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Joined: 20 Feb 2017
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The ratio of boys to girls in Class A is 1 to 4, and that in Class B i
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28 Dec 2022, 09:51
28 Dec 2022, 09:51
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The ratio of boys to girls in Class A is 1 to 4, and that in Class B is 2 to 5. In addition, there are twice as many students in Class A as in Class B. If the two classes are combined to form one class, what would the resulting ratio of boys to girls?
A) 1 to 3
B) 5 to 12
C) 8 to 27
D) 6 to 25
E) 13 to 27
A) 1 to 3
B) 5 to 12
C) 8 to 27
D) 6 to 25
E) 13 to 27
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Joined: 10 Apr 2015
Posts: 6218
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Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B i
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28 Dec 2022, 11:00
28 Dec 2022, 11:00
1
GeminiHeat wrote:
The ratio of boys to girls in Class A is 1 to 4, and that in Class B is 2 to 5. In addition, there are twice as many students in Class A as in Class B. If the two classes are combined to form one class, what would the resulting ratio of boys to girls?
A) 1 to 3
B) 5 to 12
C) 8 to 27
D) 6 to 25
E) 13 to 27
A) 1 to 3
B) 5 to 12
C) 8 to 27
D) 6 to 25
E) 13 to 27
Let's use 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) + ...
So, in this case, Weighted average of combined classes = (Class A proportion)(Class A average) + (Class B proportion)(Class B average)
CLASS A:
Ratio of boys to girls in Class A is 1 to 4
So, for every 5 students, we have 1 boy and 4 girls.
In other words, 1/5 of the students are boys.
So, we can say the class A average is 1/5 boys
CLASS B:
Ratio of boys to girls in Class B is 2 to 5
So, for every 7 students, we have 2 boys and 5 girls.
In other words, 2/7 of the students are boys.
So, we can say the class B average is 2/7 boys
There are twice as many students in Class A as in Class B.
So, for every 3 students in the COMBINED group, there are 2 students from Class A, and 1 student from Class B
In others words, Class A students comprise 2/3 of the COMBINED group, and Class B students comprise 1/3 of the COMBINED group
Now plug these values into our formula to get:
Weighted average of combined classes = (2/3)(1/5) + (1/3)(2/7)
= 2/15 + 2/21
= 14/105 + 10/105
= 24/105
= 8/35
So, in the combined group, 8/35 of the students are boys, which means 27/35 of the students are girls.
In other words, among every 35 students in the combined group, 8 are boys and 27 are girls.
So, the ratio of boys to girls = 8 to 27
Answer: C
gmatclubot
Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B i [#permalink]
28 Dec 2022, 11:00
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