Three boxes of supplies have an average (arithmetic mean) weight of 7 kilograms...

BTGmoderatorLU wrote: ↑

Fri Jan 31, 2020 3:22 pm

Source: GMAT Prep

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?

A. 1
B. 2
C. 3
D. 4
E. 5

The OA is C

We are given that three boxes of supplies have an average (arithmetic mean) weight of 7 kilograms and a median weight of 9 kilograms. We must determine the maximum weight of the lightest box.

Since the average weight of the 3 boxes is 7, the sum of the weights of the 3 boxes is 3 x 7 = 21.

We can also define a few variables.

x = lightest box
y = second heaviest box
z = heaviest box

We can create the following equation:

x + y + z = 21

Since the median is 9, y must be 9. So we now have:

x + 9 + z = 21
x + z = 12

Remember, we need the value of x to be as large as possible, so we want to minimize the value of z. Since 9 is the median weight of the boxes, the smallest value that z could possibly be is also 9. Thus, the maximum value of x is 12 – 9 = 3.

Answer: C