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# Each Employee at a certain bank is either a clerk or an agen

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Founder
Joined: 18 Apr 2015
Posts: 7747
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Each Employee at a certain bank is either a clerk or an agen [#permalink]  07 May 2019, 02:14
Expert's post
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Question Stats:

44% (03:04) correct 55% (01:51) wrong based on 9 sessions
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) $$\frac{1}{2}$$

(B) $$\frac{1}{3}$$

(C) $$\frac{1}{4}$$

(D) $$\frac{1}{5}$$

(E) $$\frac{2}{5}$$
[Reveal] Spoiler: OA

_________________
Manager
Joined: 09 Mar 2019
Posts: 53
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Kudos [?]: 13 [0], given: 0

Re: Each Employee at a certain bank is either a clerk or an agen [#permalink]  08 Jun 2019, 20:54
Founder
Joined: 18 Apr 2015
Posts: 7747
Followers: 143

Kudos [?]: 1593 [0], given: 7035

Re: Each Employee at a certain bank is either a clerk or an agen [#permalink]  09 Jun 2019, 02:06
Expert's post
This is tough. Is a mix of overlapping set and probability. However, once you have found the OS the rest is easy.

In my opinion, attacking the question using number is cumbersome.

Now, c stands for Clerks. a stands for Agents and x stands for both.

Total Clerks: c+x
Total Agents: a+x
Total: c+a+x

Divide in small chunks the question.

Of every three agents, one is also a clerk.

means that an x employee which is part of both is over the agents category only $$\frac{x}{a+x}= \frac{1}{3}$$ ; a = 2x

Of every two clerks, one is also an agent.

$$\frac{x}{c+x} = \frac{1}{2}$$ ; c=x

The probability is

$$\frac{x}{c+a+x} = \frac{x}{x+2x+x} = \frac{x}{4x} = \frac{1}{4}$$

Hope this helps
_________________
Re: Each Employee at a certain bank is either a clerk or an agen   [#permalink] 09 Jun 2019, 02:06
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