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

It is currently 16 Dec 2018, 14:05

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
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free GMAT Prep Hour

     December 16, 2018

     December 16, 2018

     03:00 PM EST

     04:00 PM EST

    Strategies and techniques for approaching featured GMAT topics
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

In an auditorium, there are ten light switches each of which control

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51229
In an auditorium, there are ten light switches each of which control  [#permalink]

Show Tags

New post 02 Apr 2017, 23:30
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

68% (00:55) correct 32% (00:57) wrong based on 181 sessions

HideShow timer Statistics

In an auditorium, there are ten light switches each of which control the lights of a different zone of the room. If there are only these 10 zones in the room and each light may only be set to "on" or "off", then how many different lighting arrangements are possible in the auditorium?

A. 10^10
B. 10!
C. 10^2
D 5!
E. 2^10

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 09 Oct 2016
Posts: 24
Location: India
Schools: DeGroote'21 (A)
Re: In an auditorium, there are ten light switches each of which control  [#permalink]

Show Tags

New post 03 Apr 2017, 04:23
10 sets of ligthing, either on/off - 2 options only ... Hence

10 * 2C1 = 2^10 (E)
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3239
Location: Canada
Re: In an auditorium, there are ten light switches each of which control  [#permalink]

Show Tags

New post 03 Apr 2017, 07:06
2
Top Contributor
Bunuel wrote:
In an auditorium, there are ten light switches each of which control the lights of a different zone of the room. If there are only these 10 zones in the room and each light may only be set to "on" or "off", then how many different lighting arrangements are possible in the auditorium?

A. 10^10
B. 10!
C. 10^2
D 5!
E. 2^10


Let the 10 light switches be Switch #1, Switch #2, Switch #3, etc.

Take the task of creating a lighting arrangement and break it into stages.

Stage 1: Set Switch #1
The switch can be ON or OFF. So, we can complete stage 1 in 2 ways

Stage 2: Set Switch #2
The switch can be ON or OFF. So, we can complete stage 2 in 2 ways

Stage 3: Set Switch #3
The switch can be ON or OFF. So, we can complete stage 3 in 2 ways

Stage 4: Set Switch #4
The switch can be ON or OFF. So, we can complete stage 4 in 2 ways
.
.
.

Stage 9: Set Switch #9
The switch can be ON or OFF. So, we can complete stage 9 in 2 ways

Stage 10: Set Switch #10
The switch can be ON or OFF. So, we can complete stage 10 in 2 ways

By the Fundamental Counting Principle (FCP), we can complete all 10 stages (and thus create a lighting arrangement) in (2)(2)(2)(2)(2)(2)(2)(2)(2)(2) ways (= \(2^{10}\) ways)

Answer:

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn the technique.

RELATED VIDEOS FROM OUR COURSE



_________________

Test confidently with gmatprepnow.com
Image

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4295
Location: United States (CA)
Re: In an auditorium, there are ten light switches each of which control  [#permalink]

Show Tags

New post 06 Apr 2017, 08:24
Bunuel wrote:
In an auditorium, there are ten light switches each of which control the lights of a different zone of the room. If there are only these 10 zones in the room and each light may only be set to "on" or "off", then how many different lighting arrangements are possible in the auditorium?

A. 10^10
B. 10!
C. 10^2
D 5!
E. 2^10


There are 10 light switches, and since each light switch has two possible options, the number of different possible lighting arrangements is 2^10.

Answer: E
_________________

Scott Woodbury-Stewart
Founder and CEO

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

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13098
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In an auditorium, there are ten light switches each of which control  [#permalink]

Show Tags

New post 08 Apr 2017, 17:30
1
Hi All,

The 'math' behind this question isn't too difficult - once you recognize the 'pattern' involved. If you don't immediately see that pattern though, then you can still get to the correct answer by 'playing around' with simpler examples - and looking for the pattern. For example...

If there was just one light switch, then there would be TWO options: Off and On

If there were two light switches, then there would be FOUR options (I'll refer to Off as "F" and On as "N"):
FF
FN
NF
NN

If there were three light switches, then there would be EIGHT options:
FFF
FFN
FNF
NFF

NNN
NNF
NFN
FNN

Notice the pattern: 2...4...8... It certainly appears that every time we add another light switch, then number of possibilities DOUBLES. Thinking in these terms, we're looking for an answer that is based around lots of 'doubling'... and there's only one answer that exclusively multiplies a bunch of 2s together....

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

CEO
CEO
User avatar
P
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2711
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: In an auditorium, there are ten light switches each of which control  [#permalink]

Show Tags

New post 08 Apr 2017, 20:00
Bunuel wrote:
In an auditorium, there are ten light switches each of which control the lights of a different zone of the room. If there are only these 10 zones in the room and each light may only be set to "on" or "off", then how many different lighting arrangements are possible in the auditorium?

A. 10^10
B. 10!
C. 10^2
D 5!
E. 2^10


For first switch total position= 2 (on or off)
For Second switch total position= 2 (on or off)
For Third switch total position= 2 (on or off)
For forth switch total position= 2 (on or off)... and so on...

Total arrangement = 2*2*2... 10 times = 2^10

Answer: Option E
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Intern
Intern
avatar
B
Joined: 22 Jun 2018
Posts: 29
Location: India
GMAT 1: 730 Q50 V39
GPA: 4
WE: Research (Telecommunications)
Re: In an auditorium, there are ten light switches each of which control  [#permalink]

Show Tags

New post 24 Aug 2018, 06:17
1
Hi, why do we not arrange the switches for each of the zones i.e. 10! way of arranging each of the switches for each of the zones and then try to either on/off the switch.
Intern
Intern
avatar
B
Joined: 25 Jul 2017
Posts: 3
Re: In an auditorium, there are ten light switches each of which control  [#permalink]

Show Tags

New post 19 Oct 2018, 12:02
I have the same doubt
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13098
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In an auditorium, there are ten light switches each of which control  [#permalink]

Show Tags

New post 19 Oct 2018, 17:16
1
Hi anse and Mridul94,

The 'math' behind this question isn't too difficult - once you recognize the 'pattern' involved. If you don't immediately see that pattern though, then you can still get to the correct answer by 'playing around' with simpler examples - and looking for the pattern. For example...

If there were three light switches, then would the total number of possibilities be 3! = 6? Try 'mapping' out the options and see. The possible arrangements would be:

FFF
FFN
FNF
NFF

NNN
NNF
NFN
FNN

That's 8 arrangements - not 6, so we are clearly NOT dealing with a factorial. If you do similar work with 1 switch (2 arraignments) and 2 switches (4 arrangements), it certainly appears that every time we add another light switch, then number of possibilities DOUBLES. Thinking in these terms, we're looking for an answer that is based around lots of 'doubling'... and there's only one answer that exclusively multiplies a bunch of 2s together....

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

GMAT Club Bot
Re: In an auditorium, there are ten light switches each of which control &nbs [#permalink] 19 Oct 2018, 17:16
Display posts from previous: Sort by

In an auditorium, there are ten light switches each of which control

  new topic 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®.