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 Algebraic solution by Tristan)

Good work, Tristan.

My solution differs a little from yours.

Now, observe one curious thing : x = 156, and using the notation of Cory, A = 78, B = 52 and C = 39. ALL MULTIPLES OF 13. A = 6 x 13, B = 4 x 13, C = 3 x 13, 6 + 4 + 3 = 13.

It's just a coincidence ?? I'm still wondering (and in fact I tried to prove, but unsucceed) if we can, since we know right from the beginning, that x is a multiple of 12, prove that it is also a multiple of 13, wich give us at once x=156.  And the values A, B, C follows in a second.

Posted by pcbouhid on 2005-05-13 14:13:09