Conty911,

I'm happy to help, but I believe something is funky about this question. Are you sure there wasn't any other text preceding the problem? There just doesn't seem to be enough information to give a sensible answer.

I am not particularly impressed with the quality of the question either --- the complicated phrase "at least one of the events A or B occurs" is a convoluted way of saying "A or B" --- in logic (at least according to the conventions GMAT follows) the word "or" implies one or the other or both --- saying "A or B happens", means A happens, or B, or both. You don't have to specify the "at least" part at all --- it's totally redundant.

Now, it's undeniably true that

P(A or B) > P(B)

so the entry in the left column must be lower than the entry in the right. At the moment, though, in the absence of any other conditions, it's not particularly clear to me that the answer couldn't be any pair in which the entry in the the left column were lower than the entry in the right. After all, P(A) could be anything, and the overlap region, P(A and B), could be anything. The requirement of P(A or B) > P(B) seems to be the only constraint in this problem. That would produce fifteen distinct right answer combinations.

Something must be missing. What is the source? What is the exact text of the question? I feel like there is some crucial condition missing.

Please let me know if you can uncover any further parts to this question.

Mike
_________________

Mike McGarry
Magoosh Test Prep

Dear Ravipprasad,

The trouble is --- that's one possible answer, but not the only one.

It could be true that
P(A) = 0.25 and P(B) = 0.25 and P(A or B) = 0.50
or that
P(A) = 0.25 and P(B) = 0.10 and P(A or B) = 0.35
or that
P(A) = 0.10 and P(B) = 0.25 and P(A or B) = 0.35
or that
P(A) = 0.40 and P(B) = 0.10 and P(A or B) = 0.50
etc. etc.

We have no guarantee that P(A) = P(B). Furthermore, I was assuming in these four cases that A & B are disjoint, that is to say, that they have no overlap.
If A & B are disjoint, then P(A or B) = P(A) + P(B)
If A & B are not disjoint, then P(A or B) = P(A) + P(B) - P(A and B)

For example, it could be true that:
P(A) = 0.25, P(B) = 0.50, P(A and B) = 0.15, so P(A or B) = 0.60

It actually would be an excellent GMAT math question simply to count all the possible answers one could make on this chart! Either the person who wrote the question was not good at writing questions, or the person who posted it omitted crucial information. Be careful making assumptions --- in a real, well-written GMAT problem, no assumptions will be necessary, and in fact, making assumptions will just get you in trouble.

Does all this make sense?

Mike
_________________

Mike McGarry
Magoosh Test Prep