GMAT Practice Question: Three boxes of supplies have an average (arithmetic mean) weight of 7 kilograms and a median...
Question
Three boxes of supplies have an average (arithmetic mean) weight of 7 kilograms and a median weight of 9 kilograms. What is the maximum possible weight, in kilograms, of the lightest box?
- 1
- 2
- 3
- 4
- 5
Topics: word problems, mean, median, inequalities
Solution
Step 1
We assign variables to the weights in sorted order to avoid ambiguity.
x = \text{weight of lightest box},\;y = \text{weight of median box},\;z = \text{weight of heaviest box}
Step 2
We translate the average weight condition into an equation.
\frac{x + y + z}{3} = 7
Step 3
We translate the median weight condition into an equation.
y = 9
Step 4
We use the two equations to find a relationship between x and z.
x + y + z = 21 x + z = 21 - y x + z = 21 - 9 x + z = 12
Step 5
Since y is the median, we know x \le y \le z. Using y=9 and x+z=12, we enforce z\ge9 to find x.
z = 12 - x z \ge 9 12 - x \ge 9 x \le 3
Answer
3 kilograms
