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Problems in More Than Three Variables

Directions for questions 7 to 8: Read the following passage and solve the questions based on it.

Five men from five different states work in an office and each of them performs a different work. Each comes to the office using a different mode of travel and most work on different shifts (There are three shifts; the second shift starts after the first shift and ends before the third shift). All the five persons working in the same shift come at the same time.

  1. Hari, who is not from West Bengal (WB), does not walk to work.
  2. Narayan is not a GL.
  3. The man who works in the third shift and whose name is not Javed does not use the bus.
  4. Simon, who is not from UP, uses a bicycle to go to work. He is not a technician.
  5. The man from Karnataka is not called Narayan and he comes to work after the assembler but before Abbas.
  6. The man from Bihar and the person who walks, both work on the first shift.
  7. The GL comes to work before the man who uses the train.
  8. Javed comes to work after the man from Gujarat but before the man who uses a scooter.
  9. Narayan and the man who uses the bus work on the same shift.
  10. The man from UP and the tester work in the second shift.
  11. The stock clerk works on the third shift.

Q 1. Which of the following statement(s) is (are) true?

  1. The man from Karnataka and the stock clerk work in the same shift.
  2. Abbas and the technician work in the same shift.
  3. The man who comes by bus and Simon work in the same shift.
  4. Hari and the man who comes walking work in the same shift.
    1. I only
    2. None
    3. IV only
    4. All are true

Q 2. Which of the following statement(s) is (are) true?

  1. The GL comes by bus and the assembler walks to work.
  2. The stock clerk comes by bus and the tester by train.
  3. The stock clerk comes by scooter and the technician by train.
  4. The assembler comes by bicycle and the tester by train.
    1. I and III only
    2. II only
    3. I only
    4. None

Solution
 

Scenario

We have already seen that this question set is of 5 variables.

1st variable – Five men

2nd variable – Five states

3rd variable – Different job

4th variable – Mode of travel

5th variable – Work-shift

  1. The five persons are—Hari, Narayan, Simon, Javed and Abbas.
  2. The five modes of travel are—Bus, Walk, Bicycle, Train and Scooter.
  3. The five states are—Bihar, UP, WB, Karnataka and Gujarat.
  4. The five works are—GL, Assembler, Tester, Technician and Stock Clerk.
  5. The three shifts are—1st shift, 2nd shift and 3rd shift.

Rules

There are two major bottlenecks with this problem set:

  • Most of the statements given in the beginning have a negative connotation.
  • A total of eleven statements are given.

Ideally, in these types of situations where a good amount of information is given, we should first go through all the statements and then find out the statement with the maximum concrete facts.


Let us first make a table denoting all the variables:

 

Shift

State

Work

Mode of Travel

Hari

 

 

 

 

Narayan

 

 

 

 

Simon

 

 

 

 

Javed

 

 

 

 

Abbas

 

 

 

 


 

 

Statement (v)

Karnataka – 2nd shift

Neither Abbas nor Narayan

Assembler – 1st shift

Abbas – 3rd shift

Statement (viii)

Javed – 2nd shift

Gujarat – 1st shift

Scooter – 3rd shift

Statement (vi)

Bihar – 1st shift

Walk – 1st shift

Statement (x)

UP – 2nd shift

Tester – 2nd shift

Statement (iv)

Narayan – 1st shift

Bus – 1st shift


What deductions can we make from the above statements?


Deduction 1 – Since there are five persons and two persons each are coming in the 1st shift and 2nd shift, so we can conclude that only one person is coming in the 3rd shift We will do more deductions after filling up the space for the person who comes in the 3rd shift.

Abbas – 3rd shift – Scooter – Stock Clerk (Using statement xi)


However we are still not sure about the state to which Abbas belongs. Let us find it out through the process of elimination:


Possible states – Bihar, UP, WB, Gujarat, Karnataka


Possible state for Abbas:

 


Hence, West Bengal is the only possibility for Abbas.


Let us fill the table with the newly acquired information:

 

Shift

State

Work

Mode of Travel

Hari

 

 

 

 

Narayan

1st

Gujarat/Bihar

 

Bus/Walk

Simon

 

 

 

 

Javed

 

 

 

 

Abbas

3rd

WB

Stock Clerk

Scooter


We can fill up some more blanks above with the various possibilities (as we did in the case of Narayan’s state).


Now we have a good amount of information regarding the persons working in the first shift:

 


 

Thus, we can have the following arrangement:
 


Still we are not sure if Narayan is an assembler or not? To find it out, we will go to some other unused statements. Let us use statement (vii):

Statement (vii): GL – 1st shift


Train user – 2nd shift (Because person who commutes by train cannot come in 3rd shift, as Abbas is coming in 3rd shift).


Using statement (ii), Narayan is not a GL, so he has to be an Assembler.

 

 
 

Let us fill up the table with the new information again:
 

 

Shift

State

Work

Mode of Travel

Hari

 

 

 

 

Narayan

1st

Gujarat

Assembler

Walk

Simon

 

 

 

 

Javed

 

 

 

 

Abbas

3rd

WB

Stock Clerk

Scooter


To find out the 2nd person working in 1st shift, now we will use the process of elimination:

 

 


The possible options for the 2nd person is either Hari or Simon. Using statement (iv), Simon comes on a bicycle. However, the 2nd person working in the 1st shift comes by bus. So, Simon is not possible in the 1st shift. Hence, Hari is the 2nd person coming in the first shift.

 

 

Shift

State

Work

Mode of travel

Hari

1st

Bihar

GL

Bus

Narayan

1st

Gujarat

Assembler

Walk

Simon

 

 

 

 

Javed

 

 

 

 

Abbas

3rd

WB

Stock Clerk

Scooter


Now we are left with the variables attached to only the 2nd shift. Let us write them one by one:

 


 

Hence, the final table is:
 

 

Shift

State

Work

Mode of travel

Hari

1st

Bihar

GL

Bus

Narayan

1st

Gujarat

Assembler

Walk

Simon

2nd

Karnataka

Tester

Bicycle

Javed

2nd

UP

Technician

Train

Abbas

3rd

WB

Stock Clerk

Scooter





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