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The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to 26 Jun 2016, 13:33
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aditi2013
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?

Thanks in advance.
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Use the unknown multiplier again, in my opinion. I tend to go straight for that approach whenever a problem asks me to do algebra with 'pieces' of ratios. A ratio itself isn't very friendly to algebra - how do you 'add' 3:4 and 4:5? - but the unknown multiplier lets you bring algebra into the equation.

Class A has 3a boys, and 4a girls.
Class B has 4b boys, and 5b girls.

You don't know a or b at the moment - they're just unknown variables.

But, you do know that there are 17 boys and 22 girls when you combine the two classes. So,

3a + 4b = 17
4a + 5b = 22

That's just a system of linear equations, and you can solve with elimination or substitution, as you please. Elimination:

12a + 16b = 17*4
12a + 15b = 22*3
b = 17*4 - 22*3 = 68 - 66 = 2

So, class B has 4(2)=8 boys, and 5(2)=10 girls.
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The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to 26 Jun 2016, 13:35
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By the way, you and anyone else who finds this line of inquiry interesting ought to write up a ratios 'tip sheet' for yourself. Run through some ratios problems, and see if you can sort them into categories. One place to start is with the variants you've listed here, which are variations on which information the problem gives you, and which information the problem asks for. Depending on what info you're given and asked for, the solution path will look a little different. If you try all of the possible varieties ahead of time, and write them out in your notes, you'll be better prepared for the ratio problems you might see on the GMAT.
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The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to 26 Jun 2016, 18:38
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EvaJager


The information the ratio of boys to girls in the combined class would be 17 to 22 is superfluous.
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You could also say that the information that class A has one more boy is superfluous, and you could also say the same about the information that class A has 2 more girls.

Either way, there is definitely redundant information in this question. Of the 3 pieces of information, only 2 are needed to solve this problem.
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The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to 26 Jun 2016, 22:27
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aditi2013
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?

Thanks in advance.
Show more

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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The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to Updated on: 28 Dec 2019, 07:36
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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changhiskhan
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
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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
Answer:
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E

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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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changhiskhan
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
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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.

Answer: E
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The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to 18 Apr 2020, 23:48
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changhiskhan
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
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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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The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to 22 Sep 2021, 03:33
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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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The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to 10 Sep 2022, 10:53
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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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The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to 23 Jul 2024, 10:02
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­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
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The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to 30 Oct 2024, 00:16
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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?

--->Ques is asking for number of girls in class A i.e. multiple of 4.
therefore, only A and E remains.

In class A, B:G will be a)6:8 or b)9:12
6+4y/8+5y= 10/13, 14/18..

when y=2, 9+4y/12+5y = 17/22. Hence answer E

or

It is mentioned that A has 1 more boy and two more girls than B.

6+5/8+6= 11/14

9+8/12+10 = 17/22
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The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to 24 Jun 2025, 08:45
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I got the answer by simple math of finding a ratio for both class A and class B which satisfied the equation.

Class A=9/12 (x=3)

Class B=8/10 (y=2)

Thus got answer

Before this was the method, I was trying to do the same through equation BUT made a silly Mistake
Class A has one more boy than Class B: I made this equation 3x+1=4y instead of taking is 3x=4y+1, this while trying to solve made me loose 4MINUTES.

changhiskhan
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
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