The product of 3 integers A, B, and C is 4096. The geometric mean of B and C is 32, whilst that of A and B is 8. Calculate C.

In a potato race, a bucket is placed at the starting point, which is $5$m from the first potato, and the other potatoes are placed $3$m apart in a straight line. There are $20$ potatoes in the line. Each competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it, and continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

The sum of 30 terms of the series $\sqrt{2} + \sqrt{8} + \sqrt{18} + \sqrt{32} + ...$ is

A lift carrying 50 passengers from the ground floor of a 100-storeyed building is moving upwards. The lift stops at the 1st, 2nd, and 3rd floor, then skips the 4th floor, again stops at the 5th, 6th, and 7th, then skips the 8th floor, and so on. Passengers get discharged in a pattern. 2, 3, 3, 2, 3, 3..... On which floor does the lift become empty?

If $p, q,$ and $r$ are in geometric progression, which of the following is true about $qr, pr,$ and $pq$?