Round Table Arrangement

Question

Eight people – A, B, C, D, E, F, G and H are sitting around a circular table facing the centre, but not necessarily in the same order. All of them are at equidistant. Each one of them teaches different subjects viz., English, Hindi, Mathematics, Biology, Psychology, Physics, Chemistry and Accounts, but not necessarily in the same order.

 The person who teaches Accounts, sits third to the right of G. C is an immediate neighbour of G. The person who teaches Mathematics sits second to the left of C. B sits third to the right of H. H teaches neither Accounts nor Mathematics. Only two persons sit between C and the person who teaches Physics. A and F are immediate neighbours of each other. Neither A nor F teaches Accounts. The person who teaches English sits second to the right of A. Two persons sit between D and the person who teaches Hindi. D does not teach Accounts. The person who teaches Psychology is an immediate neighbour of the person who teaches Accounts. The person who teaches Physics sits second to the left of A. One of the immediate neighbours of G teaches Chemistry.

 1. Who among the following teaches Chemistry?

1. A
2. H
3. D
4. G
5. None of these

Comments

https://gateoverflow.in/9770/who-among-the-following-teaches-chemistry

Answer 1

A B C D E F G

We have eight people and eight seats around a round table, so a person has two neighbours. Just writing the given conditions: '-' shows a place taken by a undecided person. (Accounts) means the person teaching Accounts.

1. G _ _ (Accounts)
2. G C or C G
3. (Maths) _ C
4. H _ _ B
5. H no Accounts no Maths
6. C _ _  (Physics) or (Physics) _ _ C
7. A F or F A - both not Accounts
8. A _ (English)
9. D _ _ (Hindi) or (Hindi) _ _ D  D not Accounts
10. (Accounts) (Psychology) or (Psychology) (Accounts)
11. (Physics) _ A
12. G (Chemistry) or (Chemistry) G

First seeing Accounts- it is not taught by G or C or H or A or F or D. So either B or E. But seeing the conditions 1 and 4, B cannot be Accounts as G != H. So, Accounts must be taught by E - condition 13. 

So,
G _ _ E
E is teaching Accounts

Now A F cannot go in the two missing places above as
G A F E would mean G A F E H _ _ B, making A and B (or F and B) the neighbors of G, but C must be a neighbor of G as per question.

So, E is teaching Accounts and AF cannot be between G and E. Also, an interesting condition given in conditions 6 and 11 because it says either C _ _ _ _ A or A C. Now lets see the possibilities for placing H _ _ B by trying to place H in all possible places.

Case 1: G H _ E B _ _ _ but we have C neighbor of G, so, we get 
G H _ E B _ _ C -After C the fifth place is taken by B. So, A C must be there. Thus, we get
G H D E B F A C as Case 1.

Case 2: G _ H E _ B _ _ only place for A F is at the end and C is a neighbor of G. So, this case leads to 
G C H E D B A F (again using C _ _ _ _ A).

Case 3: G _ _ E H _ _ B - again we can place C and AF giving G C D E H F A B as case 3.

Case 4: G B _ E _ _ H _ - again we can place C and AF giving G B D E A F H C as case 4.

Case 5: G _ B E _ _ _ H - again we can place C and AF giving G C B E D F A H as case 5. 

So, lets assign the subjects in each case:

Condition No.	Case 1 G H D E B F A C	Case 2 G C H E D B A F	Case 3 G C D E H F A B	Case 4 G B D E A F H C	Case 5 G C B E D F A H
13	E- Accounts	E - Accounts	E - Accounts	E - Accounts	E - Accounts
8	G - English	G - English	G - English	H - English	G - English
11	B - Physics	D - Physics	H - Physics	D - Physics	D - Physics
3	F - Maths	F - Maths	B - Maths	F - Maths	H - Maths violates 5
9	C - Hindi	C - Hindi violates 12	F - Hindi	C - Hindi
10	D - Psychology		D - Psychology	A - Psychology
12	H - Chemistry		C - Chemistry	B - Chemistry
	A - Biology		A - Biology	G - Biology

 

So, there are 3 possibilities for Chemistry- H, C or B. So, answer must be None of these. 

Comments

So, only 3 possibilities are there with G -- E and H -- B and totally 8 seats.
 Case 1: G H D E B F A C
 Case 2: G C H E D B A F
 Case 3: G C H E D B F A


How to construct these three cases I mean to say trick behind these three case(approach) ?

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Sorry. My answer was wrong. See now, I have explained clearly.

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it becomes a very complex question

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It's not easy. But good to practice tough questions for reasoning.