Multiple choice

Passage

Directions: Study the following information carefully and answer the given question carefully. In a railway station, three trains A, B and C would arrive and leave from the respective platforms. All the trains has different number of bogies and people in them. No two trains have the same number of bogies in them and no two trains would arrive or leave from the same platform. There are three platforms P1, P2 and P3. It is not necessary for the trains to arrive at the platforms in same order. The train which leaves from the platform with the odd prime number carries an average of 117 people in each bogie. The train which has 21 bogies arrives at P1. Train C arrives at P3. Train B leaves the platform at 8:30 p.m. The difference between the time Train A and the time Train C leave from their respective platforms is one hour. The maximum number of bogies in a train is 24. The total number of people in the train arriving at P2 is 2,618. Train A has 22 bogies. The train with the maximum number of bogies leaves the platform at 8:15 p.m. The train which leaves from P2 would leave after all the trains has left. The total number of people in all the trains altogether is 7,862 people.

What is the average number of people in each bogie of the train with 21 bogies?

  1. 117

  2. 120

  3. 112

  4. 116

  5. 119
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Based on the passage, the train with 21 bogies arrives at P1. The train leaving from an odd prime platform (P3 is prime) carries 117 people per bogie. Train C arrives at P3. Through deduction of the remaining constraints, the average for the 21-bogie train is determined to be 116.

AI explanation

The train with 24 bogies is at P2, so the train with 21 bogies is either A or C. Since Train A has 22 bogies, the 21-bogie train is at P1. The total number of people across all trains is 7862, and the P2 train has 2618 people. The train with the maximum 24 bogies at P3 carries 117 people per bogie, giving 24 * 117 = 2808 people. Subtracting the people in P2 and P3 from the total leaves 7862 - 2618 - 2808 = 2436 people in the 21-bogie train at P1. Dividing 2436 by 21 gives an average of 116 people per bogie.

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