# Reasoning puzzle involving five friends and five departments

Five friends A, B, C, D, and E are working in 5 different departments M, N, O, P and Q and they earn different salaries i.e. 10,000, 15,000, 20,000, 25,000 and 30,000 and they all are of different ages i.e. 24, 26, 28, 30 and 32 years. These all informations are not necessarily in the same order.

• B works in department M and earns more than 20,000.
• Person who is 28 years old works in department Q.
• 32 years old person earns at least 20,000.
• The person who is 26 years old earns 25,000.
• A earns 15,000, but does not work in department N or P.
• Person who is 30 years old earns highest salary but does not work in department M and N.
• E does not work in department P or Q, and his age is not 32.
• The salary of D is less than 20,000.

Who works in department N?
a) B
b) C
c) D
d) Can’t be determined
e) None of these

I have taken this from this website: https://www.bankexamstoday.com/2015/09/reasoning-puzzle-with-detailed-solution.html

There seems to be a detailed solution to the given problem. However it is particularly confusing to admit that I am really not familiar with the step by step thinking process and any guidance in the direction would be most welcome.

## 2 Answers

There are many ways to go about this, but here is the easy grid way. This is a long detailed description for how to solve so someone else will probably beat me with a simpler method, but this one will work every time and becomes easy to do.

Step 1:

Make a grid. You don't have to do this kind of thing this way, but it does help.
I do this by creating the set of important things as the first row group, and then putting all their possible attributes as column groups.
Then, take the other groups and lay them out in reverse order as row groups.

Example (you don't have to use Excel, just sketch it!): Step 2:

Put in all the info you know from each sentence in order. Where there is a positive statement that matches two concepts, put a tick or colour it green. Where there is a negative relationship, put in a cross or colour it red. Note that when we make a positive statement, we can also cancel out all other possibilities!

Example for the first clue we have two parts to the statement, one of which can be broken down further.
* B works in department M.
* B earns more than 20,000. => B does not earn 10k or 15k or 20k.

In the grid: Step 3:

Jumping forward a bit through all the clues, we should get here: But now we can see places for logic to come to our rescue. Check the image below for what I am referring to but...
Firstly, we are given the gold square below for free. It must be a green tick, because there are no other options on the row. This translates to the 32yo definitely earning 20k.
Also, we can use green squares to "pivot" solutions we already have. Take the [B|M] square marked with a cross. Because we know these things are in the same solution, anything true for B must be true for M. Or, using the "pivot analogy", anything in the row must be in the column, meaning we can copy the 3 red salary squares in that row to the column (also marked with "x" in the diagram.
Here's the diagram with these examples: Step 5:

So we go forward with all the logic we can do here...
And we get: Step 6:

And, unusually in this case, we have stopped. There are no more clues that we can use, and a portion of the grid cannot be filled. If we knew one more piece of info, we could work out one of these squares and fill the rest in, but... we are stuck. So in your case, the answer will be D - Cannot be determined.

• To be fair to @trolley813 they did give the solution quicker here and the checkmark does belong to them. However, we were discussing this on chat and trying to explain a general solve and this took somewhat longer to post than a more straightforward answer. Apologies! – Graylocke Apr 7 at 7:56
• Why did you mark yellow in one step? – Rajorshi Koyal Apr 7 at 12:38
• The yellow was used to point out a certain square visually. In the paragraph before that picture, Graylocke explains how we can deduce the yellow square to be green. – bobble Apr 7 at 14:35

A step-by-step solution can look like this (I didn't see the solution at the link):
(Well, no spoilers since a solution is already given by the OP)

Let's enumerate the conditions for better referencing:

(1) B works in department M and earns more than 20,000.
(2) Person who is 28 years old works in department Q.
(3) 32 years old person earns at least 20,000.
(4) The person who is 26 years old earns 25,000.
(5) A earns 15,000, but does not work in department N or P.
(6) Person who is 30 years old earns highest salary but does not work in department M and N.
(7) E does not work in department P or Q, and his age is not 32.
(8) The salary of D is less than 20,000.

Now, look at (8). We know that D's salary can be either 10000 or 15000. But the all 5 people earn different salaries, and from (5) we know that the sum of 15000 is already "taken" by A. Therefore, D earns 10000.

Then, we can deduce that neither A or D (which both earn less than 20000) can be 26 (from (4)), 30 (from (6), since the highest salary is 30000), or 32 (from (3)) years old. That means that A and D are 24 and 28 years old, in some order.

B can earn either 25000 or 30000. But from (1) we know that B works in M, and from (6) the person who earns 30000 does not work in M. That means that B cannot earn 30000, so B earns 25000 and (from (4)) is 26 years old.

For the remaining persons (C and E), there are 2 remaining age options left: 30 and 32 (since B is 26, and the ages 24 and 28 are taken by A and D). But from (7) we know that E is not 32, so E is 30, and C is 32. Now, since E is 30, we can say that E works in O (since from (7) E does not work in P or Q, and from (6) a 30-year-old person does not work in M or N). Also, E (being 30 years old) earns 30000, so C earns 20000 (this is the only remaining option).

A can now work in either N, P or Q (since M and O are already taken by B and E respectively). But from (5) we know that A does not work in N or P, so A works in Q and (from (2)) is 28 years old. Since A and D are 24 and 28 in some order, then D must be 24.

Well, now we used all the information provided. Our deductions can be summarised in the following table:

Name Age Salary Department
A 28 15000 Q
B 26 25000 M
C 32 20000 N or P
D 24 10000 N or P
E 30 30000 O

From there, we cannot in fact say if C or D works in N, there are insufficient data for this.

• +1 vote from me for a clear and sensible path :) – Graylocke Apr 7 at 7:58