Practice GMAT Questions

We provide hundreds of world-class practice GMAT questions with detailed explanations, study guides, and a GMAT practice test for free so that anyone can succeed on the GMAT.

GMAT Practice Question (One of Hundreds)

A test maker is to design a probability test from a list of 21 questions. The 21 questions are classified into three categories: hard, intermediate and easy. If there are 7 questions in each category and the test maker is to select two questions from each category, how many different combinations of questions can the test maker put on the test?

A)	(7!/(5!2!))3
B)	(7!/(5!))3
C)	(7!/(2!))3
D)	3*29
E)	72

Correct Answer: A

The order of questions is not important and this is a combinations problem.

1. In this problem order is not important. For example, the selection of question 1, 8 and 21 is the same as the selection of question 21, 8 and 1. Since order is unimportant, the combination formula applies.
2. The formula for a combination is:
   _nC_r= n!/((n-r)!r!)
   where n is the total number of selections available and r is the number of items to be selected.
3. Since the test maker must select a total of six questions and two questions from each category, the combination formula is used. Since there are 3 categories and two questions will be selected for each of the 3 categories, total number of combinations is:
   =₇C₂*₇C₂*₇C₂
4. There are a total of (₇C₂)³ combinations.

The best way to achieve a good score on the GMAT is to master the content tested on the GMAT and practice it extensively. We sincerely believe anybody can score a 700 or higher with enough practice and study of the content tested by the GMAT. In order to help you achieve a high score, we are pleased to provide you with a series of high-quality GMAT sample questions and detailed explanations for free. Written by our staff, these questions have helped countless students achieve a top score. In addition, we provide a daily GMAT practice question RSS feed.