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Suppose that someone starts with a chain letter. Each person who receives the letter is asked to send it on to $4$ other people. Some people do this, while some do not send any letter. How many people have seen the letter, including the first person, if none receives more than one letter and if the chain letter ends after there have been 100 people who read it but did not send it out? Also find out how many people sent out the letter?

  1. $122$ & $22$
  2. $111$ & $11$
  3. $133$ & $33$
  4. $144$ & $44$
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4 Answers

Best answer
5 votes
5 votes

Either a person sends to $4$ people or he doesn't send it. So, let $x$ be the number of persons who sends to $4$ people. $100$ people didn't send any letter. Except 1 (the initial person) all others $(x + 100)$ must have a sender. So, we can write

$\text{No. of receivers} = 4 \times \text{No. of senders} + 1 \\(\text{Initial person doesn't have a sender})$

$x + 100  = 4x + 1 \implies 3x = 99\\x = 33 $

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4 votes
4 votes

C. 133 and 33.

Explanation :

Let n represent the no of people who sent the letter out. At each stage a person sends 4 letters.

Trying the above branching diagram a couple of times tells us it is 3n+1 people who read(received) the letter but did not send out one,

Hence, 

3n + 1 = 100

n = 33.

Thus 33 people have sent out the letter and 100+33 = 133 have seen the letter.

3 votes
3 votes
ans-c

from basic,            consider one sender , he send to four other who only read

                                   "      two   "          they send to seven other        "

                                   "      three  "         they send to ten  other receiver who only read

 

this form AP having comman difference 3, and a/q  total number of reciever who only read is 100 that is our last term

so,    4+(n-1)*3=100

n=33    this is the no. of reader who send to four other

already there are 100 viewer who only read

so  total viewer will be 33+100=133
3 votes
3 votes
ans is quite implied from choices itself first ,second,and fourth choices say that the letter has been sent to 88,44(both are less than 100), and176 persons (out of which  44 has seen so 44x4 =176   so  176-43=133 not equal to  100)

only possible choice is c 33x4=132-33+1=100
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