The ratio of boys to girls in Class A is 1 to 4, and that in Class B

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?

A) 1 to 3
B) 5 to 12
C) 8 to 27
D) 6 to 25
E) 13 to 27

A) 1 to 3
B) 5 to 12
C) 8 to 27
D) 6 to 25
E) 13 to 27

EgmatQuantExpert · Accepted Answer

There are several ways to do it. Let me discuss two of them.

Method 1 :

• The ratio of the number of boys to girls in Class A is 1 : 4

o 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

o Therefore, we can say that the total number of students in Class B = 7y

• As per the given condition:

o  5x = 2*7y 
o  \frac{x}{y} = \frac{14}{5} 
o Take x = 14 and y = 5

• Thus, the combined Boys to Girls Ratio would be

= \frac{(x + 2y)}{(4x + 5y)} 
 = \frac{(14 + 10)}{(56+25)} 
 = \frac{24}{81} 
 = \frac{8}{27}

evillasis · Answer

We have three ratios:

1) Classroom A -> 1:4 -> potion of Boys =  1/(1+4)  =  1/5 
2) Classroom B -> 2:5 -> potion of Boys =  2/(2+5)  =  2/7 
3) Classrooms RATIO -> 2:1 -> portion of Class A = 2/3 and portion of Class B =  1/3

I stated the weighted portion of Boys in both classrooms:

Total Portion of Boys
 2/3*(1/5)+1/3*(2/7) 
 = 2/3*(1/5+1/7) 
 = 2/3*(12)/35 
 = 8/35

Total Portion of Girls:

1-8/35=27/35

So the final ratio is
Portion boys / Portion of girls 
8/27

Bunuel · Answer

Similar question to practice: https://gmatclub.com/forum/the-ratio-of ... 92242.html

BrentGMATPrepNow · Answer

Let's use  weighted averages .

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

Answer:  C

RELATED VIDEO
 https://www.youtube.com/watch?v=B7J6lr_qBG4

EgmatQuantExpert · Answer

Method 2 : Use the simple concept of weighted average to get the answer. • The ratio of the number of boys to girls in Class A is 1 : 4 o Number of boys will be \frac{1}{(1+4)} = \frac{1}{5}th of total o Number of girls will be \frac{4}{(1+4)} = \frac{4}{5}th of total • The ratio of the number of boys to girls in Class B is 2 : 5 o Number of boys will be \frac{2}{(2+5)} = \frac{2}{7}th of total o Number of girls will be \frac{5}{(2+5)} = \frac{5}{7}th of total • Ratio of class A : Class B = 2 : 1 Thus weighted average = (Number of boys in Class A + Class B) / (Number of Girls in Class A + Class B) = (2 * \frac{1}{5} + 1 * \frac{2}{7})/(2*\frac{4}{5} + 1 * \frac{5}{7}) = \frac{24}{35}/\frac{81}{35} = \frac{8}{27} Thanks, Saquib Quant Expert e-GMAT Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

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guialain · Answer

Another way of solving this. I believe this way is faster.

Class A: ratio a:4a and total student 5a ------------- Class B: ratio 2b:5b and total student 7b

as per question stem, 5a=2*(7b)

Ratio of the new class is (a+2b):(4a+5b)
which same ratio as (5a+10b):(20a+25b)
substitution leads to ratio 24b:81b or 24:81
Hence 8:27

Answer is C

guialain · Answer

Another way of solving this. I believe this way is faster.

Class A: ratio a:4a and total student 5a ------------- Class B: ratio 2b:5b and total student 7b

as per question stem, 5a=2*(7b)

Ratio of the new class is (a+2b):(4a+5b)
which same ratio as (5a+10b):(20a+25b)
substitution leads to ratio 24b:81b or 24:81
Hence 8:27

Answer is C

jkolachi · Answer

Not sure if my approach is easier or harder but I used the LCM method. I find it helps simplify a lot of questions.

1:4 = 5
2:5 = 7

5 & 7 LCM = 35. Since A is twice as much as B. then A must be 70 and B = 35. (even if its 140 & 70, the ratio will be same).

A= 14 boys, 56 girls. 
B= 10 boys, 25 girls.

24 boys : 81 girls divide by 3... = 8:27.

ScottTargetTestPrep · Answer

We are given that the ratio of boys to girls in Class A is 1 to 4 and that the ratio in Class B is 2 to 5.

The ratio of boys to girls in class A = x : 4x

The ratio of boys to girls in class B = 2y : 5y

Since there are twice as many students in class A as in class B, we can create the following equation:

x + 4x = 2(2y + 5y)

5x = 14y

x = 14y/5

From the two earlier ratios, we see that the total number of boys in the combined class is (x + 2y) and the total number of girls in the combined class is (4x + 5y). Thus, the ratio of boys to girls in the combined class will be (x + 2y)/(4x + 5y). Substituting 14y/5 for x, we have:

(14y/5 + 2y)/(56y/5 + 5y) = (24y/5)/(81y/5) = 24/81 = 8/27.

Answer: C

gracie · Answer

A and B=number of total students in each class
x=ratio of total boys to total students
A=2B
substituting, 2B*1/5+B*2/7=3B*x➡
x=8/35 ratio of total boys to total students
8/(35-8)=8/27=ratio of total boys to total girls
C

shivamtibrewala · Answer

Is there a way to do this sum through Alligation?

EMPOWERgmatRichC · Answer

Hi All,

This question can be solved by TESTing VALUES. Before choose your values though, you have to note the ratios involved:

1) Class A has a ratio of boys:girls = 1:4. This means that there are 4 girls for every 1 boy (and that the total number of girls MUST be a multiple of 4 and the total number of students MUST be a multiple of 5). 
2) Class B has a ratio of boys:girls = 2:5. This means that there are 5 girls for every 2 boys (and that the total number of boys MUST be a multiple of 2, the total number of girls MUST be a multiple of 5 and the total number of students MUST be a multiple of 7).

We're told that the total number of students in Class A is TWICE the total number of students in Class B. Thus, we need to TEST a multiple of 5 that is exactly TWICE a multiple of 7...

Let's TEST 
Class A = 70 students (14 boys and 56 girls) 
Class B = 35 students (10 boys and 25 girls)

By combining these two classes, we'll end up with 24 boys and 81 girls, giving us a ratio of 24:81. Since 24 and 81 are both multiples of 3, we can reduce this ratio to... 8:27

Final Answer:  C

GMAT assassins aren't born, they're made, 
Rich

isabelleo · Answer

Let total number of students in Class A be 2x. Total number of students in Class B is x. 
Class A girls to boys -> 1:4
Class B girls to boys -> 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-> 24:81 -> 8:27

Blackishmamba · Answer

Guess # of students in class B is 140, hence that of in A will be 280.
Boy/girls ratio in class a will be 56/224 and in class B will be 40/100
Overall ratio will be (56+40)/(224+100) which will reduce to 8/27

Hope it helps.

Posted from my mobile device

oskarw93s · Answer

I wouldnt classify this question as "hard". Solved it in 20 seconds. I suggest changing it to a "medium" type of question.

chayon222 · Answer

@VeritasKarishma,@bunuel

why can't I use the weighted average formula this was

2/1=(2/5-X)/(X-1/4)

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The ratio of boys to girls in Class A is 1 to 4, and that in Class B

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