There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ballin such a way that at least 1 box contains a green ball and the boxes containing green balls areconsecutively numbered. The total number of ways in which this can be done isa)5b)21c)33d)60e)40Correct answer is option 'B'. Can you explain this answer?

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

GMAT Exam > GMAT Questions > There are 6 boxes numbered 1, 2,...6. Each bo...

Join the Discussion on the App

There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ballin such a way that at least 1 box contains a green ball and the boxes containing green balls areconsecutively numbered. The total number of ways in which this can be done is

a)
5
b)
21
c)
33
d)
60
e)
40

Correct answer is option 'B'. Can you explain this answer?

FREE This question is part of

GMAT Full Mock Test- 1

Attempt Test

Attempt this Test

Verified Answer

There are 6 boxes numbered 1, 2,...6. Each box is to be filled up eith...

If only one of the boxes has a green ball, it can be any of the 6 boxes. So, this can be achieved in 6 ways.
If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.
Similarly, if 3 of the boxes have green balls, there will be 4 options.
If 4 boxes have green balls, there will be 3 options.
If 5 boxes have green balls, then there will be 2 options.
If all 6 boxes have green balls, then there will be just 1 option.
Total number of options = 6 + 5 + 4 + 3 + 2 + 1 = 21

View all questions of this test

Most Upvoted Answer

There are 6 boxes numbered 1, 2,...6. Each box is to be filled up eith...

Understanding the Problem
To fill the boxes with red or green balls, we need to satisfy two conditions:
- At least one box must contain a green ball.
- Boxes containing green balls must be consecutively numbered.
Identifying the Combinations
Let's denote the number of boxes as 6. We can determine the valid configurations of boxes that contain green balls:
1. 1 Box with Green Ball:
- Options: {1}, {2}, {3}, {4}, {5}, {6}
- Total: 6 combinations
2. 2 Consecutive Boxes with Green Balls:
- Options: {1,2}, {2,3}, {3,4}, {4,5}, {5,6}
- Total: 5 combinations
3. 3 Consecutive Boxes with Green Balls:
- Options: {1,2,3}, {2,3,4}, {3,4,5}, {4,5,6}
- Total: 4 combinations
4. 4 Consecutive Boxes with Green Balls:
- Options: {1,2,3,4}, {2,3,4,5}, {3,4,5,6}
- Total: 3 combinations
5. 5 Consecutive Boxes with Green Balls:
- Options: {1,2,3,4,5}, {2,3,4,5,6}
- Total: 2 combinations
6. 6 Boxes with Green Balls:
- Option: {1,2,3,4,5,6}
- Total: 1 combination
Calculating Total Combinations
Now, we sum all these combinations:
- 6 (1 box)
- + 5 (2 boxes)
- + 4 (3 boxes)
- + 3 (4 boxes)
- + 2 (5 boxes)
- + 1 (6 boxes)
Total = 6 + 5 + 4 + 3 + 2 + 1 = 21
Final Answer
Thus, the total number of ways to fill the boxes under the given constraints is 21. The correct answer is option B.

Answered by Talent Skill Learning · View profile

Attention GMAT Students!

To make sure you are not studying endlessly, EduRev has designed GMAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in GMAT.

GMAT Focus Edition Mock Test Series 2024

Quantitative for GMAT

Crash Course for GMAT

Data Insights for GMAT

View all answers Start learning for free

< Previous Question Next Question >

Explore Courses for GMAT exam

Similar GMAT Doubts

There are 6 boxes numbered 1, 2,....6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is ___

View answer

Directions: Read the given passage carefully and answer the question as follow.Among the speculative questions which arise in connection with the study of arithmetic from a historical standpoint, the origin of number is one that has provoked much lively discussion, and has led to a great amount of learned research among the primitive and savage languages of the human race. A few simple considerations will, however, show that such research must necessarily leave this question entirely unsettled, and will indicate clearly that it is, from the very nature of things, a question to which no definite and final answer can be given. Among the barbarous tribes whose languages have been studied, even in a most cursory manner, none have ever been discovered which did not show some familiarity with the number concept. The knowledge thus indicated has often proved to be most limited; not extending beyond the numbers 1 and 2, or 1, 2, and 3. At first thought it seems quite inconceivable that any human being should be destitute of the power of counting beyond 2. But such is the case; and in a few instances languages have been found to be absolutely destitute of pure numeral words.These facts must of necessity deter the mathematician from seeking to push his investigation too far back toward the very origin of number. Philosophers have endeavoured to establish certain propositions concerning this subject, but, as might have been expected, have failed to reach any common ground of agreement. Whewell has maintained that “such propositions as that two and three make five are necessary truths, containing in them an element of certainty beyond that which mere experience can give.” Mill, on the other hand, argues that any such statement merely expresses a truth derived from early and constant experience; and in this view he is heartily supported by Tylor.But why this question should provoke controversy, it is difficult for the mathematician to understand. Either view would seem to be correct, according to the standpoint from which the question is approached. We know of no language in which the suggestion of number does not appear, and we must admit that the words which give expression to the number sense would be among the early words to be formed in any language. They express ideas which are, at first, wholly concrete, which are of the greatest possible simplicity, and which seem in many ways to be clearly understood, even by the higher orders of the brute creation. The origin of number would in itself, then, appear to lie beyond the proper limits of inquiry; and the primitive conception of number to be fundamental with human thought.Q.What does the line, in the third para, ‘primitive conception of number to be fundamental with human thought’ mean?

View answer

Directions: Read the given passage carefully and answer the question as follow.Among the speculative questions which arise in connection with the study of arithmetic from a historical standpoint, the origin of number is one that has provoked much lively discussion, and has led to a great amount of learned research among the primitive and savage languages of the human race. A few simple considerations will, however, show that such research must necessarily leave this question entirely unsettled, and will indicate clearly that it is, from the very nature of things, a question to which no definite and final answer can be given. Among the barbarous tribes whose languages have been studied, even in a most cursory manner, none have ever been discovered which did not show some familiarity with the number concept. The knowledge thus indicated has often proved to be most limited; not extending beyond the numbers 1 and 2, or 1, 2, and 3. At first thought it seems quite inconceivable that any human being should be destitute of the power of counting beyond 2. But such is the case; and in a few instances languages have been found to be absolutely destitute of pure numeral words.These facts must of necessity deter the mathematician from seeking to push his investigation too far back toward the very origin of number. Philosophers have endeavoured to establish certain propositions concerning this subject, but, as might have been expected, have failed to reach any common ground of agreement. Whewell has maintained that “such propositions as that two and three make five are necessary truths, containing in them an element of certainty beyond that which mere experience can give.” Mill, on the other hand, argues that any such statement merely expresses a truth derived from early and constant experience; and in this view he is heartily supported by Tylor.But why this question should provoke controversy, it is difficult for the mathematician to understand. Either view would seem to be correct, according to the standpoint from which the question is approached. We know of no language in which the suggestion of number does not appear, and we must admit that the words which give expression to the number sense would be among the early words to be formed in any language. They express ideas which are, at first, wholly concrete, which are of the greatest possible simplicity, and which seem in many ways to be clearly understood, even by the higher orders of the brute creation. The origin of number would in itself, then, appear to lie beyond the proper limits of inquiry; and the primitive conception of number to be fundamental with human thought.Q.The mathematicians consider the debate on the origin of numbers as

View answer

Josh has a big drawer full of exactly 40 packets, each containing a marker which is either black or blue or red in colour. All 40 packets are sealed and are completely identical from outside. It is not possible to know which colour marker is inside unless the packet is fully opened. Out of 40, 23 packets contain a black marker each. How many packets contain a blue marker?(1) Drawer has less packets containing blue markers than those containing red markers.(2) If Josh withdraws packets without looking at their contents, he needs to draw minimum 20 packets to ensure that he has exactly 8 markers of any single colour out of red, blue, black.

View answer

A certain aquarium contains only goldfish and angelfish. If the aquarium contains a total of 75 male fish (of either species,) and 60 goldfish (of either sex,) then how many male goldfish are there in that aquarium?(1) There are 40 angelfish in that aquarium.(2) There are 25 female fish in that aquarium.

View answer

Top Courses for GMATView all

GMAT Focus Edition Mock Test Series 2024

Quantitative for GMAT

Crash Course for GMAT

Data Insights for GMAT

100 RCs for GMAT

Top Courses for GMAT

View all

Share with a Friend

Answer this doubt

Question Description
There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ballin such a way that at least 1 box contains a green ball and the boxes containing green balls areconsecutively numbered. The total number of ways in which this can be done isa)5b)21c)33d)60e)40Correct answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ballin such a way that at least 1 box contains a green ball and the boxes containing green balls areconsecutively numbered. The total number of ways in which this can be done isa)5b)21c)33d)60e)40Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ballin such a way that at least 1 box contains a green ball and the boxes containing green balls areconsecutively numbered. The total number of ways in which this can be done isa)5b)21c)33d)60e)40Correct answer is option 'B'. Can you explain this answer?.

Solutions for There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ballin such a way that at least 1 box contains a green ball and the boxes containing green balls areconsecutively numbered. The total number of ways in which this can be done isa)5b)21c)33d)60e)40Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.

Here you can find the meaning of There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ballin such a way that at least 1 box contains a green ball and the boxes containing green balls areconsecutively numbered. The total number of ways in which this can be done isa)5b)21c)33d)60e)40Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ballin such a way that at least 1 box contains a green ball and the boxes containing green balls areconsecutively numbered. The total number of ways in which this can be done isa)5b)21c)33d)60e)40Correct answer is option 'B'. Can you explain this answer?, a detailed solution for There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ballin such a way that at least 1 box contains a green ball and the boxes containing green balls areconsecutively numbered. The total number of ways in which this can be done isa)5b)21c)33d)60e)40Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ballin such a way that at least 1 box contains a green ball and the boxes containing green balls areconsecutively numbered. The total number of ways in which this can be done isa)5b)21c)33d)60e)40Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ballin such a way that at least 1 box contains a green ball and the boxes containing green balls areconsecutively numbered. The total number of ways in which this can be done isa)5b)21c)33d)60e)40Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.

Explore Courses for GMAT exam