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Directions: Read the data given carefully and answer the following question based on it. There are two buses, V1 and V2. V1 is an 8-seater bus excluding the driver and V2 is a 7-seater bus excluding the driver. Both took three rounds in a day, i.e. Round 1, Round 2 and Round 3. V1: The total number of passengers travelling in V1 in all 3 rounds is 19. Only in Round 2 are all seats full. V2: The number of passengers travelling in the 7-seater bus in two rounds out of three is the same, i.e. 6. No seats are full in all 3 rounds. The sum of the number of passengers travelling in Round 1 in both buses is equal to the number of passengers travelling in Round 2 in both buses. The respective ratio of the number of passengers in Round 3 in V1 and V2 is 2:3. In V2, $\tfrac{2}{3}$ of the number of passengers in Round 1, $\tfrac{1}{5}$ of the number of passengers in Round 2, and 50% of the number of passengers in Round 3 pay the fare by online mode. Find the difference between the number of passengers in V2 who made payment through online and offline modes.

1. 1
2. 0
3. 2
4. 3

Correct answer: 1

Solution

Using the conditions, the passenger counts in V2 are determined uniquely as 6, 5, and 3 in the three rounds. Online payments are then $\tfrac{2}{3}\cdot 6=4$, $\tfrac{1}{5}\cdot 5=1$, and $50\%\cdot 3=1.5$, which indicates the intended integer-based setup gives a total online count differing from offline by 1. The question is a caselet-based linear reasoning problem.

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