Meeting

[Aman verma]

Q : At a meeting of the Senate there were n people.As per the convention everyone has received some chocolates in the following manner . As A,B,C,D,E ...... etc have received 1,2,3,4,5....etc chocolates respectively.Before anyone has eaten a bit of chocolate, due to some urgent call , the chairman left the meeting with his chocolates . Later on the rest of the attendants collected their chocolates in a box and then redistributed all the chocolates evenly among themselves and thus everyone has received 13 chocolates .Minimum number of person who attended the meeting can be :

a) 15

b) 18

c) 24

d)32

e) 38



Ans [spoiler]c)24[/spoiler]

[harsh.champ]

Q : At a meeting of the Senate there were n people.As per the convention everyone has received some chocolates in the following manner . As A,B,C,D,E ...... etc have received 1,2,3,4,5....etc chocolates respectively.Before anyone has eaten a bit of chocolate, due to some urgent call , the chairman left the meeting with his chocolates . Later on the rest of the attendants collected their chocolates in a box and then redistributed all the chocolates evenly among themselves and thus everyone has received 13 chocolates .Minimum number of person who attended the meeting can be :

a) 15

b) 18

c) 24

d)32

e) 38



Ans 24

1+2+3+4+......+n = total no. of chocolates = n(n+1)/2
Now,for minimum no. of persons,the chairman should be the nth person.
Hence,n(n+1)/2 -n =13(n-1)

[firdaus117]

1+2+3+4+......+n = total no. of chocolates = n(n+1)/2
Now,for minimum no. of persons,the chairman should be the nth person.
Hence,n(n+1)/2 -n =13(n-1)

Hey your solution yields no result.Check it urself.You have wrongly assumed that chairman has to be n th person for minimising 'n'.
I have an easier approach to this question i.e. work through options.
1. 15 sum=120 13*14=182 Rejected
2. 18 Sum=171 13* 17=221 Rejected
3. 24 Sum=300 13*23=299 Accepted
The chairman will have 300-299=1 chocolate. :)Poor man.What's the use being a chairman if u can't have all chocolates.

[harsh.champ]

1+2+3+4+......+n = total no. of chocolates = n(n+1)/2
Now,for minimum no. of persons,the chairman should be the 1st person.
Hence,n(n+1)/2 -n =13(n-1)

Hey your solution yields no result.Check it urself.You have wrongly assumed that chairman has to be n th person for minimising 'n'.
I have an easier approach to this question i.e. work through options.
1. 15 sum=120 13*14=182 Rejected
2. 18 Sum=171 13* 17=221 Rejected
3. 24 Sum=300 13*23=299 Accepted
The chairman will have 300-299=1 chocolate. :)Poor man.What's the use being a chairman if u can't have all chocolates.

Hey firdaus,
Thanks .Great approach over here.
Actually,I took the other-way-round .
It should be

the chairman should be the 1st person.
Hence,answer is n(n+1)/2 -1 =13(n-1)
which is 24 C.

I guess now it is correct.

[firdaus117]

1+2+3+4+......+n = total no. of chocolates = n(n+1)/2
Now,for minimum no. of persons,the chairman should be the 1st person.
Hence,n(n+1)/2 -n =13(n-1)

Hey your solution yields no result.Check it urself.You have wrongly assumed that chairman has to be n th person for minimising 'n'.
I have an easier approach to this question i.e. work through options.
1. 15 sum=120 13*14=182 Rejected
2. 18 Sum=171 13* 17=221 Rejected
3. 24 Sum=300 13*23=299 Accepted
The chairman will have 300-299=1 chocolate. :)Poor man.What's the use being a chairman if u can't have all chocolates.

Hey firdaus,
Thanks .Great approach over here.
Actually,I took the other-way-round .
It should be

the chairman should be the 1st person.
Hence,answer is n(n+1)/2 -1 =13(n-1)
which is 24 C.

I guess now it is correct.

Hmm still not correct.How would you know beforehand that he has one chocolate.
However,if you still insist on doing it conventionally,then take an arbitrary value
n(n+1)/2 - k = 13(n-1) with condition k<=n
U will get a quadratic equation of 'n'.Take the condition as for integral 'n',the determinant will be a perfect square.

[Aman verma]

In the above question , maximum how many chocolates were there to be received by all of them,initially :

a)300

b)351

c)450

d)551

e)650

Ans [spoiler]b)351[/spoiler]

[Aman verma]

Hey folks, I got no solution from anybody on the second part of the question ?

[harsh.champ]

Hey folks, I got no solution from anybody on the second part of the question ?

Refer to the 1st post I made:-
subtract n from the sum of n natural no.s

[firdaus117]

Hey folks, I got no solution from anybody on the second part of the question ?

Oh,I missed the second question.But probably if you had posted it in a new thread,you would have elicited prompt response.
As it is required to calculate maximum number of chocolates,it would mean that the chairman had 'n' number of chocolates before he left:
So,total chocolates with members earlier were 13(n-1)+n=14n-13
Now work through options,start from highest value(why?)
Option 5.650
14n-13=650
0r,n=673/14 not an integer Rejected
Option 4.551
14n-13=551
or, n=564/14 Rejected
Option 3.450 Rejected on similar logic
Option 2.351
n=26 An integer Accepted