A team of workers including Tom and Dick work in the same office

Question

A team of workers including Tom and Dick work in the same office according to a schedule that ensures that exactly two team members will be present at a given time, and that in the course of the week all the team members work an equal number of hours. What is the probability that a visitor to the office who doesn’t know the schedule arrives to find both Tom and Dick in the office?

(1) The team has three members.
(2) Tom and Dick worked together for the whole of the previous day.

Show Answer

Official Answer

A

(1) The team has three members.
(2) Tom and Dick worked together for the whole of the previous day.

fugaquasi · Answer

Im very confused, I cant even figure out what this question is asking for.

Ajay09 · Answer

Hi @Bunuel, can you please post the explanation for the question?

VibhuAnurag · Answer

We need the probability that a random visitor finds both Tom and Dick in the office.
At any given time, exactly 2 team members are present.

Statement (1):  
 The team has 3 members. 
 Let the members be   Tom, Dick, and one other person.   Since exactly 2 people are present at any time, the possible pairs are: 
 Tom + Dick 
 Tom + Other 
 Dick + Other 
 Also, all team members work an equal number of hours.   That means these 3 pairs must occur for equal amounts of time. 
 So the probability that the visitor finds Tom and Dick together is   1/3. 
 Statement (1) is sufficient.

Statement (2):  
 Tom and Dick worked together for the whole of the previous day. 
 This tells us about one day only. It does not tell us   how many people are on the team,   how the rest of the schedule is arranged or   how often Tom and Dick work together during the week.   So we cannot determine the overall probability. 
 Statement (2) is not sufficient.

The answer is A.

Stella5200 · Answer

I thought of this as:

you are given there is a team and tom and dick are on it.

What isn the P(tom and dick).

pre solve: you need to know the number people on the team or some relationship

(1) give you # of members. this means the p of those two is (1/3) x (1/2) x (2! because there are 2 distinct people) = 1 x2/6 = 1/3.

Suff

(2) not relevant here

A team of workers including Tom and Dick work in the same office

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GMAT Data Sufficiency (DS) Questions

A team of workers including Tom and Dick work in the same office

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