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

It is currently 18 Jun 2018, 18:04

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

A certain multiple-choice math quiz contains five questions, each with

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

Hide Tags

Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46129
A certain multiple-choice math quiz contains five questions, each with [#permalink]

Show Tags

New post 23 Apr 2015, 03:43
3
11
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

47% (01:35) correct 53% (01:52) wrong based on 122 sessions

HideShow timer Statistics

A certain multiple-choice math quiz contains five questions, each with four answer choices: A, B, C, and D. If the correct answer to each question is randomly distributed, which of the following represents the closest approximation of the probability that no two consecutive questions will have the same answer?

A. 25%
B. 32%
C. 40%
D. 48%
E. 75%


Kudos for a correct solution.

_________________

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

1 KUDOS received
Manager
Manager
avatar
Joined: 17 Mar 2015
Posts: 121
A certain multiple-choice math quiz contains five questions, each with [#permalink]

Show Tags

New post 23 Apr 2015, 13:33
1
Well lets see, something tells me it might be wrong but I'll give it a shot.
For pair 1-2
Total amount of choices for answers are 16: (AA, AB,AC,AD, BA,BB,BC,BD, CA,CB,CC,CD, DA,DB,DC,DD), total answers that give us bad result - 4( AA, BB, CC, DD), so odds of getting good outcome are 12/16 = 3/4
For pair 2-3, 3-4 and 4-5 its same 3/4.
All these events (questions have different answers) are dependant so the odds that 1-2 are different AND 2-3 are different ... AND 4-5 are different is pretty much (3/4)^4 = 0,316 ~ 32%

Answer ends up being "B"
4 KUDOS received
Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 565
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
A certain multiple-choice math quiz contains five questions, each with [#permalink]

Show Tags

New post 23 Apr 2015, 20:20
4
1
Probability of no two consecutive question have same answer=4× 1/4 × 3/4 × 3/4 × 3/4 × 3/4 = 0.3164

Explanation : 1/4 = probability of selecting 'A'
3/4 = probability of not selecting 'A'. (b,d,c)

Answer 32% (approx )
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the Image to appreciate my post !! :-)

1 KUDOS received
Manager
Manager
avatar
Joined: 18 Dec 2014
Posts: 100
Re: A certain multiple-choice math quiz contains five questions, each with [#permalink]

Show Tags

New post 24 Apr 2015, 02:24
1
A certain multiple-choice math quiz contains five questions, each with four answer choices: A, B, C, and D. If the correct answer to each question is randomly distributed, which of the following represents the closest approximation of the probability that no two consecutive questions will have the same answer?

A. 25%
B. 32%
C. 40%
D. 48%
E. 75%


After every answer there is a chance of 3/4th that it will not be the same answer. Repeat this 4 times.

3/4 * 3/4 * 3/4 * 3/4 = 81/256 = approx 32%.

B.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46129
Re: A certain multiple-choice math quiz contains five questions, each with [#permalink]

Show Tags

New post 27 Apr 2015, 02:33
Bunuel wrote:
A certain multiple-choice math quiz contains five questions, each with four answer choices: A, B, C, and D. If the correct answer to each question is randomly distributed, which of the following represents the closest approximation of the probability that no two consecutive questions will have the same answer?

A. 25%
B. 32%
C. 40%
D. 48%
E. 75%


Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

This question feels like a doozy. Probability questions tend to give fits to even top-performing test-takers. You simply have to remember, however, what probability is:

number of desired outcomes divided by number of possible outcomes

Let's start out by finding the number of total outcomes. There are five questions on the quiz, so let's draw out five slots:

How many possible outcomes are there for the first slot? Well, given that there are four answer choices, A, B, C, and D, there are four possible outcomes.

4_ __ ____ ____ ____

The same will be true for all of the other questions, as each question has exactly four possible results: A, B, C, and D.

4_ _4 4_ 4_ _4

Since there are four possibilities for each of five slots, there are a total of 4 * 4 * 4 * 4 * 4 possibilities, or 4^5 possible outcomes. This number will go in the denominator of our probability fraction.

Now, let's focus on the number of desired outcomes. As it was before, the number of possibilities in the first slot will be four, as the correct answer to the first question could be A, B, C, or D.

4_ ____ ____ ____ ____

Here is where things get a bit tricky. The answer to the second question can be anything except the answer to the first. For example, if the answer to Question 1 is A, then Question 2 can only be B, C, or D.

If the answer to Question 1 is B, then Question 2 can only be A, C, or D. In any case, there are exactly three possibilities for the second slot.

4_ 3_ ____ ____ ____

Based on the answer to Question 2, there are three possibilities for Question 3 (because Question 3 cannot have the same answer as Question 2). Thus, there will also be three possibilities for the fourth and fifth slots, as their only restrictions are not having the same answer as the question immediately preceding it.

4_ 3_ 3_ 3_ 3_

Multiply these together, and you get 4 * 3 * 3 * 3 * 3, or 4 * 3^4 as the number of desired outcomes. So here is the probability fraction, and its subsequent reduction:

desired outcomes = 4 * 3^4

possible outcomes = 4^5

And since you're dividing them, you can factor out the common 4 to get a fraction of (3^4)/(4^4), which is 81/256.

Resist the temptation to do this math and figure out the exact percentage! You know that 80 / 240 = 33.333%, so 81/256 will be slightly less. The only answer that works is 32%, or answer choice B.
_________________

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

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 6995
Premium Member
Re: A certain multiple-choice math quiz contains five questions, each with [#permalink]

Show Tags

New post 13 Jun 2018, 10:57
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: A certain multiple-choice math quiz contains five questions, each with   [#permalink] 13 Jun 2018, 10:57
Display posts from previous: Sort by

A certain multiple-choice math quiz contains five questions, each with

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


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®.