It is currently 13 Dec 2017, 11:03

Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1


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

Events & Promotions in June
Open Detailed Calendar

In how many ways can a teacher write an answer key for a min

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

Hide Tags

1 KUDOS received
Intern
Intern
User avatar
Joined: 15 Mar 2007
Posts: 16

Kudos [?]: 20 [1], given: 0

In how many ways can a teacher write an answer key for a min [#permalink]

Show Tags

New post 28 Oct 2007, 16:32
1
This post received
KUDOS
21
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

81% (01:28) correct 19% (01:39) wrong based on 412 sessions

HideShow timer Statistics

In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?

A. 88
B. 90
C. 96
D. 98
E. 102

[Reveal] Spoiler:
first total possibilities no exclusions: 3t/f: 2mc
2*2*2 * 4*4 "mc" no restrictions

now compute number of exclusions:
2*1*1 *4*4 (how is this so?) wierd! How so??????

SO, 128-32= ok
[Reveal] Spoiler: OA

Kudos [?]: 20 [1], given: 0

Manager
Manager
avatar
Joined: 18 Jun 2007
Posts: 55

Kudos [?]: 7 [0], given: 0

 [#permalink]

Show Tags

New post 28 Oct 2007, 16:50
For TF:
3^2=9
Since 3 answers can't be the same, i subtracted 3 from the answer (post-facto, which for me means that i probably wont get this tomorrow on test day)
For MC:2^4=16
16*9=96 possibilities

Kudos [?]: 7 [0], given: 0

Manager
Manager
avatar
Joined: 15 Feb 2011
Posts: 240

Kudos [?]: 201 [0], given: 9

Probability - Answer Key!! [#permalink]

Show Tags

New post 10 Aug 2011, 06:26
In how many ways can a teacher write an answer key for a mini quiz that contains 3 true false questions followed by 2 multiple choice questions with 4 answer choice each, if the correct answer to all true false questions cannot be the same?

I could come up to 2*2*2*4*4 but what next?? how can we include the constraint mentioned in the last line of the ques..pls help..

Kudos [?]: 201 [0], given: 9

Director
Director
User avatar
Status: -=Given to Fly=-
Joined: 04 Jan 2011
Posts: 827

Kudos [?]: 250 [0], given: 78

Location: India
Concentration: Leadership, Strategy
Schools: Haas '18, Kelley '18
GMAT 1: 650 Q44 V37
GMAT 2: 710 Q48 V40
GMAT 3: 750 Q51 V40
GPA: 3.5
WE: Education (Education)
Re: Probability - Answer Key!! [#permalink]

Show Tags

New post 10 Aug 2011, 08:01
Technically, the question is flawed. There is only one way in which the teacher can write an answer key provided each question has only one correct answer!

However, there are multiple ways in which a student can answer the questions.
_________________

"Wherever you go, go with all your heart" - Confucius

Useful Threads

1. How to Review and Analyze your Mistakes (Post by BB at GMAT Club)

2. 4 Steps to Get the Most out out of your CATs (Manhattan GMAT Blog)

My Experience With GMAT

1. From 650 to 710 to 750 - My Tryst With GMAT

2. Quest to do my Best - My GMAT Journey Log

Kudos [?]: 250 [0], given: 78

2 KUDOS received
Director
Director
User avatar
Status: -=Given to Fly=-
Joined: 04 Jan 2011
Posts: 827

Kudos [?]: 250 [2], given: 78

Location: India
Concentration: Leadership, Strategy
Schools: Haas '18, Kelley '18
GMAT 1: 650 Q44 V37
GMAT 2: 710 Q48 V40
GMAT 3: 750 Q51 V40
GPA: 3.5
WE: Education (Education)
Re: Probability - Answer Key!! [#permalink]

Show Tags

New post 10 Aug 2011, 08:08
2
This post received
KUDOS
It's given that the correct answer for each true or false question cannot be the same. The possibility or all TRUE and all FALSE must be eliminated from the total number of possibilities.

Total number of ways in which:
a student can answer the 1st true or false question = 2

a student can answer the 2nd true or false question = 2

a student can answer the 3rd true or false question = 2

Total number of ways in which a student can answer the true or false questions = 2 x 2 x 2 = 8

Now this includes the two cases in which all answers are the same (all true and all false)

Therefore, the total number of ways in which the true and false questions such that the response for all the questions is not the same = 8 - 2 = 6

Number of ways in which the two MCQs can be answered = 4 x 4 = 16

Total number of ways in which the entire test can be answered = 16 x 6 = 96 ways...


Now... I have assumed that the student must compulsorily attempt each question :)

If the student has the option to skip questions, the approach is different.
_________________

"Wherever you go, go with all your heart" - Confucius

Useful Threads

1. How to Review and Analyze your Mistakes (Post by BB at GMAT Club)

2. 4 Steps to Get the Most out out of your CATs (Manhattan GMAT Blog)

My Experience With GMAT

1. From 650 to 710 to 750 - My Tryst With GMAT

2. Quest to do my Best - My GMAT Journey Log

Kudos [?]: 250 [2], given: 78

21 KUDOS received
Senior Manager
Senior Manager
avatar
B
Joined: 24 Aug 2009
Posts: 493

Kudos [?]: 878 [21], given: 276

Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: In how many ways can a teacher write an answer key for a min [#permalink]

Show Tags

New post 23 Aug 2013, 23:22
21
This post received
KUDOS
11
This post was
BOOKMARKED
aishu4 wrote:
In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions
followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false
questions cannot be the same?
A. 88
B. 90
C. 96
D. 98
E. 102


2 multiples-choice questions can be answered in = 4 x 4 = 16 ways
3 true-false questions can be answered in = 2x2x2 = 8 ways
But out of the 8 ways, 2 ways [(True-True-True) (False-False-False)]will contain same answers

Thus 3 true-false questions can be answered in = 2x2x2 = 6 ways
Total ways to answer the quiz = 16 x 6 = 96
Answer C
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Kudos [?]: 878 [21], given: 276

Manager
Manager
User avatar
Joined: 18 Jul 2013
Posts: 69

Kudos [?]: 101 [0], given: 114

Location: Italy
GMAT 1: 600 Q42 V31
GMAT 2: 700 Q48 V38
Re: In how many ways can a teacher write an answer key for a min [#permalink]

Show Tags

New post 26 Aug 2013, 09:03
fameatop wrote:
aishu4 wrote:
In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions
followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false
questions cannot be the same?
A. 88
B. 90
C. 96
D. 98
E. 102


2 multiples-choice questions can be answered in = 4 x 4 = 16 ways
3 true-false questions can be answered in = 2x2x2 = 8 ways
But out of the 8 ways, 2 ways [(True-True-True) (False-False-False)]will contain same answers

Thus 3 true-false questions can be answered in = 2x2x2 = 6 ways
Total ways to answer the quiz = 16 x 6 = 96
Answer C


hi, you forgot to substract 2.
2x2x2 - 2 = 6 ways
but kudos for your explanation.

Kudos [?]: 101 [0], given: 114

Intern
Intern
User avatar
Joined: 07 Jan 2013
Posts: 26

Kudos [?]: 7 [0], given: 491

Location: Poland
GPA: 3.8
Re: In how many ways can a teacher write an answer key for a min [#permalink]

Show Tags

New post 14 Oct 2013, 21:31
fameatop wrote:
aishu4 wrote:
In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions
followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false
questions cannot be the same?
A. 88
B. 90
C. 96
D. 98
E. 102


2 multiples-choice questions can be answered in = 4 x 4 = 16 ways
3 true-false questions can be answered in = 2x2x2 = 8 ways
But out of the 8 ways, 2 ways [(True-True-True) (False-False-False)]will contain same answers

Thus 3 true-false questions can be answered in = 2x2x2 = 6 ways
Total ways to answer the quiz = 16 x 6 = 96
Answer C

But out of the 8 ways, 2 ways [(True-True-True) (False-False-False)]will contain same answers
I don't get it! What does it mean exactly? pls help.

Kudos [?]: 7 [0], given: 491

Current Student
User avatar
Joined: 06 Sep 2013
Posts: 1965

Kudos [?]: 759 [0], given: 355

Concentration: Finance
GMAT ToolKit User
Re: In how many ways can a teacher write an answer key for a min [#permalink]

Show Tags

New post 18 Nov 2013, 11:35
mww7786 wrote:
In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?

A. 88
B. 90
C. 96
D. 98
E. 102

[Reveal] Spoiler:
first total possibilities no exclusions: 3t/f: 2mc
2*2*2 * 4*4 "mc" no restrictions

now compute number of exclusions:
2*1*1 *4*4 (how is this so?) wierd! How so??????

SO, 128-32= ok


Ya, I don't get it either. Why do we need to subtract two on the True-True-True and False-False-False? Any clue?

Cheers
J :)

Kudos [?]: 759 [0], given: 355

Intern
Intern
User avatar
Joined: 17 Feb 2012
Posts: 2

Kudos [?]: 5 [0], given: 11

Location: Peru
Concentration: Finance, Entrepreneurship
GMAT 1: 680 Q47 V38
GPA: 3
WE: General Management (Telecommunications)
Re: In how many ways can a teacher write an answer key for a min [#permalink]

Show Tags

New post 20 Nov 2013, 17:37
jlgdr wrote:
mww7786 wrote:
In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?

A. 88
B. 90
C. 96
D. 98
E. 102

[Reveal] Spoiler:
first total possibilities no exclusions: 3t/f: 2mc
2*2*2 * 4*4 "mc" no restrictions

now compute number of exclusions:
2*1*1 *4*4 (how is this so?) wierd! How so??????

SO, 128-32= ok


Ya, I don't get it either. Why do we need to subtract two on the True-True-True and False-False-False? Any clue?

Cheers
J :)


Because the question says:

In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?

so you need to eliminate the t-t-t and f-f-f scenarios.

Kudos [?]: 5 [0], given: 11

Current Student
User avatar
Joined: 06 Sep 2013
Posts: 1965

Kudos [?]: 759 [0], given: 355

Concentration: Finance
GMAT ToolKit User
Re: In how many ways can a teacher write an answer key for a min [#permalink]

Show Tags

New post 20 Nov 2013, 17:49
cachaval wrote:
jlgdr wrote:
mww7786 wrote:
In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?

A. 88
B. 90
C. 96
D. 98
E. 102

[Reveal] Spoiler:
first total possibilities no exclusions: 3t/f: 2mc
2*2*2 * 4*4 "mc" no restrictions

now compute number of exclusions:
2*1*1 *4*4 (how is this so?) wierd! How so??????

SO, 128-32= ok


Ya, I don't get it either. Why do we need to subtract two on the True-True-True and False-False-False? Any clue?

Cheers
J :)


Because the question says:

In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?

so you need to eliminate the t-t-t and f-f-f scenarios.


Good catch Buddy
Many thanks
Cheers!
J :)

Kudos [?]: 759 [0], given: 355

Current Student
User avatar
Joined: 06 Sep 2013
Posts: 1965

Kudos [?]: 759 [0], given: 355

Concentration: Finance
GMAT ToolKit User
Re: In how many ways can a teacher write an answer key for a min [#permalink]

Show Tags

New post 29 Dec 2013, 16:04
Actual way of solving this one is

2*2*2*4*4 all possible scenarios

2*1*1*4*4 unwanted scenarios

So it bouls down to 128 - 32 = 96

Answer is C as correctly stated above

Hope it helps!
Cheers!
J :)

Kudos [?]: 759 [0], given: 355

Current Student
User avatar
Joined: 03 Feb 2013
Posts: 943

Kudos [?]: 1089 [0], given: 548

Location: India
Concentration: Operations, Strategy
GMAT 1: 760 Q49 V44
GPA: 3.88
WE: Engineering (Computer Software)
Reviews Badge
Re: In how many ways can a teacher write an answer key for a min [#permalink]

Show Tags

New post 20 Dec 2014, 09:20
Suppose I am not able to understand the condition : "if the correct answers to all true-false questions cannot be the same?"

Then 4*4 = 16 -> As there is no more condition on this part, the answer option should be an multiple of 16.
Only 96 = 16*6 is there.
So C)
_________________

Thanks,
Kinjal
My Debrief : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267.html#p1449379
My Application Experience : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267-40.html#p1516961
Linkedin : https://www.linkedin.com/in/kinjal-das/

Please click on Kudos, if you think the post is helpful

Kudos [?]: 1089 [0], given: 548

Senior Manager
Senior Manager
User avatar
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 437

Kudos [?]: 143 [0], given: 169

Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: In how many ways can a teacher write an answer key for a min [#permalink]

Show Tags

New post 26 Dec 2014, 02:16
Hello, I ended up in the same answer, but I think that I read the question in a totally different way... Your opinion on this would be very useful!

I used this way (trying to arrange the questions in an answer sheet):
We have 3 TF questions and 2 MC questions, which have 4 answer choices each.

The TF questions could be arranged in 3 different ways. Each one of them 1st, 2nd or 3rd
Each MC question could be arranged in 4*4= 16 ways. So, the 2 MC questions in 16*2= 32 ways.

So, 3*32= 96

Ws

Was this just a lucky mistake?

Thank you.

Kudos [?]: 143 [0], given: 169

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42583

Kudos [?]: 135519 [0], given: 12697

Re: In how many ways can a teacher write an answer key for a min [#permalink]

Show Tags

New post 26 Dec 2014, 08:13
Expert's post
2
This post was
BOOKMARKED
pacifist85 wrote:
In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?

A. 88
B. 90
C. 96
D. 98
E. 102


Hello, I ended up in the same answer, but I think that I read the question in a totally different way... Your opinion on this would be very useful!

I used this way (trying to arrange the questions in an answer sheet):
We have 3 TF questions and 2 MC questions, which have 4 answer choices each.

The TF questions could be arranged in 3 different ways. Each one of them 1st, 2nd or 3rd
Each MC question could be arranged in 4*4= 16 ways. So, the 2 MC questions in 16*2= 32 ways.

So, 3*32= 96

Ws

Was this just a lucky mistake?

Thank you.


This is wrong. We have 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each:

Q1: ?
Answer: True or False

Q2: ?
Answer: True or False

Q3: ?
Answer: True or False


M1: ?
Answer: A, B, C, or D

M2: ?
Answer: A, B, C, or D


So, the answer key could be: TTF - AB, FTT - AA, ...

For 3 true-false questions there are 2*2*2 = 8 combinations possible but since we are told that the correct answers to all true-false questions cannot be the same, then we should subtract the cases TTT and FFF, so for 3 true-false questions we get 8 - 2 = 6 combinations.

For 2 multiples-choice questions with 4 answer choices each there are 4*4 = 16 combinations possible.

Thus there are total of 6*16 ways a teacher can write an answer key for the quiz.

Answer: C.

Hope it's clear.
_________________

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

Kudos [?]: 135519 [0], given: 12697

Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10378

Kudos [?]: 3685 [1], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: In how many ways can a teacher write an answer key for a min [#permalink]

Show Tags

New post 26 Dec 2014, 09:39
1
This post received
KUDOS
Expert's post
Hi pacifist85,

You did get lucky on this question, but here's how you can handle similar questions in the future.

When you're dealing with a "layered" permutation question, it's important to define what you're trying to calculate before you actually calculate it. Here, we're looking for the number of WAYS to write out the ANSWER KEY for a test that includes 3 True/False questions and 2 Four-answer Multiple Choice questions. We have an added restriction though - the 3 T/F questions CANNOT ALL have the SAME answer (so this will effect the calculation a bit since we have to eliminate some of the possibilities).

Since T/F questions have 2 possible answers, there would normally be (2)(2)(2) = 8 different sets of answers for 3 questions. You can see them in the following list:

TTT
TTF
TFT
FTT

FFF
FFT
FTF
TFF

According to the prompt, 2 of the options are NOT allowed though (TTT and FFF), so we have to remove them from consideration. That means we now have only 6 possible sets of answers for those 3 questions.

The 4-answer Multiple Choice questions are easy to deal with since there are no restrictions; there are (4)(4) = 16 possibilities there. You can also "map" them out if necessary:

AA, AB, AC, AD
BA, BB, BC, BD
CA, CB, CC, CD
DA, DB, DC, DD

The last step is to multiply the possibilities: (6)(16) = 96

Final Asnwer:
[Reveal] Spoiler:
C


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!***********************

Kudos [?]: 3685 [1], given: 173

Moderator
avatar
D
Joined: 21 Jun 2014
Posts: 956

Kudos [?]: 489 [0], given: 113

Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
Premium Member CAT Tests
Re: In how many ways can a teacher write an answer key for a min [#permalink]

Show Tags

New post 24 Sep 2016, 10:01
2 choice for first 3 questions each and 4 choices for the next 2 questions. this gives us 128 total choices. here is how:
1 2 3 4 5 --->question numbers
2 2 2 4 4 = 128 --> total choices (multiplied the choices)
T F F a b ---- example key

T T T a b --- example key where first 3 questions have TTT. but there can be 16 keys in which first 3 letters would be TTT.
1 1 1 4 4 = 16

similarly for FFF:
F F F a b
1 1 1 4 4 = 16

Ways to write the key excluding the given condition = 128-16-16 = 96
_________________

---------------------------------------------------------------
Target - 720-740
http://gmatclub.com/forum/information-on-new-gmat-esr-report-beta-221111.html
http://gmatclub.com/forum/list-of-one-year-full-time-mba-programs-222103.html

Kudos [?]: 489 [0], given: 113

Intern
Intern
avatar
B
Joined: 15 May 2012
Posts: 11

Kudos [?]: 3 [0], given: 9

Re: In how many ways can a teacher write an answer key for a min [#permalink]

Show Tags

New post 24 Nov 2017, 15:14
I didn't quite got the 2 part of the question.

But I knew whatever happens in T/F part for multiple choice part it will be 4*4

So the answer will be a multiple of 16, and only 96 agrees.

Kudos [?]: 3 [0], given: 9

Re: In how many ways can a teacher write an answer key for a min   [#permalink] 24 Nov 2017, 15:14
Display posts from previous: Sort by

In how many ways can a teacher write an answer key for a min

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.