Bunuel wrote:
Machine A is made up of a rectangular box filled with x cylinders of ball bearings placed together such that the diameter of the bearings and the cylinders are equal, and the cylinders line up evenly, touching, with no extra room inside the box. If the cylinders are the same height as the box, and the box is 18 inches long and 10 inches wide, what’s the value of x?
(1) 9 cylinders can line up along the length of the box.
(2) Each ball bearing has a radius of 1.
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTIONThe correct response is (D). In order to find the value of x, we need to know the diameter of each cylinder. This is given to up by Statement (2) since twice the radius of the ball bearing will equal the cylinder’s diameter. If each cylinder has a diameter of 2, then 45 will fit inside the box. Statement (1) is also sufficient. If the box is 18 inches long and 9 cylinders fit along that length, then they must each have a diameter of 2.
If you chose (A), Statement (2) is also sufficient since we know the radius is one-half of the diameter.
If you chose (B), Statement (1) is also sufficient since the problem specified there was “no extra room inside the box.”
If you chose (C), the statements are actually independently sufficient already. You may have needed to draw and label a diagram to better visualize the question.
If you chose (E), the statements are sufficient on their own. Try some more word problems involving data sufficiency to better get the hang of mining the length descriptions in these questions for the important information.