GMAT Focus EditionQuantitative ReasoningEasy
A local charity is organizing a raffle. They are selling tickets numbered from 100 to 999, inclusive. How many unique 3-digit ticket numbers are available for sale?
- A999
- B901
- C899
- D900
Show answer & explanationAnswer & explanation
Correct answer: D. 900
To find the number of integers in an inclusive range (from A to B), use the formula B - A + 1. In this case, 999 - 100 + 1 = 899 + 1 = 900. These are all the 3-digit numbers.
Why the other options are wrong
- A. This is the total number of tickets if they started from 1, not 100.
- B. Incorrect calculation.
- C. This is 999 - 100, which excludes one of the endpoints.
Counting Integers in a Range
To count the number of integers in an inclusive range from 'a' to 'b' (where 'a' and 'b' are integers and a ≤ b), the formula is b - a + 1.
- Applies to consecutive integers.
- The '+ 1' accounts for including both the start and end numbers.
- Useful for problems involving sequences, raffle tickets, or page numbers.
Memory trick: End Minus Start Plus One is Done.