GMAT Practice Question: List S...
Question
List S consists of the positive integers that are multiples of 9 and are less than 100 . What is the median of the integers in S ?
- 36
- 45
- 49
- 54
- 63
Topics: divisibility, median, sequences & series
Solution
Step 1
We first list the elements of S and determine how many terms there are.
S = \{9, 18, ..., 99\} n = \frac{99 - 9}{9} + 1 = \frac{90}{9} + 1 = 10 + 1 = 11
Step 2
We note that S is an evenly spaced set so its median equals its average.
\text{median} = \frac{9 + 99}{2} = \frac{108}{2} = 54
Answer
54
