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Q154. The question is followed by three statements I, II and III. Determine which statement or statements are sufficient to answer the question. The slant height of a cone is x cm. If the side of a square is (x+5) cm, then find the area of the square. I. The ratio of the diameter of the cone to its height is 3:2. II. The base and height of a cylinder are the same as the base and height of the cone respectively. The volume of the cylinder is 450\pi cm^3. III. The total surface area of the cone is 600\pi cm^2 and the curved surface area of the cone is 375\pi cm^2. A) Statement II and III together are sufficient to answer the question B) Statement I alone is sufficient to answer the question C) All the three statements taken together are necessary to answer the question D) Statement I and II together are sufficient but III alone is not sufficient E) Either statement I and II together or statement III alone is sufficient to answer the question

1. Statement II and III together are sufficient to answer the question
2. Statement I alone is sufficient to answer the question
3. All the three statements taken together are necessary to answer the question
4. Statement I and II together are sufficient but III alone is not sufficient
5. Either statement I and II together or statement III alone is sufficient to answer the question

Correct answer: Either statement I and II together or statement III alone is sufficient to answer the question

Solution

The area of the square depends on x, so we need x. Statement I alone is not enough, but I and II together can determine the cone’s dimensions and hence x. Statement III alone gives enough information to find the cone’s radius and slant height directly, so either I and II together or III alone is sufficient.

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