Discussion
Thirty-six vehicles are parked in a parking area in a single row. After the first car, there is one scooter. After the second car, there are two scooters and so on. Work out the number of scooters in the second half of the row.
Answer: C
There are 15 scooters in the second half.
Each car is followed by a growing number of scooters: car 1 then 1 scooter, car 2 then 2 scooters, and so on. After the 7th car and its 7 scooters, the row holds 7 + (1 + 2 + ... + 7) = 7 + 28 = 35 vehicles, so the 36th vehicle is the 8th car.
Numbering the positions: cars stand at 1, 3, 6, 10, 15, 21, 28 and 36, and every other position holds a scooter. The second half is positions 19 to 36. Its scooters are at 19 and 20 (2, after car 5), 22 to 27 (6, after car 6) and 29 to 35 (7, after car 7): 2 + 6 + 7 = 15.
As a check, the row has 28 scooters in all, so the first half holds 13, and 13 + 15 = 28.
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