In a group of children, the average (arithmetic mean) weight

Hi All,

We're told that in a group of children, the average (arithmetic mean) weight of the boys is 60 pounds, the average weight of the girls is 48 pounds and the average weight of ALL of the children in the group is 50 pounds. We're asked for the ratio of the number of boys to the number of girls. This question can be solved in a number of different ways, including by TESTing THE ANSWERS. There's an interesting Number Property pattern that you can also take advantage of though (that can save you a bit of work REGARDLESS of which approach you use).

To start, since the average weight of ALL the children is 50 pounds, we know that the TOTAL weight of the children is a MULTIPLE OF 50... and that total ends in a '0.' Since the average weight of the boys is 60 pounds, we know that that sum will end in a '0.' The average weight of the girls is 48 pounds though, so will also need the total weight of this group to also be a multiple of 10... otherwise the sum of ALL the children won't end in a '0.' The only ways for that to occur are when the total number of girls is a MULTIPLE OF 5....

Looking at the answer choices, there's only one answer that fits... but here's how you can prove it's the correct answer by TESTing THE ANSWERS:

IF we have 1 boy and 5 girls...
then the total weight is 1(60) + 5(48) = 60 + 240 = 300
and the average weight is 300/6 = 50 pounds.
This fits what we were told, so the ratio MUST be 1:5 = 1/5

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

swerve wrote:In a group of children, the average (arithmetic mean) weight of the boys is 60 pounds, and the average weight of the girls is 48 pounds. If the average weight of all of the children in the group is 50 pounds, what is the ratio of the number of boys to the number of girls?

A. 1/12
B. 1/6
C. 1/5
D. 1/4
E. 1/3

We can also use weighted averages to solve this
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

Let G = number of girls
Let B = number of boys
So, G+B = TOTAL number of children

And G/(G+B) = proportion of girls in the group
And B/(G+B) = proportion of boys in the group

Plug all values into formula to get: 50 = [B/(G+B)][60] + [G/(G+B)][48]
Rewrite to get: 50 = 60B/(G+B) + 48G/(G+B)
Multiply both sides by (G+B) to get: 50(G+B) = 60B + 48G
Expand left side to get: 50G + 50B = 60B + 48G
Subtract 48G from both sides to get: 2G + 50B = 60B
Subtract 50B from both sides to get: 2G = 10B
Divide both sides by 10 to get: 2G/10 = B
Divide both sides by G to get: 2/10 = B/G
Simplify: 1/5 = B/G

So, the ratio of boys to girls = B/G = 1/5

Answer: C

For more information on weighted averages, you can watch this video: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Here are some additional practice questions related to weighted averages:
- https://www.beatthegmat.com/weighted-ave ... 17237.html
- https://www.beatthegmat.com/weighted-ave ... 14506.html
- https://www.beatthegmat.com/average-weig ... 57853.html
- https://www.beatthegmat.com/averages-que ... 87118.html

Cheers,
Brent

swerve wrote:In a group of children, the average (arithmetic mean) weight of the boys is 60 pounds, and the average weight of the girls is 48 pounds. If the average weight of all of the children in the group is 50 pounds, what is the ratio of the number of boys to the number of girls?

A. 1/12
B. 1/6
C. 1/5
D. 1/4
E. 1/3

The OA is C

Source: Magoosh

Letting b and g equal the number of boys and girls, respectively, we can create the weighted average equation:

(60b + 48g)/(b + g) = 50

60b + 48g = 50b + 50g

10b = 2g

5b = g

b/g = 1/5

Answer: C