Multiple choice

Passage

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question.

Find the total surface area of cylinder. (i) The ratio of the total surface area to the curved surface area of the cylinder is 5 : 2. (ii) The difference of the radius of cylinder and the height of the cylinder is 7 cm.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statements (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Both statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total surface area = 2*pi*r*(r+h). Curved surface area = 2*pi*r*h. (i) (r+h)/h = 5/2, so 2r + 2h = 5h, 2r = 3h. (ii) r - h = 7. We have a system of two equations with two variables, which is sufficient to find r and h, and thus the surface area.

AI explanation

The total surface area of a cylinder is 2 times pi times r times the sum of r and h, while the curved surface area is 2 times pi times r times h, so statement one gives the ratio of r plus h to h as 5 to 2, which simplifies to r equals 1.5 times h. Statement two provides the difference between the radius and the height, but without their ratio from the first statement we cannot find their actual values. By substituting r equals 1.5 times h into the second equation, we can solve for both variables and determine the total surface area. The result is that both statements together are sufficient, but neither alone is sufficient.

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