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CAT 1999 — QA Question 31

MiscellaneousEasy
Passage / Data

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.

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

Answer & solution

  • A

    m4

  • Smallest integer greater than or equal to (n2)

  • C

    n

  • D

    Greatest integer less than or equal to (n2)

Solution

Let m = 1 and n = 1. Option (a) gives the answer as 14 and option (d) gives the answer as ‘greatest integer less than or equal to 12. So, both of these cannot be the answer. Option (b) gives the answer as ‘smallest integer greater than or equal to 12 and option (c) gives the answer as 1. But the actual answer can be greater than 1 as the volume of the vessel is 2 l.
Hence, (b) is the answer.

CAT 1999 QA Q31: Let the number of white vessels needed be n 1 for the emptying process described above, if the volume of each — Solution | TheCATExam