Multiple-Choice, One Answer on the GRE Math Test — Practice Questions
The GRE Math test contains several multiple-choice questions where you are given a list of five answer choices and you have to pick the correct one.
In the following practice questions, you’re asked to solve a simple volume/surface area problem, and then a word problem involving probability.
If the volume of a cube is 27, what is the surface area?
A lottery machine randomly selects three balls, one at a time and without replacement, from n balls in a barrel. The balls are labeled numerically 1 through n, with no two balls the same. If an employee adds one more uniquely numbered ball to the barrel, in terms of n, how many three-number combinations can be produced by the lottery machine?
Answers and explanations
The volume of a cube is e3, where e represents an edge, so back solve the cube with a volume of 27 to find the edge length of 3. The surface area is the sum of the areas of each face. Because each edge is 3, each face is 9. Six faces give the cube a surface area of 54.
Because the employee added a new ball, the number of balls in the machine is n + 1, which is also the number of possibilities for the first ball selected. The numbers of possibilities for the second and third balls selected are n and n – 1, respectively. Multiply these together for n(n2 – 1).