Welcome to The Library

The Library is your online learning center. Instructors post intriguing problems here for you to solve in collaboration with other students. Whether you’re looking for SAT prep or some other academic challenge, The Library has something for you. Problems cover a variety of disciplines and a range of difficulty levels. Solutions are also available to be checked out from The Library, all written by the instructors themselves. If you don’t find what you need here, more resources are available in the form of private tutoring sessions and test prep courses. Contact us to inquire further about these options.

Here are some sample SAT problems for you to get started with. You can also search The Library at any time to discover many more stimulating and challenging exercises.

SAT test makers like to ask questions about even and odd integers. Part (c) of this problem is similar to an actual SAT question (the multiple choice options are removed). Use parts (a) and (b) to help answer part (c). Then explore even and odd numbers in more depth with parts (d) and (e).

1. Explain why multiplying any integer by 2 results in an even integer.
2. If is a positive integer, write an expression for the following.
1. An even integer
2. An odd integer
3. If is a positive integer, write an expression for en even integer that is twice the value of an odd integer.
4. When the positive odd integer is doubled, the result is three times . Which of the following, if any, MUST be false?
1. is an even integer
2. is an odd integer
3. is not an integer
5. Twice the sum of three consecutive odd integers is the same as the sum of three consecutive even integers. Find one possible set of such integers.