Last Updated on May 11, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We need to determine the number of people in the line who are behind Beth, given that Beth is standing behind Adam and the number of people in front of Adam plus the number of people behind Beth is 18. If we know the number of people who are in front of Adam and the number of people who are strictly between Adam and Beth, then we can determine the number of people who are behind Beth.
Statement One Alone:
There are a total of 32 people in the line.
Since there are a total of 32 people in the line, subtracting Adam, Beth, and the 18 people who are either in front of Adam or behind Beth, we know that there are 12 people between Adam and Beth. However, since we don’t know the exact number of people who are in front of Adam, we can’t determine the number of people who are behind Beth. Statement one alone is not sufficient.
Statement Two Alone:
23 people in the line are behind Adam.
We are given that 23 people in the line are behind Adam. However, since we don’t know the number of people who are between Adam and Beth, we can’t determine the number of people who are behind Beth. Statement two alone is not sufficient.
Statements One and Two Together:
From the two statements, we know that there are a total of 32 people in the line and that 23 people in the line are behind Adam. Thus, there must be 32 – 23 – 1 = 8 people who are in front of Adam (note the number 1 is for Adam). From statement one, we also know that 12 people are between Adam and Beth. Thus, there are 32 – 8 – 12 – 2 = 10 people behind Beth (note the number 2 is for Adam and Beth).
Answer: C
