Knewton Brutal Challenge (Math Edition) - Week 21

by Knewton, Aug 25, 2010

Get those explanation-muscles ready, because this week's Brutal Math Question is not messing around. No shirts this week (they'll be back soon!), but the pride in explaining the right answer first knows no bounds.

Leave your best shot in the comments. Good luck!

A vertically oriented cylindrical tank, a rectangular solid tank, and a cubic tank sit flat on the floor of a factory. Three pumps are turned on simultaneously, each of which pumps water at a different, constant rate, one pump from the cylindrical tank to the rectangular solid tank, one pump from the rectangular solid tank to the cubic tank, and one pump from the cubic tank to the cylindrical tank. The pumping mechanisms are already filled with water before pumping begins, so that there is no change in the amount of water contained within the pumping mechanisms. If the area of the base of the cylindrical tank is equal to the area of one face of the cubic tank, how many feet will the water level (the height which the water reaches in a tank) have risen in the cylindrical tank after 45 minutes? Assume that none of the tanks overflows or completely drains in 45 minutes.

1. After 30 minutes, the water level of the cubic tank has decreased by 2 feet, and the water level of the rectangular solid tank, whose bottom face has a length and width that are respectively twice and three times as long as an edge of the cubic tank, has decreased by 3 feet.

2. After 30 minutes, the volume of water in the cubic tank has decreased by 800 cubic feet, and the volume of the rectangular solid tank has decreased by 7,200 cubic feet.

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

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

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.