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CAT 2025 Set-1 | Data Interpretation and Logical Reasoning | Question-16

Comprehension:

A train travels from Station $\text{A}$ to Station $\text{E}$, passing through stations $\text{B, C}$, and $\text{D}$, in that order. The train has a seating capacity of $200$. A ticket may be booked from any station to any other station ahead on the route, but not to any earlier station.

A ticket from one station to another reserves one seat on every intermediate segment of the route. For example, a ticket from $\text{B}$ to $\text{E}$ reserves a seat in the intermediate segments $\text{B-C}$, $\text{C-D}$, and $\text{D-E}$.

The occupancy factor for a segment is the total number of seats reserved in the segment as a percentage of the seating capacity. The total number of seats reserved for any segment cannot exceed $200$.

The following information is known.

  1. Segment $\text{C - D}$ had an occupancy factor of $95 \%$. Only segment $\text{B - C}$ had a higher occupancy factor.
  2. Exactly $40$ tickets were booked from $\text{B}$ to $\text{C}$ and $30$ tickets were booked from $\text{B}$ to $\text{E}$.
  3. Among the seats reserved on segment $\text{D}-\text{E}$, exactly four-sevenths were from stations before $\text{C}$.
  4. The number of tickets booked from $\text{A}$ to $\text{C}$ was equal to that booked from $\text{A}$ to $\text{E}$, and it was higher than that from $\text{B}$ to $\text{E}$.
  5. No tickets were booked from $\text{A}$ to $\text{B}$, from $\text{B}$ to $\text{D}$ and from $\text{D}$ to $\text{E}$.
  6. The number of tickets booked for any segment was a multiple of $10$.
How many tickets were booked from Station $\text{C}$?

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