CAT 1999 — QA Question 30
Answer the next 2 questions based on the following information.
There are blue vessels with known volumes v1, v2..., vm, arranged in ascending order of volume, v1 > 0.5 litre, and vm < 1 litre. Each of these is full of water initially. The water from each of these is emptied into a minimum number of empty white vessels, each having volume 1 litre. The water from a blue vessel is not emptied into a white vessel unless the white vessel has enough empty volume to hold all the water of the blue vessel. The number of white vessels required to empty all the blue vessels according to the above rules was n.
Among the four values given below, which is the least upper bound on e, where e is the total empty volume in the white vessels at the end of the above process?
Answer & solution
- A
mvm
- B
m(1 - vm)
- C
mv1
m(1 - v1)
Let m = 1. So, option (a) will give the answer as Vm and option (c) will give the answer as V1. Both of these cannot be the answers as Vm and V1 are the amount of volume filled.
Let m = 2. So, option (b) will give the answer as 2 (1 – V2) and option (d) will give the answer as 2(1 – V1). Now consider option (b).
Actual empty volume > 2(1 – V2). Therefore, for this situation m(1 – V1) is the only possible answer.
Hence, option (d).