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School A is 40% girls and school B is 60% girls. The ratio

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School A is 40% girls and school B is 60% girls. The ratio

by BTGmoderatorDC » Sat Nov 30, 2019 7:19 pm
School A is 40% girls and school B is 60% girls. The ratio of the number of girls at school A to the number of girls at school B is 4:3. if 20 boys transferred from school A to school B and no other changes took place at the two schools, the new ratio of the number of boys at school A to the number of boys at school B would be 5:3. What would the difference between the number of boys at school A and at school B be after the transfer?

A) 20
B) 40
C) 60
D) 80
E) 100

OA B

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by deloitte247 » Sun Dec 01, 2019 3:04 am
Let total student in School A = x
Let total student in School B = y
Girls in school A = 40% of x = 0.4x
Girls in school B = 60% of y = 0.6x
Boys in school A = 60% of x = 0.6x
Boys in school B = 40% of x = 0.4x
The ratio of girls in school A to scholl B = 4/3
$$\frac{0.4x}{0.6y}=\frac{4}{3}$$
3 (0.4x) = 4 (0.6y)
1.2x = 2.4y
x = 2y

20 boys were transferred from school A to B.
Therefore, boys in school A = 0.6x - 20
Boys in school B = 0.4y + 20
New ratio of boys at school A to B = 5:3
$$\frac{0.6x-20}{0.4y+20}=\frac{5}{3}$$
3 (0.6x - 20) = 5 (0.4y + 20)
1.8x - 60 = 2y + 100
1.8 (2y) - 60 = 2y + 100
3.6y - 2y = 100 + 60
1.6y = 160
y = 160/1.6 = 100

The difference between the number of boys at school A and school B after the transfer
= (0.6x - 20) - (0.4y + 20)
= 0.6x - 20 - 0.4y - 20
where x = 2y and y = 100; so x = 200
= 0.6 (200) - 20 - 0.4 (100) - 20
= 120 - 20 - 40 - 20
= 40

Answer = option B
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by Brent@GMATPrepNow » Sun Dec 01, 2019 6:12 am
BTGmoderatorDC wrote:School A is 40% girls and school B is 60% girls. The ratio of the number of girls at school A to the number of girls at school B is 4:3. if 20 boys transferred from school A to school B and no other changes took place at the two schools, the new ratio of the number of boys at school A to the number of boys at school B would be 5:3. What would the difference between the number of boys at school A and at school B be after the transfer?

A) 20
B) 40
C) 60
D) 80
E) 100

OA B

Source: Veritas Prep
Let A = TOTAL population of School A
Let B = TOTAL population of School B

School A is 40% girls and School B is 60% girls
So, number of GIRLS at School A = 0.4A
And number of GIRLS at School B = 0.6B

The ratio of the number of girls at School A to the number of girls at School B is 4:3
We can write: 0.4A/0.6B = 4/3
Cross multiply to get: (3)(0.4A) = (4)(0.6B)
Simplify to get: 1.2A = 2.4B
Divide both sides by 1.2 to get A = 2B

Let's re-examine the following: School A is 40% girls and School B is 60% girls
So, current number of BOYS at School A = 0.6A
And current number of BOYS at School B = 0.4B

If 20 boys transferred from School A to School B....
So, NEW number of BOYS at School A = 0.6A - 20
And NEW number of BOYS at School B = 0.4B + 20

...., the new ratio of boys at School A to boys at School B would be 5:3
So, we can write: (0.6A - 20)/(0.4B + 20) = 5:3
Cross multiply to get: (3)(0.6A - 20) = (5)(0.4B + 20)
Simplify to get: 1.8A - 60 = 2B + 100
Add 60 to both sides to get: 1.8A = 2B + 160
Subtract 2B from both sides to get: 1.8A - 2B = 160

We now have a system of equations to solve:

Divide both sides by 1.2 to get A = 2B
1.8A - 2B = 160

Take 1.8A - 2B = 100 and replace A with 2B to get: 1.8(2B) - 2B = 160
Expand: 3.6B - 2B = 160
Simplify: 1.6B = 160
Solve: B = 100
So, the (current) TOTAL population at School B is 160
Since we know that A = 2B, we can conclude that the (current) TOTAL population at School A = (2)(100) = 200

Now that we know the values of A and B, we can complete our calculations.
Current number of BOYS at School A = 0.6A = 0.6(200) = 120
And current number of BOYS at School B = 0.4B = 0.4(100) = 40

So, NEW number of BOYS (after the transfer) at School A = 100
And NEW number of BOYS (after the transfer) at School B = 60

What would the difference between the number of boys at School A and at School B be after the transfer?
100 - 60 = 40


Answer: B

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by Scott@TargetTestPrep » Mon Dec 09, 2019 5:35 pm
BTGmoderatorDC wrote:School A is 40% girls and school B is 60% girls. The ratio of the number of girls at school A to the number of girls at school B is 4:3. if 20 boys transferred from school A to school B and no other changes took place at the two schools, the new ratio of the number of boys at school A to the number of boys at school B would be 5:3. What would the difference between the number of boys at school A and at school B be after the transfer?

A) 20
B) 40
C) 60
D) 80
E) 100

OA B

Source: Veritas Prep

If School A has 40% girls, it also has 60% boys, giving us a ratio of 4 : 6. We can let the number of girls and boys in School A be 4x and 6x, respectively. Similarly, we can let the number of girls and boys in School B be 6y and 4y, respectively. Therefore, we can express the ratio of girls at School A to girls at School B as 4x/6y, and we are given that this ratio is also equal to 4 : 3. Thus:

4x/6y = 4/3

For the boys, School A lost 20 boys, giving us (6x - 20) boys at School A, and School B gained those 20 boys, so School B now has (4y + 20) boys. The new ratio is given as 5 : 3. Thus:

(6x - 20)/(4y + 20) = 5/3

Solving the first equation, we have:

12x = 24y

x = 2y

Solving the second equation, we have:

18x - 60 = 20y + 100

18x = 20y + 160

9x = 10y + 80

Since x = 2y, we have:

9(2y) = 10y + 80

18y = 10y + 80

8y = 80

y = 10

Thus, x = 2(10) = 20. After the transfer of 20 boys, School A has 6x - 20 = 6(20) - 20 = 100 boys and School B has 4(10) + 20 = 60 boys. So, the difference is 100 - 60 = 40.

Answer: B

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by GMATGuruNY » Mon Dec 09, 2019 5:46 pm
BTGmoderatorDC wrote:School A is 40% girls and school B is 60% girls. The ratio of the number of girls at school A to the number of girls at school B is 4:3. if 20 boys transferred from school A to school B and no other changes took place at the two schools, the new ratio of the number of boys at school A to the number of boys at school B would be 5:3. What would the difference between the number of boys at school A and at school B be after the transfer?

A) 20
B) 40
C) 60
D) 80
E) 100
An alternate approach is to TEST CASES.
Since 20 boys are transferred, the number of boys at each school is almost certainly a MULTIPLE OF 10, implying that the number of girls at each school also is a MULTIPLE OF 10.

The ratio of the number of girls at School A to the number of girls at School B is 4:3.
(girls at A) : (girls at B) = 4:3 = 40:30 = 80:60 = 120:90 = 160:120...

Case 1: girls at A = 40, girls at B = 30
School A is 40% girls.
Since girls:boys = 40:60, girls = 40, boys = 60.
School B is 60% girls.
Since girls:boys = 60:40 = 30:20, girls = 30, boys = 20.

If 20 boys transferred from School A to School B and no other changes took place at the two schools, the new ratio of the number of boys at School A to the number of boys at School B would be 5:3.
School A:
new boys = 60-20 = 40.
School B:
new boys = 20+20 = 40.
Resulting ratio = 40:40 = 1:1.
Doesn't work.

Case 2: girls at A = 80, girls at B = 60
School A is 40% girls.
Since girls:boys = 40:60 = 80:120, girls = 80, boys = 120.
School B is 60% girls.
Since girls:boys = 60:40, girls = 60, boys = 40.

If 20 boys transferred from School A to School B and no other changes took place at the two schools, the new ratio of the number of boys at School A to the number of boys at School B would be 5:3.
School A:
new boys = 120-20 = 100.
School B:
new boys = 40+20 = 60.
Resulting ratio = 100:60 = 5:3.
Success!

Thus:
new boys at A - new boys at B = 100-60 = 40.

The correct answer is B.
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by [email protected] » Tue Dec 10, 2019 11:52 am
Hi All,

This is a layered algebra question that would take a number of "math steps" to solve. The math involved isn't too hard, but you have to do a lot of work to get the job done....

"School A is 40% girls (thus 60% boys) and School B is 60% girls (thus 40% boys)"

We can write these ratios as:

School A
B:G
3:2

School B
B:G
2:3

Since ratios are all about multiples, I'm going to add a "variable" into each ratio (since the schools are different, I need to use a different variable for each).

School A
B:G
3x:2x

School B
B:G
2y:3y

"The ratio of girls at School A to girls at School B is 4:3"

We can write this ratio as...

2x/3y = 4/3

And cross-multiply....

6x = 12y
x = 2y

"If 20 boys transferred from School A to School B...the new ratio of boys at School A to boys at School B would be 5:3"

We can write this ratio as....

(3x - 20)/(2y + 20) = 5/3

And cross-multiply...

9x - 60 = 10y + 100
9x = 10y + 160

We now have 2 variables and 2 equations, so we can solve using "System" math to solve for the two variables...

x = 2y
9x = 10y + 160

By substituting in, we get...

9(2y) = 10y + 160
18y = 10y + 160
8y = 160
y = 20

Plugging back in, we get...

x = 40

The question asks for the DIFFERENCE in the number of boys at School A and at School B AFTER the transfer:

Number at School A after the transfer = 3x - 20 = 120-20 = 100
Number at School B after the transfer = 2y + 20 = 40 + 20 = 60

The difference = 100 - 60 = 40

Final Answer: B

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Rich
Contact Rich at [email protected]
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