300 students participated in a symposium with 3 conferences in sequence.
Half of the students that attended the first conference, attended neither the other two.
One-third of the students that attended the second conference, attended neither the other two.
And one-fourth of the students that attended the third conference, attended neither the other two.
Knowing that the three conferences were attended by the same number of students, and that each of the 300 students attended at least one conference :
a) how many students attended each conference ?
b) how many students attended only one conference ?
c) how many students attended only two conferences ?
d) how many students attended all 3 conferences ?
One unique solution !
(In reply to
re: Answer by pcbouhid)
When I was working out the problem, I used A, B and C because those are
the letters I usually use when making a list. I use x, y and z
for equations... I guess that's just my preference. I know... I
should have changed the A, B and C to 'First Conference', 'Second
Conference' and 'Third Conference' in the answer.
As far as how I reached my answer...
Since 1/2 of the people attended only the First Conference, 1/3 the
Second Conference and 1/4 the Third Conference, and since the same
number of people attended each conference, the number of people who
attended each conference must be a multiple of 12.
I made a spreadsheet that listed the first multiples of 12 and then
listed 1/2, 1/3 and 1/4 of each multiple, which would be the number of
people who attended only one conference.
I then added three columns to list the number of people who went to
only to the first and second conference, second and third conference,
and first and third conference. These are unknowns for the moment
and where I did my trial and error.
I then set up three columns to list how many people attended each of
the conferences (e.g. for the first conference, add [only those who
attended first conference] + [those attended only first conference and
second conference] + [those attended only first conference and third
conference]).
I then changed the [number of people who attended the first conference
and second conference] and the [number of people who attended the first
conference and third conference] until the number of people who
attended each conference was the same.
I then added a column for people who attended all three
conferences. I then changed this number until the total number of
people who attended conferences equaled 300.
I then compared the number of people who attended each conference to
the multiple of 12 it was supposed to equal. If it matched, then
it's the answer, otherwise, go back and change the numbers of people
who attended more than one conference.
re(2): Answer
