GMAT Practice Question: 3, k, 2, 8, m, 3 The arithmetic mean of the list of numbers above is 4 . If k and m...
Question
3, k, 2, 8, m, 3 The arithmetic mean of the list of numbers above is 4 . If k and m are integers and k is not equalt to m what is the median of the list?
- 2
- 2.5
- 3
- 3.5
- 4
Topics: mean, median, word problems
Solution
Step 1
Write the equation relating the arithmetic mean to the sum of the six numbers.
3 + k + 2 + 8 + m + 3 = 4 \times 6
Step 2
Simplify each side of the equation.
16 + k + m = 24
Step 3
Isolate the sum of k and m.
k + m = 8
Step 4
Since k and m are distinct integers whose sum is 8, one must be less than 4 and the other greater than 4.
\min(k,m) < 4 < \max(k,m)
Step 5
When the six numbers are arranged in ascending order, the two original 3's occupy the third and fourth positions.
\{\min(k,m),\,2,\,3,\,3,\,\max(k,m),\,8\}
Step 6
Since we have an even number of values, the median is the average of the two middle values (third and fourth numbers in the ordered list).
\frac{3 + 3}{2} = 3
Answer
3 (C)
