##### GRE

On the GRE Math test, Quantitative Comparison problems cover a wide range of subjects. For example, a word problem might require you to work with mixtures, Venn diagrams, counting methods, and work problems.

In a Quantitative Comparison question, the problem lists Quantity A and Quantity B, which can be numbers, variables, equations, words, figures, and so on. Your job is to compare these two quantities and determine whether one is greater, they're equal, or the relationship can't be determined.

The following practice questions ask you to compare wood lengths and distances traveled.

## Practice questions

1. A 10-foot plank of wood is cut into four pieces, with three having equal lengths and one having a shorter length. Which quantity is greater?

A: The length of one of the equal pieces

B: 3 feet

A. Quantity A is greater.

B. Quantity B is greater.

C. The quantities are equal.

D. It cannot be determined from the information given.

2. A beach resort is 2 kilometers from the city, and a sports complex is 10 kilometers from the city. The city, resort, and sports complex all lie at sea level. Which quantity is greater?

A: The distance from the beach resort to the sports complex

B: 7 kilometers

A. Quantity A is greater.

B. Quantity B is greater.

C. The quantities are equal.

D. It cannot be determined from the information given.

## Answers and explanations

1. D. It cannot be determined from the information given.

The length of the equal parts could be 3, in which case the leftover part would be 1 foot long. But, nothing says that the equal parts have to be integer values. For example, if the equal parts were 3.1 feet each, then the leftover part would be 0.7 feet.

The relationship cannot be determined from the information given, Choice (D).

2. A. Quantity A is greater.

The easiest approach to this is to draw a sketch. Put a point for the city. Draw a circle with a radius of 2 centered on the city, on which the beach resort can lie. Draw a circle with a radius of 10 centered on the city, on which the sports center can lie. Wherever you put the resort and the sports center on these circles, they can never be closer than 8 kilometers, which is the shortest distance between the circles. Choice (A) is the correct answer.