in Quantitative Aptitude retagged by
753 views
5 votes
5 votes

A total of $n$ points are equally spaced around a circle and are labelled with the integers $1$ to $n$, in order. Two points are called diametrically opposite if the line segment joining them is a diameter of the circle. If the points labelled $7$ and $35$ are diametrically opposite, then $n$ equals

  1. $54$
  2. $55$
  3. $56$
  4. $57$
in Quantitative Aptitude retagged by
753 views

2 Comments

Good question
0
0

just using some intuition here !

all points are equally spaced means the points are dividing the circle into equal regions, 

if you carefully analyze the options then n is at least 54, 54 is not dividing circle into equally spaced regions because 35-7 = 28 points then remaining 54-28 = 26 points are on the other side (unbalanced)

56 = 7 * 8 which is creating 8 partitions in circle with 7 points in one group and every pair of points which are multiple of 7 form the diameter 

                                     7                         

           

                                    35

56 satisfies all requirements of the question !

0
0

1 Answer

3 votes
3 votes
The number of points on the circle equals the number of spaces between the points around the circle. Moving from the point labelled $7$ to the point labelled $35$ requires moving $35-7=28$ points and so $28$ spaces around the circle. Since the points labelled $7$ and $35$ are diametrically opposite, then moving along the circle from $7$ to $35$ results in travelling halfway around the circle. Since $28$ spaces makes half of the circle, then $2 \cdot  28=56$ spaces make the whole circle. Thus, there are $56$ points on the circle, and so $n=56$.
edited by

1 comment

from figure we can see that 7-35 are opposite and there are 56 points 1-56

3
3
Answer:

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true