CAT 2007 — QA Question 19
Answer the next 2 questions based on the information given below.
Let a1 = p and b1 = q, where p and q are positive quantities.
Define:
an = pbn−1 bn = qbn−1, for even n > 1 and
an = pan − 1 bn = qan − 1, for odd n > 1.
Each question is followed by two statements A and B. Answer each question using the following instructions.
Mark (1) if the question can be answered by using statement A alone but not by using statement B alone.
Mark (2) if the question can be answered by using statement B alone but not by using statement A alone.
Mark (3) if the question can be answered by using both the statements together but not by using either of the statements alone.
Mark (4) if the question cannot be answered on the basis of the two statements.
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.
Answer & solution
- A
1
2
- C
3
- D
4
- E
5
Let the inner radius be r meter. Capacity of tank = (1 m3 = 1 kilolitre)
From statement A, since r ≥ 4m
∴ Capacity of tank > 256 m3
Since the capacity needed is more than 256 m3 statement A is insufficient.
From statement B,
Volume of the material of tank = mass/density = 30000kg/(3 gm/cc) = 10,000,000 cm3 = 10 m3
Hence the inner volume of tank = Outer volume – Volume of material of tank
Therefore, we can say that the tank capacity is adequate.
Hence, option (b).