In a certain dance troupe, there are 55 women and 33 men. If all of th

Question

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

BrentGMATPrepNow · Accepted Answer

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

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Lampard42 · Answer

Soultion : ((55*62)+(33*70))/(55+33). taking 11 common results in 11*(5*62+3*70)/11*8 = 65.

CrackverbalGMAT · Answer

We know that averages = Sum of observations / Total Observations
When we have two or more groups where the number of observations are different, then we use weighted averages.

Weighted average is an extension of the basic averages formula

= (Sum of observation 1 + Sum of observations 2+ ....) / (number of observations 1 + number of observations 2 + ....)

For the women: Average height = 62, number of women = 55. Therefore Sum of heights = 55 * 62 = 3410
For the men: Average height = 70, number of men = 33. Therefore Sum of heights = 33 * 70 = 2310

Therefore the Average Height of all the dancers in the troupe = (3410 + 2310) / (55 + 33) = 5720/88 = 65 inches

Answer: Option D

Arun Kumar

TheNightKing · Answer

Women:Men = 55:33
We can consider Women to be 5 and men to 3 in number.

Total Height = 5*62 + 3*70 = 310 + 210 = 520

Average Height =520/8 = 65

P.S: You don't need to consider number of women and men as 55 and 33. The ration will do the exact same justice to average.

Sabby · Answer

This question can be solved in 50 sec at best using weighted averages :

Women = 55 out of 88 =>5/8 
Women AVG= 62

Men = 33 out of 88 => 3/8 
Men AVG = 70

Base point = 60 (we count on a base of 60 inches)

Women AVG is +2 the base point
Men AVG is +10 the base point

5/8*2= 10/8
3/8*10=30/8

10/8+30/8= 40/8=5

AVG for Men and Women is +5 the base point : 60+5=65inches

Answer D)

ScottTargetTestPrep · Answer

Solution:
 
We calculate the weighted average height of the dancers::

(55 x 62 + 33 x 70) / (55 + 33) = (5 x 62 + 3 x 70) / (5 + 3) = 520/8 = 65 inches

Answer: D

randomavoidplease · Answer

The way I solved it within 30 secs is, Answer choices range from 60 - 65. ABC are out because they are out of range of average, E is out because between 55 and 33, the value is too small and thus 65. Ans D.

bumpbot · Answer

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In a certain dance troupe, there are 55 women and 33 men. If all of th

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