A certain class is divided into two sections A and B of equal number o

Question

A certain class is divided into two sections A and B of equal number of students. If the ratio of girls to boys for whole class is 3/5 and the ratio of girls to boys in section A is 5/7. What is the ratio of girls to boys in section B?

A. 3 to 1
B. 2 to 1
C. 1 to 3
D. 1 to 2
E. 7 to 12

Experts please help identify the different ways to solve such questions. Thanks

A. 3 to 1
B. 2 to 1
C. 1 to 3
D. 1 to 2
E. 7 to 12

KarishmaB · Accepted Answer

Note that it is a weighted average question in which weights are equal!

The class is divided into sections with equal no of students so weights are same.

Avg concentration of girls = 3/8
Concentration of girls in A = 5/12
Concentration of girls in B = x

(5/12 + x)/2 = 3/8
x = 1/3

Girls:Boys in B = 1:2

Answer (D)

MidhilaMohan · Answer

I did this question by selectingsmart numbers.

G total/B total= 3/5 that is 
G total=3/8 of the total strength
B total=5/8 of the Toal strength

G classA/B ClassA= 5/7 that is 
G ClassA=5/12 of the total strength of A
B ClassA=7/12 of the Toal strength ofA

Now lets assume a number to be total strength of the class. Let that number be 24(LCM of 8,12)

Gtotal= 24x3/8 =9
Btotal= 24x 5/8 =15

strength of A=strength of B=12

G class a= 12x5/12=5
B class a=12x7/12=7

G class B=9-5=4
B class B=15-7=8

hence 1:2 IMO option D

Mseemab · Answer

how much time did it take you?

MidhilaMohan · Answer

After you take the total strength into picture it will take you hardly a minute

Mseemab · Answer

This question was my undoing. It was so easy, n yet couldn't grasp it properly. Ended up wasting 10 minutes, before finally deciding to use smart numbers..

Can you think of any Algebraic way to solve this question?

firas92 · Answer

Let the percentage of girls in class B be  x

When  \frac{5}{12}  of A's class combine with  \frac{x}{100}  of B's class we get  \frac{3}{8}  of (A+B)'s class. That is,

\frac{5}{12}A + \frac{x}{100}B = \frac{3}{8}(A+B)

We know  A=B

\frac{5}{12}A + \frac{x}{100}A = \frac{3}{8}(A+A)

Solving this we get  x=\frac{1}{3}

This means, girls are  \frac{1}{3}  of class B and so boys are  \frac{2}{3}  of class B

Ratio of girls to boys in class B =  \frac{1}{2}

GMATMBA5 · Answer

Let T be total students. Section A and B will each have T/2 Boys and Girls.

Gt = total girls; Ga = Girls in section A; Gb= Girls in section B
Bt = total boys; Ba = Boys in section A; Bb = boys in section B

Given that, Gt/Bt = 3/5
this means, Gt=(3/8)*T and Bt = (5/8)*T

Also given that, Ga/Ba = 5/7
this means, Ga = (5/12)*T/2 and Ba = (7/12)*T/2

Gt = Ga + Gb
(3/8)*T = (5/12)*T/2 + Gb
 Gb  = 3T/8 - 5T/24 = T/6

Bt = Ba + Bb
(5/8)*T = (7/12)*T/2 + Bb
 Bb  = 5T/8 - 7T/24 =  T/3

Therefore, Gb/Bb = (T/6)/(T/3) = 1/2

Ans - D

----------------------------------------
 Kudos if helpful!

nick1816 · Answer

10/24................a/24
..........9/24.........
1.........................1

a=8

Girls to boys ratio in section B= 8/(24-8)= 1/2

Prasannathawait · Answer

I did it this way:

Given For section (A): G:B = 5:7 
For section (B): let G:B = x:y

Given Total ratio : G:B = 3:5

we can make a equation 
 \frac{(5+x)}{(7+y)}  =  \frac{(3)}{(5)} 
also taking x+y = 12 (as per question)

Solving this will give y=8, x=4. That is a ratio of 1:2

Am I doing correct ?

Kinshook · Answer

Given: A certain class is divided into two sections A and B of equal number of students. 
Asked: If the ratio of girls to boys for whole class is 3/5 and the ratio of girls to boys in section A is 5/7. What is the ratio of girls to boys in section B?

Let the number of students in each section be x.

Section A + Section B: 
Girls = 3*2x/8 = 3x/4
Boys = 5*2x/8 = 5x/4
Total = 2x

Section A: 
Girls = 5x/12
Boys = 7x/12
Total = x

Section B: 
Girls = 3x/4 - 5x/12 = 4x/12 = x/3
Boys = 5x/4 - 7x/12 = 8x/12 = 2x/3
Total = x
Ratio of girls to boys in Section B = 1/2

IMO D

Rebaz · Answer

KarishmaB

Could you please explain why you divide (5/12 + x) by 2?

Thanks in advance!

KarishmaB · Answer

This is because both sections have equal number of students. This means that they have equal weights. So the average concentration of girls will just be the simple average of the concentration of girls in the two sections. In section A, concentration of girls is 5/12 In section B, concentration of girls is x Average concentration of girls is 3/8. This will be the simple average of 5/12 and x. This is why sum of 5/12 and x is divided by 2 - to find the simple average (arithmetic mean). Check out these discussions on Weighted averages and Arithmetic mean: https://www.youtube.com/watch?v=_GOAU7moZ2Q https://youtu.be/W-qhIZ29UIs

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=83099 Harsha GMAT-Club-Forum-e8gcgmkm.png

mbaaccount1234 · Answer

How I solved quickly

Class A is 5x/7x, so it is a multiple of 12
Whole class is 3y/5y, or 6y/10y, or 9y/15y, ...

Using the answer choices, we see that 1/2 is the same as 4/8. As they are equal in number of students, if you sum this in 5/7 you get 9/15

So, answer 1/2

Usernamevisible · Answer

KarishmaB  can we solve this question by using alligation approach ?

A certain class is divided into two sections A and B of equal number o

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A certain class is divided into two sections A and B of equal number o

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards