A grocer, a doctor, a lawyer, a tailor and a barber are the five perso

Question

A grocer, a doctor, a lawyer, a tailor and a barber are the five persons seated in a row. The grocer does not wish to sit immediately next to the barber. The barber and the tailor sit immediately next to each other. The lawyer is at the right end of the row. The grocer is immediately to the left of the lawyer. Who is in the middle of the row?

(A) tailor
(B) doctor
(C) barber
(D) Cannot be determined

Show Spoiler

D

(A) tailor 
(B) doctor 
(C) barber 
(D) Cannot be determined

D

Regor60 · Answer

By the question stem the grocer and lawyer occupy these positions:

_ _ _ G L

The barber, tailor and doctor could occupy as follows:

B T D G L and B & T could of course switch positions

OR

D B T G L

So since either the doctor or the tailor could occupy the middle position it cannot be determined

Izee · Answer

C

napolean92728 · Answer

Official Answer:

We have five people (grocer, doctor, lawyer, tailor, barber) seated in a row with the following constraints: 
 
  The lawyer is at the right end of the row  
  The grocer is immediately to the left of the lawyer  
  The barber and tailor sit immediately next to each other  
  The grocer does not wish to sit immediately next to the barber

From constraints 1 and 2, we can immediately determine:
 
  Position 4:  Grocer (G) 
  Position 5:  Lawyer (L)  
This gives us the partial arrangement:  _ _ _ G L

The remaining three people (doctor, barber, tailor) must occupy positions 1, 2, and 3.
From constraint 4: The grocer cannot sit next to the barber, so the barber cannot be in position 3 (which would be adjacent to the grocer in position 4).
From constraint 3: The barber and tailor must be adjacent to each other.

Since the barber cannot be in position 3, the barber must be in position 1 or 2.
 Case 1:  Barber in position 1
 
 Tailor must be in position 2 (to satisfy adjacency) 
 Doctor must be in position 3 
  Arrangement:  B T D G L

Case 2:  Barber in position 2
 
 Tailor can be in position 1 OR position 3 (both are adjacent to position 2) 
  Sub-case 2a:  T B D G L (tailor in position 1, doctor in position 3) 
  Sub-case 2b:  D B T G L (doctor in position 1, tailor in position 3)

All three arrangements satisfy the given constraints:
 
  B T D G L:  ✓ All constraints met, doctor in middle 
  T B D G L:  ✓ All constraints met, doctor in middle 
  D B T G L:  ✓ All constraints met, tailor in middle

Since we have valid arrangements where either the  doctor  or the  tailor  could occupy the middle position (position 3), the identity of the person in the middle cannot be uniquely determined from the given information.

Answer: (D) Cannot be determined

napolean92728 · Answer

Congratulations  Regor60   for giving the right answer.  Izee , I hope you have understood the right approach to solve the question.

P.S. You have been awarded kudos for trying the problem.

A grocer, a doctor, a lawyer, a tailor and a barber are the five perso

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