if you want to remove an article from website contact us from top.

n persons stand on the circumference of a circle at distinct points. each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. if the total time taken for singing is 28 minutes, what is n?

Category :

Mohammed

Guys, does anyone know the answer?

get n persons stand on the circumference of a circle at distinct points. each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. if the total time taken for singing is 28 minutes, what is n? from screen.

N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two

N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song o

Home > English > Class 14 > Maths > Chapter >

Permutations And Combinations

>

N persons stand on the circumf...

N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N

Updated On: 27-06-2022

Text Solution Open Answer in App A 5 B 7 C 9 D none of these Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

Related Videos

644089246 0 5.3 K 4:27

There are n persons sitting around a circular table. They start singing a 2 minute song in pairs such that no two persons sitting together will sing together. This process is continued for 28 minutes. Find n.

130850294 1.2 K 3.7 K 6:59

There are n persons sitting around a circular table. They start singing a 2 minute song in pairs such that no two persons sitting together will sing together. This process is continued for 28 minutes. Find n.

643971084 0 2.3 K 4:17

n persons are seated on n chairs at a round table. Find the probability that two specified persons are sitting next to each other.

195772002 0 9.2 K 2:09

The waiting time ,t in mixture, for the

n th nth

person is a queue, is given by the relation :

t=12.5n−15 t=12.5n-15

. If each person taken 10 minutes of be serviced what , is the minutes , between when the services for a person is completed and the service for the next person begins ?

646931222 0 10.0 K 0:54

Two men are standing on opposite ends of a bridge 1200 metres long. If they walk towards each other at the rate of 5m/minute and 10m/minute respectively in how much time will they meet each other ?

643350090 0 2.1 K 2:59

एक वृत्ताकार मैदान का क्षेत्रफल 616 वर्गमीटर है। मैदान के केंद्र पर एक व्यक्ति खड़ा है। मैदान पर खड़े एक-दूसरे व्यक्ति की अधिक से-अधिक दूरी पहले व्यक्ति से क्या होगी?

Popular Chapters by Class:

Class 6 Algebra

Basic Geometrical Ideas

Data Handling Decimals Fractions Class 7

Algebraic Expressions

Comparing Quantities

Congruence of Triangles

Data Handling

Exponents and Powers

Class 8

Algebraic Expressions and Identities

Comparing Quantities

Cubes and Cube Roots

Data Handling

Direct and Inverse Proportions

Class 9

Areas of Parallelograms and Triangles

Circles Coordinate Geometry Herons Formula

Introduction to Euclids Geometry

Class 10

Areas Related to Circles

Arithmetic Progressions

Circles Coordinate Geometry

Introduction to Trigonometry

Class 11 Binomial Theorem

Conic Sections

Introduction to Three Dimensional Geometry

Limits and Derivatives

Class 12

Application of Derivatives

Application of Integrals

Continuity and Differentiability

Determinants

Differential Equations

Terms And Conditions

स्रोत : www.doubtnut.com

N persons stand on the circumference of a circle at distinct points. : Problem Solving (PS)

N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a ...

GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

close Forum Home GMAT Quantitative

Problem Solving (PS)

Unanswered Active Topics Register GMAT Club Tests Decision Tracker My Rewards New posts New comers' posts

MBA Spotlight Fair on October 18 & 19. Register to reserve your spots.MBA Podcast - My MBA journey at London Business School. Listen here!

N persons stand on the circumference of a circle at distinct points.

3 POSTS

Print view NEW TOPIC SORT BY: Date Kudos Show Tags L

Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 86747

N persons stand on the circumference of a circle at distinct points. [#permalink]

12 Mar 2021, 02:16 3 Bookmarks Expert Reply 00:00 A B C D E

SHOW TIMER STATISTICS

N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two –minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?

(A) 7 (B) 6 (C) 5 (D) 4 (E) 3 Show Answer _________________

New to the GMAT CLUB Forum?

Posting Rules: QUANTITATIVE | VERBAL.

Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant

Questions' Bank By Tags and Difficulty: GMAT Club's Complete Questions' Bank

My Signature Questions' Collection:

Bunuel's Signature Questions' Collection

What are GMAT Club Tests?

Extra-hard Quant Tests with Brilliant Analytics

chetan2u

Math Expert

Joined: 02 Aug 2009

Posts: 10582

Re: N persons stand on the circumference of a circle at distinct points. [#permalink]

12 Mar 2021, 18:27 1 Bookmarks Expert Reply Bunuel wrote:

N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two –minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?

(A) 7 (B) 6 (C) 5 (D) 4 (E) 3

Total number of ways to choose a pair = NC2

Number of pairs in which both the persons are standing next to each other =N

Ways in which the persons are not next to each other =NC2-N

However it will also be equal to 28/2, as each possible pair sings for 2 minutes.

Thus, N(N−1) 2 −N= 28 2 N(N−1)2−N=282 N(N−1)−N=28 N(N−1)−N=28 N 2 −3N−28=0 N2−3N−28=0 (N−7)(N+4)=0 (N−7)(N+4)=0

So N can be 7 or -4. As it cannot be negative, N=7.

A _________________

1. Absolute modulus:. 2. Fractions: 3. Percentage increase: 4. Combinations:

L

ScottTargetTestPrep

Target Test Prep Representative

Joined: 14 Oct 2015

Status:Founder & CEO

Affiliations: Target Test Prep

Posts: 16248

Location: United States (CA)

Re: N persons stand on the circumference of a circle at distinct points. [#permalink]

23 Mar 2021, 04:43 1 Kudos Expert Reply Bunuel wrote:

N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two –minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?

(A) 7 (B) 6 (C) 5 (D) 4 (E) 3 Solution:

Assume the N people are vertices of an N-gon. Then all possible pairs of people that can be formed without any pair standing next to each other is also the number of diagonals of the N-gon. Recall that the number of diagonals of an N-gon is N(N - 3) / 2, and we see that a total of 28/2 = 14 songs are sung; therefore, we can create the equation:

N(N - 3)/2 = 14 N(N - 3) = 28

Without solving the equation algebraically, we see that N must be 7 since 7(7 - 3) = 7(4) = 28.

Scott Woodbury-Stewart | Founder and CEO | [email protected]

Perfect 5-Star Rated GMAT Course

5-Day Full Access Trial For Just \$1

110-Point Score Improvement Guarantee

See why Target Test Prep is the top rated GMAT course on GMAT Club. Read Our Reviews

Re: N persons stand on the circumference of a circle at distinct points. [#permalink]

23 Mar 2021, 04:43 NEW TOPIC

Similar topics

N persons stand on the circumference of a circle at distinct points.

AUTHOR Bunuel 13 Dec 2020, 05:26 7 Replies 5 ER

X persons stand on the circumference of a circle at distinct points.

AUTHOR LMP

स्रोत : gmatclub.com

N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two

Answer (1 of 3): for a person no of such pair = N-3 ( excluding himself, and 2 of it adjacent persons) so total no. of pair for N person = N×(N-3) but here each pair has been counted twice so actual no. of pair = N×(N-3)/2 so total singing time = N×(N-3)/2×2 = N×(N-3) so N×(N-3) = 28 so N = 7

N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?

Ad by Amazon Web Services (AWS)

AWS is how.

AWS removes the complexity of building, training, and deploying machine learning models at any scale.

Sort Prakhar Mastain 2y

for a person no of such pair = N-3 ( excluding himself, and 2 of it adjacent persons)

so total no. of pair for N person = N×(N-3)

but here each pair has been counted twice so actual no. of pair = N×(N-3)/2

so total singing time = N×(N-3)/2×2 = N×(N-3)

so N×(N-3) = 28 so N = 7 Related questions

What is (n-1)! *(n-2)! /n^n^2?

A tank can be filled in by one pipe in 4 minutes and by another pipe in 12 minutes. If both pipes are opened simultaneously, in how much time will the tank be filled in?

If one takes 6 minutes while another takes 7 and half minutes to take a walk around a circle if they start together from the same spot and same direction around the circle, at what time will they both be at the starting point again?

If 4 boys or 6 girls can do work in 40 days . How many days will 4 boys and 14 girls take to do the same work?

If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days what is time taken by 15 men and 20 boys?

Munish Fauzdar

Founder: www.algo-classes.com, IIT'ian, Maths, Physics, TechAuthor has 294 answers and 158.2K answer views2y

Clearly there are 14 songs which got sung in the conference, meaning which there are possible 14 such pairs which can be formed picking two when doesn’t include adjacent pairs.

Let n be the number of people standing in a circle.

Thought: The steps will be that if we take two people out of n, there are nC2 selections possible. However from these selections there will be n selections which would be reduced due to being formed with the adjacent person.

Hence, if total songs played were for 28 mins, => 14 songs were played => 14 pairs were formed.

n C 2 - n = 14 n (n-1)/2 - n = 14 n^2 - n - 2n = 28 n^2 -

Tushar Kaviti

B. Tech in Electronics and Communication Engineering, JNTUK University College of Engineering Narsaraopet (Graduated 2020)Author has 72 answers and 50.8K answer views2y

28 min makes 14 pairs. now the persons are standing in circle and persons not standing next to each other are forming 14 pairs. imagine connecting the pairs and you see polygons. the pairs not adjacent to each other form 14 pairs. this is like counting the no of diagonals because diagonals are formed between non adjacent points except here we have persons as points here. noe diagonals should be 14

so nc2-n= 14 which gives us no of sides as 7.

if you like short stories reach out Tushar Wiritings

Andrew Winkler

PhD in Mathematics, Courant Institute of Mathematical Sciences, NYU (Graduated 1987)Upvoted by

Valerian Mahdi Pratama

, M.S. Mathematics, Bandung Institute of Technology (2022) and

Peter Ferguson

, MSci Theoretical Physics & Mathematics, Lancaster University (2018)Author has 2.4K answers and 3.5M answer views3y

Related

Can you summarize the personality of each major field of mathematics in one sentence each?

Every major field of mathematics is some variation on the theme of what happens when a binary operation is partially defined, but is as associative as it can be. Then what happens when multiple such structures interact.

Graphs and quivers are what you get when such operations have units, and no extra structure.

Semigroups arise when the binary operation is fully defined.

Topology is what you get when you minimize costs among paths in quivers. (A graph is a special kind of quiver, where there’s at most one arrow from any given vertex to another.)

Categories are what you get when your semigroup lose

Jason Chu

Enjoy problem solving, Math and CSAuthor has 1.1K answers and 306.8K answer viewsMay 26

Related

Two points on the circumference of a circle of radius √2 are chosen 1 at a time and at random. From each, left or right is randomly chosen and then a chord of length 2 is drawn in this direction. What's the probability that the two chords intersect?

First, note that a chord of length 2 in a circle of radius

2 – √ 2

corresponds to a quarter circle. WLOG, we can assume that the first point chosen is at the top of the circle, and we drew a chord to the right as shown below:

The second point can be chosen from either red, blue, or green arc, with the probabilities 1/4, 1/2, 1/4, respectively. If chosen from the red arc, no matter which direction the chord is drawn, two cords always intersect. If chosen from the green arc, two cords will never intersect regardless which direction the chord is drawn. In the blue arc, the chords intersect on one