CAT 2007 Question 2

Instructions

Directions for the following four questions: Each question is followed by two statements A and B. Indicate your responses based on data sufficiency

Question 2

ABC Corporation is required to maintain at least 400 Kilolitres of water at all times in its factory, in order to meet safety and regulatory requirements. ABC is considering the suitability of a spherical tank with uniform wall thickness for the purpose. The outer diameter of the tank is 10 meters. Is the tank capacity adequate to meet ABC’s requirements?

A: The inner diameter of the tank is at least 8 meters.

B: The tank weighs 30,000 kg when empty, and is made of a material with density of 3 gm/cc.

Solution

Using statement A alone, we can determine the inner volume of the tank to be at least 4/3 $$\pi$$ (125-64) = 256 $$m^3$$.
But we do not know if it is more than 400 $$m^3$$. So, using statement A alone, we cannot determine the answer.
Using statement B alone, volume of tank = 30000 kg / 3gm/cc = $$10^7 * 10^{-6}$$  = 10 $$m^3$$
So, inner volume = 4/3 $$\pi$$ 125 - 10 > 400 $$m^3$$
So, using statement B alone, we can answer the question



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