sanju09 wrote:There are 55 ways in which both A and B, or any one of the two can read their vocalizations, 71 ways in which both B and C, or any one of the two can read their vocalizations, and 62 ways in which both C and A, or any one of the two can read their vocalizations. In how many ways can any one of the three, A, B, and C, read their vocalizations?
A. 188
B. 94
C. 47
D. 24
E. 21


MBM

A + B -(A intersect B) =55

B + C - (B intersect C)= 71

C + A -( C intersect A) = 62

It is not possible for any two persons to read one vocalization, hence the events are disjoint and the intersections are empty. Either they split the number of ways to read their vocalization or one of them reads and the other has 0 ways to read= does not read at all. This simplifies to
A + B=55

B + C =71

C + A = 62

from which it follows that


55-A +(62-A)=71
A=23
B=32

C=39

A ways + B ways + C ways= 94

Choose B.

But B doesn't match IMO.

what the heck is read their vocalizations supposed to mean? What kind of English is that?


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avenus wrote:what the heck is read their vocalizations supposed to mean? What kind of English is that?


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It's the title of the question analogous to “recite their poems”, dear angry young man.

If A has to recite one poem out of its collection of x, and B has to recite one poem out of its collection of y, then if both were given a chance, then they can recite their works in x y number of ways; whereas if any one is given the chance, then a poem in that case could be recited in x + y number of ways. Now, if there are n ways in which both A and B or any one of the two can recite their poems, then we can interpret that as:

x y + x + y = n.

Try like that!! All the very best!!!

Still not sure where to go with this...

Sanjev - would be helpful to get less condensing posts and a more through walkthrough of the answer if you know it. Otherwise, I'm not sure giving us half a clue to the answer is helpful; might as well not post at all.

Cheers.

Still not sure where to go with this...

Sanjev - would be helpful to get less condensing posts and a more through walkthrough of the answer if you know it. Otherwise, I'm not sure giving us half a clue to the answer is helpful; might as well not post at all.

Cheers.

odod wrote:Still not sure where to go with this...

Sanjev - would be helpful to get less condensing posts and a more through walkthrough of the answer if you know it. Otherwise, I'm not sure giving us half a clue to the answer is helpful; might as well not post at all.

Cheers.

We are here to create and exploit the learning atmosphere, odod! Anybody can ask anybody for help, if required, and I am sure that nobody here will turn a deaf ear for a help call. If you think that the little clue from me about the present question is still not sufficient for you to crack it further, please feel free to ask your doubts and let the discussion move on and on till all your doubts regarding a particular problem are cleared; you never know of how much help that could be for many others who use this forum passively. So please let's also know what you really want to know here instead of suggesting members a walk.

Sanjeev