GATE CSE 1997 | Question: 6.2

Question

Let $G$ be the graph with $100$ vertices numbered $1$ to $100$.  Two vertices $i$ and $j$ are adjacent  if $\vert i-j \vert =8$ or $\vert i-j \vert=12$. The number of connected components in $G$ is

• A. $8$
• B. $4$
• C. $12$
• D. $25$

Comments

Plz have a look at :

https://gateoverflow.in/2258/gate1997_6-2

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if que given was like this | i-j |=10, or | i-j |= 20 then ans will be 10 right .

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Yes , right. Nice interpretation b/w

Answer 1

This makes easier to understand..!

Answer 2

A method I tried, Arjun sir, Rajesh Pradhan sir please check:

P(Number of disconnected components with |i-j|=12)   floor(12/100)/100= 8/100

P(Number of disconnected components with |i-j|=8)   floor(8/100)/100= 12/100

P(Number of disconnected components with |i-j|=12 or |i-j|=8)   12/100 * 8/100 = 96/100

Therefore connected components=1-96 = 4/100 i.e 4? 

Does it makes sense? please check