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Data Sufficiency - Spherical tank water capacity

CAT 2007 Slot 1 · Quantitative Ability · Medium · Data Sufficiency

This is a medium Quantitative Ability question from the CAT 2007 Slot 1 paper. It tests Data Sufficiency. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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.

  1. A.

    Question can be answered using A alone but not using B alone

  2. B.

    Question can be answered using B alone but not using A alone

  3. C.

    Question can be answered using A and B together, but not using either A or B alone

  4. D.

    Question cannot be answered even using A and B together

Answer

B

Explanation

Statement A gives an inner diameter of at least 8 meters, which means volume is at least 43π(4)3≈268\frac{4}{3}\pi (4)^3 \approx 268 kilolitres, but could be larger or smaller than 400 kilolitres. Statement B gives weight and density, which allows exact calculation of the material volume, and thus the exact inner radius and exact water capacity. B alone is sufficient.

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