The Ratio of Boys to Girls in Class A is 1 to 4, and that in Class B is 2 to 5 GMAT Problem Solving

Question - 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?

1. 1 to 3
2. 5 to 12
3. 8 to 27
4. 6 to 25
5. 13 to 27

‘The ratio of boys to girls in Class A is 1 to 4, and that in Class B is 2 to 5’ - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution 1
The ratio of the number of boys to girls in Class A is 1 : 4
Therefore, we can say that the total number of students in Class A = 5x
The ratio of the number of boys to girls in Class B is 2 : 5
Therefore, we can say that the total number of students in Class B = 7y
As per the given condition:
5x=2*7y
x/y=14/5

We can take x = 14 and y = 5
Thus, the combined Boys to Girls Ratio would be:
=(x+2y)/(4x+5y)
=(14+10)/(56+25)
=24/81
=8/27
Hence, C is the correct answer.\

Correct Answer: C

Approach Solution 2
Explanation:
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
Hence, C is the correct answer.

Correct Answer: C

Approach Solution 3

Let total number of students in Class A be 2x. Total number of students in Class B is x.
Class A girls to boys has a proportion of 1:4
Class B girls to boys has a proportion of 2:5
Therefore,
Total number of boys: 1/5(2x) + 2/7(x) = 24x/35
Total number of girls: 4/5(2x) + 5/7(x) = 81x/35

Hence, total boys: girls is 24:81 which implies 8:27

Correct Answer: C

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