Last visit was: 19 Jul 2025, 14:58 It is currently 19 Jul 2025, 14:58
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 July 2025
Posts: 102,627
Own Kudos:
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,627
Kudos: 742,783
 [48]
5
Kudos
Add Kudos
43
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 July 2025
Posts: 102,627
Own Kudos:
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,627
Kudos: 742,783
 [14]
4
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
User avatar
Lucky2783
Joined: 07 Aug 2011
Last visit: 08 May 2020
Posts: 418
Own Kudos:
1,998
 [9]
Given Kudos: 75
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT 1: 630 Q49 V27
Posts: 418
Kudos: 1,998
 [9]
7
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
General Discussion
User avatar
Zhenek
Joined: 17 Mar 2015
Last visit: 08 Jun 2021
Posts: 106
Own Kudos:
277
 [1]
Given Kudos: 4
Posts: 106
Kudos: 277
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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"
avatar
SavageBrother
Joined: 18 Dec 2014
Last visit: 03 Oct 2015
Posts: 95
Own Kudos:
51
 [4]
Given Kudos: 5
Posts: 95
Kudos: 51
 [4]
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
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.
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 18 Jul 2025
Posts: 21,145
Own Kudos:
26,205
 [4]
Given Kudos: 296
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,145
Kudos: 26,205
 [4]
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
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.



Since the first question can be any choice, its probability of being different is 4/4 = 1. However, since the second question has to be a different choice that the first, its probability of being different is 3/4. Similarly, the probability that the third question has a different answer from the second is 3/4, the fourth from the third is 3/4, and the fifth from the fourth is 3/4. Therefore, the probability that no two consecutive questions will have the same answer is:

1 x 3/4 x 3/4 x 3/4 x 3/4 = 81/256 = 0.316 ≈ 32%

Answer: B
avatar
saumya2805
Joined: 25 Nov 2017
Last visit: 28 Jan 2020
Posts: 8
Own Kudos:
Given Kudos: 17
Posts: 8
Kudos: 2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Part 1 of 2 of the answer screenshot.

Posted from my mobile device
Attachments

C57F8C2C-DB44-4C87-B0A3-E29CDCC8CA40.png
C57F8C2C-DB44-4C87-B0A3-E29CDCC8CA40.png [ 4.16 MiB | Viewed 12829 times ]

avatar
saumya2805
Joined: 25 Nov 2017
Last visit: 28 Jan 2020
Posts: 8
Own Kudos:
Given Kudos: 17
Posts: 8
Kudos: 2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Part 2 of 2 of the answer screenshot.

The app doesn’t allow uploading multiple files or a pdf file! So had to split the answer.

This was a very tough question to understand... and I didn’t find the solution anywhere, so just had to post a layman understanding and solution to it!

It seems painful at first glance, but like all GMAT questions, it only tries to truly test your understanding & comprehension of the question & your crisis mgmt skills rather than your memory skills!

All the best guys!

Posted from my mobile device
Attachments

1CC0B84F-C9ED-45E9-AE14-2A588FB066A4.png
1CC0B84F-C9ED-45E9-AE14-2A588FB066A4.png [ 3.73 MiB | Viewed 12724 times ]

User avatar
Basshead
Joined: 09 Jan 2020
Last visit: 07 Feb 2024
Posts: 927
Own Kudos:
Given Kudos: 432
Location: United States
Posts: 927
Kudos: 287
Kudos
Add Kudos
Bookmarks
Bookmark this Post
total possible outcomes: 4^5

In the first question there are 4 possible outcomes. (4)

In the 2nd choice there are 3 out of 4 favorable outcomes (3).

In the 3rd choice there are 3 out of 4 favorable outcomes (3)

In the 4th choice there are 3 out of 4 favorable outcomes (3)

In the 5th choice there are 3 out of 4 favorable outcomes (3)

total favorable outcomes: 4 * 3^4 = 324

324 / 4^5 = 324 /1024 = approximately 32%
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,078
Own Kudos:
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,078
Kudos: 18,761
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The number of questions is 5.

Consecutive pairs: [(1,2), (2,3),(3,4),(4,5)] = Total 4

Total answer choices: 4. Probability of each answer choice to be the correct answer: \(\frac{1}{4}\) and not be the answer choice will be \(\frac{3}{4}\).

The probability that no two consecutive questions will have the same answer: 1 question has the correct answer choice and the other 4 has the wrong answer choice. And this is possibly happening in 4 consecutive pairs distinctly.

=> 4 * \(\frac{1}{4} * \frac{3}{4} * \frac{3}{4} * \frac{3}{4} * \frac{3}{4} \)

=> \(\frac{81}{256}\) * 100 = 31.6 = 32%

Answer B
User avatar
riri3026
Joined: 28 Apr 2024
Last visit: 21 Jan 2025
Posts: 22
Own Kudos:
Given Kudos: 27
Posts: 22
Kudos: 4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
just simply think of it like Q1. has 4 options (4/4) = 1
then Q2. will have all options possible but the one selected above = 3/4
then Q3. will have all options but the option selected in Q2 = 3/4
then Q4 will have all but option used in Q3. = 3/4
lastly, Q5 will have all options but option used in Q4 above = 3/4

1 * (3/4)^4 = 81/256 and then divide to find probability = 32%
User avatar
7Amulya
Joined: 28 Mar 2022
Last visit: 19 Jul 2025
Posts: 25
Own Kudos:
Given Kudos: 538
Posts: 25
Kudos: 1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Bunuel,

I have one doubt, so won't this be added for other 4 questions? when 2nd and 3rd questions will not have same answer. similarly for other set of questions
Bunuel
Bunuel
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.
Moderators:
Math Expert
102626 posts
PS Forum Moderator
698 posts