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Haven't you already failed the aptitude test by having to ask?
(no disrespect intended)
More seriously, I suspect the question could be read in different ways and lead to different answers.
... but perhaps this is where aptitude comes in, realising that the question can be read more than one way.
Maybe it is HOW you answer that shows aptitude, more than giving one of several possible right answers?
... or maybe stating your assumptions would show aptitude, since there is one obvious way to interpret the question, and one or more less obvious interpretations.
...or maybe the correct answer would be "can you clarify the question please?".
...or maybe I do not understand?
... or maybe I am thinking too deep, and the person testing your aptitude is simply looking for the one obvious answer to the obvious interpretation.
in which case... start by thinking of the chances of one person entering the room within a particular 10 minute period. Think the logic through from there.
This is a nice problem for a course of probability theory, but honestly I don't think that is a good aptitude question under this interpretation. I mean to say that I don't think that the questioner expects an answer like "Assuming that the times of arrival are indepent and uniformly distributed between 5 am and 6 am, the probability that the two enter times lie into a gap of 10 minutes is 0.3056". (Unless it is a very very very specific test.)
I'd think rather in some of the hexreader's interpretation.
Was it a spoken interview or a written test?
In the first case, if I was the questiones I would expect a request for clarification from you.
In the second case, an answer like "The probability is very high if they come together" would not be so bad.
Suppose person A enters at some arbitrary time Ta, which is within the 5-6am period, or a 60 minute period.
Then what is the prob that person B entered in a time period which is +/- 10 min of this time Ta, subject to the 5-6am limits.
Now thats a duration of 20 minutes if 5.10am < Ta < 5.50am
And a reducing period, minute for minute, for Ta within the 1st 10 minutes & last 10 minutes.
So as a simplistic answer, i'd say 20/40 + 5/20 = 0.5.
Wow... its a 50% probability ! Heh...
On a more serious note - this seems to be a puzzle in queueing theory, where arrival times of events is usually modeled by Poisson distribution. Or not. I forget now how to play with those equations.... but yes, definitely an unusual question for a standard aptitude test.
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