Question
How many shopkeepers auctioned between the one, who
auctioned Levis and the one, who has Toyota cars? Study the following information carefully and answer the questions given below it. Seven shopkeepers namely – Z, Y, X, W, V, U and T auctioned different shoes viz. Puma, Adidas, Nike, Levis, Woodland, Liberty and Reebok from Monday to Sunday. Each of them has different cars viz. Honda, Ford, BMW, Toyota, Volvo, Mahindra and Renault. All the above given information is not necessary in same order. There were three days gap between the one who has Volvo and the one who auctioned Reebok. The one, who auctioned Puma, auctioned on any day after Friday. There were two days gap between the one, who have Toyota and U who auctioned Puma. There were three days gap between W and the one who auctioned Nike. One person auctioned between the one who auctioned Reebok and X, who has Honda. The one, who auctioned Woodland, auctioned on adjacent day of the one who has Mahindra. At least three person auctioned between the one, who auctioned Levis and the one, who has Renault. There were two days gap between T and the one who auctioned Ford, who auctioned on adjacent day of the one who has Toyota. X neither auctioned on adjacent day of the one has Toyota nor on adjacent day of U. Z auctioned Adidas on Tuesday. T neither has Volvo nor auctioned before the one who auctioned Woodland and he auctioned Liberty. W and the one who has BMW, auctioned the shoes on adjacent days. Neither W nor Y auctioned Nike. There were two days gap between Z and the one who has Mahindra.Solution
The one, who auctioned Puma, auctioned on any day after Friday, that means we have two possible day for the one who auctioned Puma, in case (1) the one who auctioned Puma, auctioned on Saturday, in case (2) the one who auctioned Puma, auctioned on Sunday. There were two days gap between the one, who have Toyota and U who auctioned Puma. Z auctioned Adidas on Tuesday. There were two days gap between Z and the one who has Mahindra. The one, who auctioned Woodland, auctioned on adjacent day of the one who has Mahindra, that means we have three possible day for the one who auctioned Woodland, in case (1) & case (2a) the one who auctioned Woodland auctioned on Thursday, in case (2b) the one who auctioned Woodland auctioned  on Saturday. Based on above given information we have- 
We have:  X neither auctioned on adjacent day of the one has Toyota nor on adjacent day of U. One person auctioned between the one who auctioned Reebok and X, who has Honda, that means X auctioned on Monday. There were three days gap between the one who has Volvo and the one who auctioned Reebok. T neither has Volvo nor he auctioned before the one who auctioned Woodland and he auctioned Liberty. There were two days gap between T and the one who auctioned Ford, who auctioned on adjacent day of the one who has Toyota, that means case (2b) is not valid, in case (1) T auctioned on Friday, in case (2a) T auctioned on Saturday. Based on above given information we have: 
Case (2b) is not valid as T doesn’t like before the one who auctioned Woodland. Again, we have: The one who has BMW and W auctioned on adjacent days. There were three days gap between W and the one who auctioned Nike, that means in case (1) W auctioned on Wednesday, in case (2) W auctioned on Friday. Neither W nor Y auctioned Nike, that means in case (1) Y auctioned Woodland. At least three person auctioned between the one, who auctioned Levis and the one, who has Renault, that means case (2a) is not valid. Based on above given information we have final arrangement we have: 
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