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

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In a group of children, the average (arithmetic mean) weight of the bo  [#permalink]

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New post 23 Aug 2018, 23:33
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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

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Re: In a group of children, the average (arithmetic mean) weight of the bo  [#permalink]

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New post 23 Aug 2018, 23:39
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Let the number of boys be X.
Let the number of girls be Y.
Now,
\(\frac{{60X+48Y}}{{X+Y}}\) = 50.

Cross multiplying gives 60X+48Y = 50X+50Y
10X = 2Y
\(\frac{X}{Y}\) = \(\frac{2}{10}\) = \(\frac{1}{5}\).

C is the answer.
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Re: In a group of children, the average (arithmetic mean) weight of the bo  [#permalink]

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New post 24 Aug 2018, 04:06
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Bunuel 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



Through Allegation one can solve this one easily. 30 sec approach.
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Re: In a group of children, the average (arithmetic mean) weight of the bo  [#permalink]

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New post 24 Aug 2018, 08:04
Bunuel 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


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

Or, \(10b = 2g\)

So, \(5b = g\)

Or, \(b : g = 1 : 5\), Answer must be (C)
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Re: In a group of children, the average (arithmetic mean) weight of the bo  [#permalink]

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New post 19 Mar 2019, 20:31
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

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Re: In a group of children, the average (arithmetic mean) weight of the bo   [#permalink] 19 Mar 2019, 20:31
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