Graduate Management Admission Test (GMAT) Practice Test

In mathematical terms, what does the factorial symbol represent?

1. The product of a number and all positive integers less than it

2. The sum of a number and all positive integers less than it

3. The largest integer less than a number

4. The smallest integer greater than a number

The correct answer is: The product of a number and all positive integers less than it

The factorial symbol, denoted by an exclamation point (n!), represents the product of a number and all positive integers less than that number. For instance, if n is 5, then 5! (5 factorial) is calculated as 5 × 4 × 3 × 2 × 1, which equals 120. This definition is fundamental in combinatorics, statistics, and various areas of mathematics, as it provides a way to count arrangements or permutations of a set of objects. When considering the other options, they do not accurately describe the factorial operation. The second option deals with summation rather than multiplication. The third option refers to the floor function, which identifies the largest integer less than or equal to a given number. The fourth option is related to the ceiling function, indicating the smallest integer greater than or equal to the number. Understanding the specific definition of factorial is crucial in solving problems that involve arrangements or selections, making option A the only correct representation of the factorial symbol.