Data Sufficiency

Hi Sri,

vaibhav108 made a slight error in his interpretation of this question, but his overall answer is correct.

We're told that events A and B are independent and have EQUAL PROBABILITY of occurring. We're asked for the probability that event A occurs.

Fact 1: The probability that AT LEAST one of the events occurs is .84

This means that A, or B or BOTH occurs = .84

We can restate this to mean that the probability that neither A, nor B nor BOTH occurs = .16

(Not A)(Not B) = .16

Since we're told that A and B have equal probabilities of occurring, they also have equal probabilities of NOT occurring. So....

(Not A) = (Not B)

Combining these 2 equations gives us the probability that A will not occur.....

(.4)(.4) = .16

The probability that A DOES NOT occur = .4
The probability that A DOES occur = .6
Fact 1 is SUFFICIENT

Fact 2: The probability that B occurs and A DOES NOT occur = .24

This tells us that....

(B)(Not A) = .24

From the prompt, we know that...

A = B
(Not A) = (Not B)
A + (Not A) = 1

In this scenario, the values are .4 and .6, but we don't know which is which (one is the probability the event occurs, the other is the probability that the event does NOT occur). Either one COULD be the answer.
Fact 2 is INSUFFICIENT.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich