### CAT 1999 Question Paper Question 39

Instructions

DIRECTIONS for the following questions: These questions are based on the situation given below:

There are m blue vessels with known volumes $$V1, V2 , ...., V_m$$, arranged in ascending order of volume, where $$v_1 > 0.5$$ litre, and $$V_m < 1$$ 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.

Question 39

# Let the number of white vessels needed be n1 for the emptying process described above, if the volume of each white vessel is 2 liters. Among the following values, which is the least upper bound on n1?

Solution

To find the limiting value, let us consider that all the blue vessels are of 1 litre capacity.

If all the blue vessels have 1 litre capacity, then the number of white vessels required is smallest integer greater than or equal to (m/2).

But, blue vessels are all not of the same capacity => the above value of n1 is the upper bound.