Problem Solving

BTGmoderatorDC wrote: ↑

Mon May 17, 2021 4:16 pm

In a certain dance troupe, there are 55 women and 33 men. If all of the women are 62 inches tall and all of the men are 70 inches tall, what is the average height of the dancers in the troupe?

(A) 60 inches
(B) 61 inches
(C) 62 inches
(D) 65 inches
(E) 63 inches


OA D

Source: Manhattan Prep

This looks like a job for weighted averages!

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

55 + 33 = 88
So, there are 88 people in total.

55/88 = the proportion proportion of WOMEN in the group
And 33/88 = the proportion proportion of MEN in the group

So, the weighted average = (55/88)(62) + (33/88)(70)
= (5/8)(62) + (3/8)(70) I simplified the two fractions
= 310/8 + 210/8
= 520/8
= 260/4
= 130/2
= 65

Answer: D