Bunuel wrote:
A certain lighthouse is a tall thin cylinder of brick, with a light chamber at the top. The brick extends from the ground to the floor of the light chamber. The brick siding of lighthouse is in need of painting. How many square feet of brick does it have?
(1) The outer diameter of the brick portion of the lighthouse is 28 ft
(2) There are 274 steps from ground level to the floor of the light chamber, and each one is 8 inches high.
Kudos for a correct solution.
MAGOOSH OFFICIAL SOLUTION:The lighthouse is essentially a cylinder, and the area that needs to be painted is the lateral surface area. We would need both r and h to calculate this.
Statement #1 tells us diameter = 28, which means radius = 14. We know the radius, but not the height. Statement #1 by itself is insufficient.
In Statement #2, the 274 steps go from the very bottom to the very top of the cylinder in question. We know each step is 8 inches, so the total height traversed by the steps is 274*8 in. We would have to change that result from inches to feet, but essentially, with this piece of information, we have the height. We know the height, but not the radius. Statement #2 by itself is insufficient.
Combined. Statement #1 gives us the radius, statement #2 gives us the height, and we’re in business! We now have enough information to calculate the lateral surface area. Combined, the statements are sufficient.
Answer = C.