Clerks and Agents

[Deepthi Subbu]

Each Employee at a certain bank is either a clerk or an agent or both. Of every three agents, one is
also a clerk. Of every two clerks, one is also an agent. What is the probability that an employee
randomly selected from the bank is both an agent and a clerk?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 2/5

My take : Suppose the 12 ppl are A B C D E F G H I J K L

Then according to the problem - one out of every 3 agents are clerks so , C F I L are both clerks and agents . And one out of every 2 clerks are agents , so B D F H J L are both clerks and agents .Combining both F and L are both clerks and agents . So the probability should be 2/12 = 1/6. Where am i going wrong ?

[shankar.ashwin]

I posted a solution here
https://www.beatthegmat.com/clerk-agent-t91743.html

[Geva@EconomistGMAT]

Each Employee at a certain bank is either a clerk or an agent or both. Of every three agents, one is
also a clerk. Of every two clerks, one is also an agent. What is the probability that an employee
randomly selected from the bank is both an agent and a clerk?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 2/5

My take : Suppose the 12 ppl are A B C D E F G H I J K L

Then according to the problem - one out of every 3 agents are clerks so , C F I L are both clerks and agents . And one out of every 2 clerks are agents , so B D F H J L are both clerks and agents .Combining both F and L are both clerks and agents . So the probability should be 2/12 = 1/6. Where am i going wrong ?

What if there were only three agents? Then only one would be a clerk and not CFIL. The same for clerks - what if there were only six agents, so only three of them are both?



You're assuming that the one out of three ratio holds for the entire group, when in fact it jsut indicates the ratio of both for THAT group.

[Deepthi Subbu]

I somehow assumed there are 12 people. Thanks ashwin and Geva.