Last Updated on May 9, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We need to determine how many integers are between, but not including, r and s.
To find the number of integers between two integers (not including them), we subtract 1 from the difference of the two integers.
To illustrate, let’s say the two integers r and s are 4 and 10, respectively; then, the number of integers between 4 and 10 (not including them) is 10 – 4 – 1 = 5. Sure enough, there are 5 integers between 4 and 10, namely 5, 6, 7, 8 and 9.
Thus, in this question we need to determine s – r – 1.
Statement One Alone:
s – r = 10
Since s – r = 10, s – r – 1 = 9. Thus, there are 9 integers between s and r. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C and D.
Statement Two Alone:
There are 9 integers between, but not including, r + 1 and s + 1.
Since we are given the number of integers that are between r + 1 and s + 1 we can create the following equation:
s + 1 – (r + 1) – 1 = 9
s + 1 – r – 1 – 1 = 9
s – r – 1 = 9
We again see that there are 9 integers between r and s. Statement two alone is also sufficient to answer the question.
Answer: D
