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

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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio [#permalink]

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18 Jan 2014, 20:00
I took an algebraic approach, although I'm always on the lookout for the potential application of the weighted avg formula...Karishma, any tips on where/when the best times are to apply it? I have seen it efficiently used on a broad range of problems, sometimes in ways that kind of negate some of the the problem's more confusing aspects/calculations, so I'm always on the lookout for its application...

anyways....

A: Boys/Girls= 3a/4a
B: Boys/Girls = 4b/5b
A+B: Boys/Girls = 17/22

(3a+4b)/(4a+5b)=17/22

A has one more boy total: 3a = 4b+1
A has two more girls total: 4a = 5b+2

apply these to above combined equation and solve (b=2)
5*2+2 = 12 or e
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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio [#permalink]

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19 Jan 2014, 22:50
Abdul29 wrote:
Assuming I was short of time on the real test, is it safe to eliminate choices B,C and D on the spot? since 9,10,11 are not divisible by 4?

Yes, the ratio is given in its lowest terms 3:4.
So number of boys must be 3a and number of girls must be 4a where a is an integer.
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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio [#permalink]

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20 Jan 2014, 11:03
Class A: $$\frac{Boys}{Girls} = \frac{3}{4}$$

Class A+B: $$\frac{Boys}{Girls} = \frac{17}{22}$$

Class B ratio not needed.

$$Boys(b) = Boys(a) - 1$$

$$Girls(b) = Girls(a) - 2$$

Accordingly Class A+B:
$$\frac{Boys}{Girls} = \frac{Boys(a) + Boys(a) -1}{Girls(a) + Girls(a) -2} = \frac{2* Boys(a) -1}{2*Girls(a) -2}$$

Now we check our solutions:
A. 8
B. 9
C. 10
D. 11
E. 12

Class A: $$\frac{n*3}{n*4}$$.
Answer A: n=2, so 6 Boys and 8 Girls. We check that in our Class A+B Equation. NO.
Answer B: No need to check as we need an integer as the amount of boys!
Answer C: No need to check as we need an integer as the amount of boys!
Answer D: No need to check as we need an integer as the amount of boys!
Answer E: n=3, so 9 Boys and 12 Girls. We check that in our Class A+B Equation. YES!
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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio [#permalink]

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10 Oct 2014, 09:50
Bunuel wrote:
imhimanshu wrote:
Hey Bunuel,
While giving test, I have been able to solve it correctly using back solving. However, when I revisited this question, I was unable to solve it at the first go. Request you to help me out..

Let the multiplier be x for Class A . Therefore, number of boys: 3x and number of girls 4x
Let the multiplier be y for Class B. Therefor, number of boys: 4y and number of girls : 5y
It is given that -
3x= 4y+1 ----(A)
and
4x=5y+2 -----(B)
Also
As per question:-
3x+4y/4x+5y = 17/22 (combined boys: combined girls) ---(C)
Putting the value from A and B in Equation C giving me weird results -
y is coming out to be 6/13

I have also gone through the replies posted above and I am not too sure that I would be able to ignore the superfluous statement in the real time exam... so hoping to see the solution utilizing the info.
Thanks
H

This problem is a rare example of a question which provides redundant information: we CAN solve the question without knowing that the ratio of boys to girls in the combined class is 17 to 22.

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 ration of boys to girls in Class A is 3 to 4: # of boys is 3x and # of girls is 4x, for some positive integer multiple x;
The ration of boys to girls in Class B is 4 to 5: # of boys is 4y and # of girls is 5y, for some positive integer multiple y;

Class A has one more boy and two more girls than class B: 3x=4y+1 and 4x=5y+2. Now, we have the system of two distinct linear equations with two unknowns, which means that we can solve it. Solving for x we get x=3. Since # of girls in Class A is 4x the there are 4*3=12 girls.

So, as you can see you've done everything right, you just should have solved the system of equations rather than applying some kind of substitution.

Hope it helps.

Hi Bunnel,

Can you please point me to the similar ratio problems ? pls

-AJ
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Posts: 46991
Re: The ratio of boys to girls in Class A is 3 to 4. The ratio [#permalink]

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11 Oct 2014, 04:17
ajaym28 wrote:
Bunuel wrote:
imhimanshu wrote:
Hey Bunuel,
While giving test, I have been able to solve it correctly using back solving. However, when I revisited this question, I was unable to solve it at the first go. Request you to help me out..

Let the multiplier be x for Class A . Therefore, number of boys: 3x and number of girls 4x
Let the multiplier be y for Class B. Therefor, number of boys: 4y and number of girls : 5y
It is given that -
3x= 4y+1 ----(A)
and
4x=5y+2 -----(B)
Also
As per question:-
3x+4y/4x+5y = 17/22 (combined boys: combined girls) ---(C)
Putting the value from A and B in Equation C giving me weird results -
y is coming out to be 6/13

I have also gone through the replies posted above and I am not too sure that I would be able to ignore the superfluous statement in the real time exam... so hoping to see the solution utilizing the info.
Thanks
H

This problem is a rare example of a question which provides redundant information: we CAN solve the question without knowing that the ratio of boys to girls in the combined class is 17 to 22.

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 ration of boys to girls in Class A is 3 to 4: # of boys is 3x and # of girls is 4x, for some positive integer multiple x;
The ration of boys to girls in Class B is 4 to 5: # of boys is 4y and # of girls is 5y, for some positive integer multiple y;

Class A has one more boy and two more girls than class B: 3x=4y+1 and 4x=5y+2. Now, we have the system of two distinct linear equations with two unknowns, which means that we can solve it. Solving for x we get x=3. Since # of girls in Class A is 4x the there are 4*3=12 girls.

So, as you can see you've done everything right, you just should have solved the system of equations rather than applying some kind of substitution.

Hope it helps.

Hi Bunnel,

Can you please point me to the similar ratio problems ? pls

-AJ

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Hope it helps.
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The ratio of boys to girls in Class A is 3 to 4. The ratio [#permalink]

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22 Oct 2014, 01:05
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?

For Class B,

let Boys = 4x & Girls = 5x

Ratio $$= \frac{4x}{5x}$$

Class A has one more boy and two more girls than class B $$= \frac{4x+1}{5x+2} = \frac{3}{4}$$

Solving, we get x = 2

Girls in class A = 5x + 2 = 12

Note: Done using single variable. No need of the highlighted portion in computation of result
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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio [#permalink]

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22 Feb 2015, 07:24
Bunuel wrote:
imhimanshu wrote:
Hey Bunuel,
While giving test, I have been able to solve it correctly using back solving. However, when I revisited this question, I was unable to solve it at the first go. Request you to help me out..

Let the multiplier be x for Class A . Therefore, number of boys: 3x and number of girls 4x
Let the multiplier be y for Class B. Therefor, number of boys: 4y and number of girls : 5y
It is given that -
3x= 4y+1 ----(A)
and
4x=5y+2 -----(B)
Also
As per question:-
3x+4y/4x+5y = 17/22 (combined boys: combined girls) ---(C)
Putting the value from A and B in Equation C giving me weird results -
y is coming out to be 6/13

I have also gone through the replies posted above and I am not too sure that I would be able to ignore the superfluous statement in the real time exam... so hoping to see the solution utilizing the info.
Thanks
H

This problem is a rare example of a question which provides redundant information: we CAN solve the question without knowing that the ratio of boys to girls in the combined class is 17 to 22.

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 ration of boys to girls in Class A is 3 to 4: # of boys is 3x and # of girls is 4x, for some positive integer multiple x;
The ration of boys to girls in Class B is 4 to 5: # of boys is 4y and # of girls is 5y, for some positive integer multiple y;

Class A has one more boy and two more girls than class B: 3x=4y+1 and 4x=5y+2. Now, we have the system of two distinct linear equations with two unknowns, which means that we can solve it. Solving for x we get x=3. Since # of girls in Class A is 4x the there are 4*3=12 girls.

So, as you can see you've done everything right, you just should have solved the system of equations rather than applying some kind of substitution.

Hope it helps.

The 17/22 ratio is given just for distraction and honestly speaking i fell prey of it . 17 is a prime number so i thought there is some short route and i can solve without using pen and paper but as i did nt have luxury of time , after wasting 20secs i gave up on it and move ahead with simultaneous eq to arrive at answer E.
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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio [#permalink]

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23 Feb 2015, 00:15
1
Lucky2783 wrote:

The 17/22 ratio is given just for distraction and honestly speaking i fell prey of it . 17 is a prime number so i thought there is some short route and i can solve without using pen and paper but as i did nt have luxury of time , after wasting 20secs i gave up on it and move ahead with simultaneous eq to arrive at answer E.

Actually, you are not wrong. As I mentioned in my post on the previous page, you shouldn't need to make any equations. The only thing is that what will help you arrive at the answer is this "there is one more boy in class A than in class B..."

Here is how you can solve it:

You have the ratios 3:4 and 4:5.
You know that the number of boys in class A is 1 more so try and multiply the ratios to figure out where you get a difference of 1. I should multiply 3:4 by a bigger number since the number of boys is more in class A.

(3:4)*3 = 9:12
(4:5)*2 = 8:10

In this case, the ratio of the total will be 9+8:12+10 = 17:22

The numbers are very simple so you can arrive at the answer very quickly.
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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio [#permalink]

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23 Feb 2015, 00:41
VeritasPrepKarishma wrote:
Lucky2783 wrote:

The 17/22 ratio is given just for distraction and honestly speaking i fell prey of it . 17 is a prime number so i thought there is some short route and i can solve without using pen and paper but as i did nt have luxury of time , after wasting 20secs i gave up on it and move ahead with simultaneous eq to arrive at answer E.

Actually, you are not wrong. As I mentioned in my post on the previous page, you shouldn't need to make any equations. The only thing is that what will help you arrive at the answer is this "there is one more boy in class A than in class B..."

Here is how you can solve it:

You have the ratios 3:4 and 4:5.
You know that the number of boys in class A is 1 more so try and multiply the ratios to figure out where you get a difference of 1. I should multiply 3:4 by a bigger number since the number of boys is more in class A.

(3:4)*3 = 9:12
(4:5)*2 = 8:10

In this case, the ratio of the total will be 9+8:12+10 = 17:22

The numbers are very simple so you can arrive at the answer very quickly.

Awesome !! .
thanks karishma .
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The ratio of boys to girls in Class A is 3 to 4. The ratio [#permalink]

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24 Jun 2016, 01:16
VeritasPrepKarishma wrote:
Actually speaking, you should not be making any equations. You have the ratio 3:4 and 4:5
You know that the number of boys is class A is 1 more so try and multiply the ratios to figure out where you get a difference of 1. I should multiply 3:4 by a bigger number since the number of boys is more in class A.

(3:4)*3 = 9:12
(4:5)*2 = 8:10

The numbers are very simple so you can arrive at the answer very quickly.

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

Hi VeritasPrepKarishma,

If the question did not give the condition of number of Boys 1 more in A & 2 less number of girls in B, and just mentioned an absolute number for boys in Class A lets say 9 (as we figured above). Can we still find out the number of girls in Class B??

I am stuck to solve this using above reasoning.

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

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Updated on: 14 Nov 2016, 21:21
let g=number of girls in class a
g+(g-2)=22
given 17/22 combined boy/girl ratio, answer choices preclude more than 22 total girls
g=12

Originally posted by gracie on 24 Jun 2016, 11:34.
Last edited by gracie on 14 Nov 2016, 21:21, 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 [#permalink]

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24 Jun 2016, 15:15
1
VeritasPrepKarishma wrote:
Actually speaking, you should not be making any equations. You have the ratio 3:4 and 4:5
You know that the number of boys is class A is 1 more so try and multiply the ratios to figure out where you get a difference of 1. I should multiply 3:4 by a bigger number since the number of boys is more in class A.

(3:4)*3 = 9:12
(4:5)*2 = 8:10

The numbers are very simple so you can arrive at the answer very quickly.

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

Hi VeritasPrepKarishma,

If the question did not give the condition of number of Boys 1 more in A & 2 less number of girls in B, and just mentioned an absolute number for boys in Class A lets say 9 (as we figured above). Can we still find out the number of girls in Class B??

I am stuck to solve this using above reasoning.

I'm not Karishma, but I thought this was an interesting question!

The short answer is: it would make the question a little less simple, but you could still answer it. Interestingly, changing the problem like this means that it now requires all of the given information to solve. That makes it a bit more GMAT-like!

If there are 9 boys in Class A, there are 12 girls. There are also 4x boys in Class B, and 5x girls. (You don't know the value of x, but it could be any integer. For instance, there could be 40 boys and 50 girls with x=10, or 16 boys and 20 girls with x=4.)

When you combine the classes together, there are 9 + 4x boys in total, and 12 + 5x girls.

You also know that the ratio, after combining the classes, is 17 to 22.

So, you've got a two-sided equation. The ratio of boys to girls is (9 + 4x) / (12 + 5x). It's also 17/22. One option is to put an equals sign between them, and solve:

(9+4x)/(12+5x) = 17/22
22(9) + 22(4x) = 17(12) + 17(5x)
88x - 85x = 204 - 198
3x = 6
x = 2

8 boys, 10 girls.

The smarter thing to do, would be to check some small values for x, and see whether they give you a 17 to 22 ratio. x = 2 is pretty simple to check, and it works out perfectly: 9 + 4(2) = 17, and 12 + 5(2) = 22.
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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio [#permalink]

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24 Jun 2016, 19:56
VeritasPrepKarishma wrote:
Actually speaking, you should not be making any equations. You have the ratio 3:4 and 4:5
You know that the number of boys is class A is 1 more so try and multiply the ratios to figure out where you get a difference of 1. I should multiply 3:4 by a bigger number since the number of boys is more in class A.

(3:4)*3 = 9:12
(4:5)*2 = 8:10

The numbers are very simple so you can arrive at the answer very quickly.

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

Hi VeritasPrepKarishma,

If the question did not give the condition of number of Boys 1 more in A & 2 less number of girls in B, and just mentioned an absolute number for boys in Class A lets say 9 (as we figured above). Can we still find out the number of girls in Class B??

I am stuck to solve this using above reasoning.

Yes, it becomes a perfect candidate for weighted average formula in that case.

Class A - Fraction of boys = 3/7
Class B - Fraction of boys = 4/9
Combined - fraction of boys = 17/39

wA/wB = (4/9 - 17/39)/(17/39 - 3/7) = (1/3*39)/(2/7*39) = 7/6

Ratio of students in class A : students in class B = 7:6
Say, number of students in class A is 7n and the number in class B is 6n.
Class A has (3/7)*7n = 9 boys
n = 3
Number of girls in class B = (5/9)*6n = 10
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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio [#permalink]

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26 Jun 2016, 01:20
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?

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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio [#permalink]

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26 Jun 2016, 13:33
1
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?

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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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio [#permalink]

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26 Jun 2016, 13:35
1
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 [#permalink]

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26 Jun 2016, 18:38
EvaJager wrote:

The information the ratio of boys to girls in the combined class would be 17 to 22 is superfluous.

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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Re: The ratio of boys to girls in Class A is 3 to 4. The ratio [#permalink]

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26 Jun 2016, 22:27
1
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 [#permalink]

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27 Jun 2016, 00:55
Thank you ccooley & VeritasPrepKarishma. Your guidance & suggestions on this forum helps me immensely.
Re: The ratio of boys to girls in Class A is 3 to 4. The ratio   [#permalink] 27 Jun 2016, 00:55

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