 2019

January 22, 2019

10:00 PM PST

11:00 PM PST

In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.

# A chain is comprised of 10 identical links, each of which in

Author Message
TAGS:

### Hide Tags

Manager
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 136
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)
A chain is comprised of 10 identical links, each of which in  [#permalink]

### Show Tags

05 Jan 2013, 05:35
8
00:00

Difficulty:

45% (medium)

Question Stats:

64% (01:28) correct 36% (01:39) wrong based on 280 sessions

### HideShow timer Statistics

A chain is comprised of 10 identical links, each of which independently has a 1% chance of breaking under a certain load. If the failure of any individual link means the failure of the entire chain, what is the probability that the chain will fail under the load?

(A) $$(0.01)^{10}$$
(B) $$10(0.01)^{10}$$
(C) $$1-(0.10)(0.99)^{10}$$
(D) $$1-(0.99)^{10}$$
(E) $$1-(0.99)^{(10*9)}$$

_________________

Don't give up on yourself ever. Period.
Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html

VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1109
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: A chain is comprised of 10 identical links, each of which in  [#permalink]

### Show Tags

05 Jan 2013, 06:01
1
Optimus66 wrote:
A chain is comprised of 10 identical links, each of which independently has a 1% chance of breaking under a certain load. If the failure of any individual link means the failure of the entire chain, what is the probability that the chain will fail under the load?

(A) $$(0.01)^{10}$$
(B) $$10(0.01)^{10}$$
(C) $$1-(0.10)(0.99)^{10}$$
(D) $$1-(0.99)^{10}$$
(E) $$1-(0.99)^{(10*9)}$$

There are 10 links, each of which has the probability of 0.99 of not failing. If any of them breaks, the chain will not survive.
To find the probability that the chain will fail under the load implies to find the the probability that any link breaks. To do so, find the reverse probability: the probability that the chain will not break or none of the 10 links break.
Since there are 10 links, hence probability that none of the link breaks is $$0.99^{10}$$.
Hence P that the chain will break is $$1-0.99^{10}$$.
_________________
Senior Manager
Joined: 27 Jun 2012
Posts: 371
Concentration: Strategy, Finance
Schools: Haas EWMBA '17
Re: A chain is comprised of 10 identical links, each of which in  [#permalink]

### Show Tags

05 Jan 2013, 11:12
Background: The whole chain will fail if atleast one of the 10 links fails.

Probability [that a single link will NOT break] $$= 0.99$$

Probability [that none of the 10 links will break] $$= (0.99)^{10}$$

Thus probability [that atleast 1 of the link will break] $$= 1 - (0.99)^{10}$$

Hence (D).
_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

Math Expert
Joined: 02 Sep 2009
Posts: 52344
Re: A chain is comprised of 10 identical links, each of which in  [#permalink]

### Show Tags

07 Jan 2013, 00:47
daviesj wrote:
A chain is comprised of 10 identical links, each of which independently has a 1% chance of breaking under a certain load. If the failure of any individual link means the failure of the entire chain, what is the probability that the chain will fail under the load?

(A) $$(0.01)^{10}$$
(B) $$10(0.01)^{10}$$
(C) $$1-(0.10)(0.99)^{10}$$
(D) $$1-(0.99)^{10}$$
(E) $$1-(0.99)^{(10*9)}$$

Similar question to practice: a-string-of-10-light-bulbs-is-wired-in-such-a-way-that-if-131205.html
_________________
Intern
Joined: 11 Jul 2012
Posts: 10
Re: A chain is comprised of 10 identical links, each of which in  [#permalink]

### Show Tags

08 Jan 2013, 11:02
Marcab wrote:
Optimus66 wrote:
A chain is comprised of 10 identical links, each of which independently has a 1% chance of breaking under a certain load. If the failure of any individual link means the failure of the entire chain, what is the probability that the chain will fail under the load?

(A) $$(0.01)^{10}$$
(B) $$10(0.01)^{10}$$
(C) $$1-(0.10)(0.99)^{10}$$
(D) $$1-(0.99)^{10}$$
(E) $$1-(0.99)^{(10*9)}$$

There are 10 links, each of which has the probability of 0.99 of failing. If any of them breaks, the chain will not survive.
To find the probability that the chain will fail under the load implies to find the the probability that any link breaks. To do so, find the reverse probability: the probability that the chain will not break or none of the 10 links break.
Since there are 10 links, hence probability that none of the link breaks is $$0.99^{10}$$.
Hence P that the chain will break is $$1-0.99^{10}$$.

not failing you mean! am sure you got caught up!
_________________

all you need is a will.

VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1109
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: A chain is comprised of 10 identical links, each of which in  [#permalink]

### Show Tags

08 Jan 2013, 18:18
sorry....edited the typo!!
thanks
_________________
Senior Manager
Joined: 13 May 2013
Posts: 425
Re: A chain is comprised of 10 identical links, each of which in  [#permalink]

### Show Tags

16 May 2013, 13:56
My three weaknesses on the GMAT are combinatorics, word problems, and probability!!!

I am having difficulty figuring out how to solve this problem. The book says to take the probability of each link NOT failing, multiplying them by one another and subtracting the result from one. I understand superficially that this is a time/work saving measure, but why does it work and how would I know how to do that come test time?!

While we're on the topic, does anyone have a good guide on basic, intermediate and advanced probability/combinatoric skills? I have been using the Manhattan guides and in general they are quite good, but they don't have a lot of problems on probability nor do they have many lessons lessons on them.

Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 52344
Re: A chain is comprised of 10 identical links, each of which in  [#permalink]

### Show Tags

16 May 2013, 22:38
WholeLottaLove wrote:
My three weaknesses on the GMAT are combinatorics, word problems, and probability!!!

I am having difficulty figuring out how to solve this problem. The book says to take the probability of each link NOT failing, multiplying them by one another and subtracting the result from one. I understand superficially that this is a time/work saving measure, but why does it work and how would I know how to do that come test time?!

While we're on the topic, does anyone have a good guide on basic, intermediate and advanced probability/combinatoric skills? I have been using the Manhattan guides and in general they are quite good, but they don't have a lot of problems on probability nor do they have many lessons lessons on them.

Thanks!

This topic might help with your doubts: a-string-of-10-light-bulbs-is-wired-in-such-a-way-that-if-131205.html

In addition check probability chapter of Math Book for theory: math-probability-87244.html

Also check some probability questions to practice:
DS: search.php?search_id=tag&tag_id=33
PS: search.php?search_id=tag&tag_id=54

Hard questions on combinations and probability with detailed solutions: hardest-area-questions-probability-and-combinations-101361.html (there are some about permutation too)

Hope it helps.
_________________
Manager
Joined: 10 Jun 2015
Posts: 118
Re: A chain is comprised of 10 identical links, each of which in  [#permalink]

### Show Tags

17 Aug 2015, 22:47
daviesj wrote:
A chain is comprised of 10 identical links, each of which independently has a 1% chance of breaking under a certain load. If the failure of any individual link means the failure of the entire chain, what is the probability that the chain will fail under the load?

(A) $$(0.01)^{10}$$
(B) $$10(0.01)^{10}$$
(C) $$1-(0.10)(0.99)^{10}$$
(D) $$1-(0.99)^{10}$$
(E) $$1-(0.99)^{(10*9)}$$

It is easier to find if you apply 1- P(the chain never breaks)=P( the chain will fail)
the probability that one link does not break is 1-.01=.99
the entire chain does not break if the first link does not break and the second link does not break and the third link does not break and so on till the tenth link
therefore, 0.99*0.99*0.99*... ten times
Hence, the correct option is D
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4351
Location: India
GPA: 3.5
Re: A chain is comprised of 10 identical links, each of which in  [#permalink]

### Show Tags

12 Nov 2016, 11:20
daviesj wrote:
A chain is comprised of 10 identical links, each of which independently has a 1% chance of breaking under a certain load.If the failure of any individual link means the failure of the entire chain, what is the probability that the chain will fail under the load?

(A) $$(0.01)^{10}$$
(B) $$10(0.01)^{10}$$
(C) $$1-(0.10)(0.99)^{10}$$
(D) $$1-(0.99)^{10}$$
(E) $$1-(0.99)^{(10*9)}$$

Probability of failure = Probability of non failure of atleast 1 link

Probability of failure of the chain = 1 - Probability of no failure

Probability of failure of the chain = $$1-(0.99)^{10}$$

Hence, answer will definitely be (D) $$1-(0.99)^{10}$$
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Director
Joined: 26 Oct 2016
Posts: 636
Location: United States
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: A chain is comprised of 10 identical links, each of which in  [#permalink]

### Show Tags

14 Mar 2017, 16:09
Qualitatively, many failure scenarios could occur:
• None of the links will fail,
• Exactly 1 of the links will fail,
• Exactly 2 of the links will fail,
• etc.
Given the complexity of the failure scenarios, it is easier for us to look at the opposite scenario:
probability that at least 1 link will fail = 1 – probability that all links will not fail

For each of the links, the probability that it will not fail is 1 – 0.01 = 0.99.
The probability that all ten will not fail is thus (0.99)^10, since the probability that all ten will not fail is simply the product of
the probabilities of the individual links not failing.
Therefore, the Probability that at least 1 link will fail = 1 – (0.99)^10.
_________________

Thanks & Regards,
Anaira Mitch

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4557
Location: United States (CA)
Re: A chain is comprised of 10 identical links, each of which in  [#permalink]

### Show Tags

20 Mar 2017, 05:50
1
daviesj wrote:
A chain is comprised of 10 identical links, each of which independently has a 1% chance of breaking under a certain load. If the failure of any individual link means the failure of the entire chain, what is the probability that the chain will fail under the load?

(A) $$(0.01)^{10}$$
(B) $$10(0.01)^{10}$$
(C) $$1-(0.10)(0.99)^{10}$$
(D) $$1-(0.99)^{10}$$
(E) $$1-(0.99)^{(10*9)}$$

We can use the following equation:

1 = P(at least 1 of 10 links failing) + P(nolinks failing)

Since we need to determine the probability that the chain will fail, we are looking for P(at least 1 of 10 links failing). However, we can solve for P(nolinks failing) and then subtract that probability from 1.

Since each link has a 1% chance of failing, each link has a 99% chance of NOT failing.

Thus, P(nolinks failing) = (0.99)^10, so:

P(at least 1 of 10 links failing) = 1 - (0.99)^10.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 533
Location: India
Re: A chain is comprised of 10 identical links, each of which in  [#permalink]

### Show Tags

21 Mar 2017, 03:20
daviesj wrote:
A chain is comprised of 10 identical links, each of which independently has a 1% chance of breaking under a certain load. If the failure of any individual link means the failure of the entire chain, what is the probability that the chain will fail under the load?

(A) $$(0.01)^{10}$$
(B) $$10(0.01)^{10}$$
(C) $$1-(0.10)(0.99)^{10}$$
(D) $$1-(0.99)^{10}$$
(E) $$1-(0.99)^{(10*9)}$$

P(link fails) = 1 - P(link not fail) = 1 - (1-0.01)(1-0.01)(1-0.01)(1-0.01)(1-0.01)(1-0.01)(1-0.01)(1-0.01)(1-0.01)(1-0.01) = 1 - 0.99^10
_________________

GMAT Mentors

Re: A chain is comprised of 10 identical links, each of which in &nbs [#permalink] 21 Mar 2017, 03:20
Display posts from previous: Sort by