clerk/agent

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mehrasa: Master | Next Rank: 500 Posts; Posts: 279; Joined: Fri Nov 05, 2010 5:43 pm; Thanked: 15 times; Followed by:1 members

clerk/agent

by mehrasa » Sun Sep 25, 2011 5:30 am

Each employee at a certain bank is either a clerk or an agent or both. of every 3 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 a bank is boh an agent and a clerk?
A 1/2
B 1/3
C 1/4
D 1/5
E 2/5

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Source: Beat The GMAT — Problem Solving | Sun Sep 25, 2011 5:30 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 am; Thanked: 230 times; Followed by:21 members

by shankar.ashwin » Sun Sep 25, 2011 5:38 am

C IMO.

IF there is 1 person who is both clerk and agent, then according to the question we have 2 others who are agents alone and 1 person who is only a clerk. Totally 4 people

mehrasa wrote:Each employee at a certain bank is either a clerk or an agent or both. of every 3 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 a bank is boh an agent and a clerk?
A 1/2
B 1/3
C 1/4
D 1/5
E 2/5

Quote

mehrasa: Master | Next Rank: 500 Posts; Posts: 279; Joined: Fri Nov 05, 2010 5:43 pm; Thanked: 15 times; Followed by:1 members

by mehrasa » Sun Sep 25, 2011 5:42 am

good job Shankar... I was looking for a easy and quick solution...
[spoiler]OA: C[/spoiler]

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pm; Thanked: 114 times; Followed by:11 members

by knight247 » Sun Sep 25, 2011 5:51 am

This is a neat problem.
Let the number of only Clerks be C
Let the number of only Agents be A
Let the number of those who are both agents and clerks be B

C+A+B=Total

We need to find B/(A+C+B)

Now, when we isolate the agents and the ppl who are both and pick any one person from among them, the probability that he will be both is B/(A+B) and this equals 1/3 so B/(A+B)=1/3 and 2B=A

Similarly, when we segregate the clerks and pick any one person from among them, the probability that he will be both is B/(C+B)and this equals 1/2 so B/(C+B)=1/2 so B=C

Now, we have B/(A+C+B)=B/(2B+B+B)=b/4B=1/4 Hence C

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Wed May 30, 2018 4:18 pm

mehrasa wrote:Each employee at a certain bank is either a clerk or an agent or both. of every 3 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 a bank is boh an agent and a clerk?
A 1/2
B 1/3
C 1/4
D 1/5
E 2/5

If there are 6 agents, 2 of them are also clerks and 4 of them are agents only.

If there are 4 clerks, 2 of them are also agents and 2 of them are clerks only.

Therefore, if there are 8 employees in the bank, 4 of them are agents only, 2 of them are clerks only and 2 of them are both. Therefore, the probability that a randomly selected employee is both an agent and a clerk is 2/8 = 1/4.

Answer: C

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