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# The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to

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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to [#permalink]
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Thank you ccooley & VeritasPrepKarishma. Your explanation helps a lot in understanding the concept better.

I also tried one more thing with the question to check my understanding.

What if the question mentioned that the combined class has 17 boys and we need to determine number of students of Class A.

So, the question stem gives following :

Class A, Boys : Girls = 3: 4
Class B, Boys : Girls = 4:5
Combined Class, Boys : Girls = 17 : 22
Total number of boys in Combined Class = 17
Find the number of students in Class A?

Using the weighted average formula, Ratio of total number of students in Class A : Total in Class B = 7 : 6 (Though the calculation took time, is there an alternative method to find this step? )...(#)

No. of Boys in combined class => $$\frac{3}{7}$$*7n + $$\frac{4}{9}$$*6n = 17
n= 3

From (#), 7n = 21 students in Class A.

Hope this is correct.

Is there any other method to solve this?

Your solution is correct. That is how I would solve it too.

Note that in the original question, you don't need to use the ratio 17:22. Your modified question needed it. In an actual GMAT question, in such a case, the given ratio would be easier. I have rarely found a "tough to work with ratio" in even practice GMAT questions, let alone actual GMAT questions (old or current). Hence, don't be concerned about the difficult calculations here.
Also, I advise my students to know the multiplication tables till 20. They add value by helping one speed up in some questions.
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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to [#permalink]
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changhiskhan wrote:
The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to girls in Class B is 4 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?

A. 8
B. 9
C. 10
D. 11
E. 12

The ratio of boys to girls in Class A is 3 to 4.
Let B = number of boys in class A
Let G = number of girls in class A
We get: B/G = 3/4
Cross multiply to get: 4B = 3G

Class A has one more boy and two more girls than class B
So B - 1 = number of boys in class B
So G - 2 = number of girls in class B

The ratio of boys to girls in Class B is 4 to 5
We get: (B - 1)/(G - 2) = 4/5
Cross multiply to get: 5(B - 1) = 4(G - 2)
Expand: 5B - 5 = 4G - 8

So, we now have the following system to solve for G:
4B = 3G
5B - 5 = 4G - 8

Take 4B = 3G and solve for B to get: B = 3G/4

Take 5B - 5 = 4G - 8 and replace B with 3G/4
We get: 5(3G/4) - 5 = 4G - 8
Expand: 15G/4 - 5 = 4G - 8
Multiply both sides by 4 to get: 15G - 20 = 16G - 32
Solve to get: G = 12

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Originally posted by BrentGMATPrepNow on 14 Nov 2016, 07:44.
Last edited by BrentGMATPrepNow on 28 Dec 2019, 07:36, edited 1 time in total.
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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to [#permalink]
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Some great Solutions above.
Here's what i think of it now =>

The combined ratio given to us is just painfully useless.
WE can get the values of x and y from these two equations alone=>
3x=4y+1
4x=5y+2

Girls in class A => 12

Hence E
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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to [#permalink]
changhiskhan wrote:
The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to girls in Class B is 4 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?

A. 8
B. 9
C. 10
D. 11
E. 12

We can create the ratios:

Class A:

Boys : girls = 3x : 4x

Class B:

Boys : girls = 4y : 5y

Combining, we have:

(3x + 4y)/(4x + 5y) = 17/22

22(3x + 4y) = 17(4x + 5y)

66x + 88y = 68x + 85y

3y = 2x

Also, we are given that class A has one more boy and two more girls than class B. So we have:

3x = 4y + 1 and 4x = 5y + 2

Since 3y = 2x, we know that 6y = 4x, and therefore we have:

6y = 5y + 2

y = 2

Since class A has 4x girls and 4x = 5y + 2, we have 5(2) + 2 = 12 girls in class A.

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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to [#permalink]
changhiskhan wrote:
The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to girls in Class B is 4 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?

A. 8
B. 9
C. 10
D. 11
E. 12

Given:
1. The ratio of boys to girls in Class A is 3 to 4.
2. The ratio of boys to girls in Class B is 4 to 5.
3. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22.

Asked: If Class A has one more boy and two more girls than class B, how many girls are in Class A?

1. The ratio of boys to girls in Class A is 3 to 4.
bA : gA = 3:4
bA = 3k ; gA = 4k; cA = 7k

2. The ratio of boys to girls in Class B is 4 to 5.
bB : gB = 4:5
bB = 4m ; gB = 5m : cB = 9m

3. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22.
bA + bB : gA + gB = 3k + 4m : 4k + 5m = 17:22
66k + 88m = 68k + 85m
2k = 3m
k = 1.5m

If Class A has one more boy and two more girls than class B, how many girls are in Class A?
bA = bB + 1
3k = 4m + 1
4.5m = 4m + 1
m = 2
k = 3

gA = 4k = 12

IMO E
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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to [#permalink]
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Boys A / Girls A = 3 / 4 = (x + 1)/ (y + 2)
Boys B / Girls B = 4 / 5 = x / y

(2x + 1)/ (2y + 2) = 17 / 22

split the numerator and denominator: (2x + 1) = [2(8) + 1] = 17 , (2y + 2) = [2(10) + 2] = 22

Hence y = 10, Girls in class A = (y + 2) = 12
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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to [#permalink]
The trick is really just taking x for class A and y for class B.

Given that the relationship between boys and girls from Class A and B is given, we can quickly come to this:

6x-1/8x-2 = 17/22

x = 3

Class A girls --> 4 * 3 = 12

(I also quickly checked this by plugging 12 into all equations to come up with a satisfying resolution - only doing this if i have time on the real test though)
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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to [#permalink]
­The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to girls in Class B is 4 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?

A. 8
B. 9
C. 10
D. 11
E. 12

Ratio of B to G is 3/4 aka 3k/4k
The number of girls have to be 4 or multiple of 4. This rules out B,C,D.
Assuming girls are 8, Boys will be 6.

This makes Boys and girls in class B 7 and 10 making ration 7/10 which is not the case. Eliminate option A

If girls were 12 in class A, boys would be 9 making boys in Class B be 8 and girls 10 making ration 4/5 which is correct
Re: The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to [#permalink]
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