GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Jan 2019, 08:55

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

January 21, 2019

January 21, 2019

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.
• ### The winners of the GMAT game show

January 22, 2019

January 22, 2019

10:00 PM PST

11:00 PM PST

In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 16 Nov 2013
Posts: 28
Location: United States
Concentration: Entrepreneurship, General Management
GPA: 3.49
School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

16 Nov 2013, 21:53
4
22
00:00

Difficulty:

55% (hard)

Question Stats:

71% (03:37) correct 29% (03:24) wrong based on 291 sessions

### HideShow timer Statistics

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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8803
Location: Pune, India
Re: School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

18 Mar 2014, 20:20
4
3
registerincog 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

Sometimes, the question becomes very easy with a little bit of reasoning. People often ask - how do we go from Q48 to Q51? The difference often lies in utilization of this reasoning. Let me tell you my thought process when I saw this question.

School A - 40% girls
School B - 60% girls

"The ratio of the number of girls at school A to the number of girls at school B is 4:3"
When I read this line, I went back to the previous line with the % figures. I noticed that school A has more girls than school B (4:3) but its % of girls is lower (only 40% compared to 60% in B). This means that school A has more students than school B. Say something like school A has 200 students while school B has 100. So school A has 80 girls while school B has 60 girls. This gave me a ratio of 4:3. (If I had not got 4:3 on my first try, I might have tweaked the assumed numbers a bit but would have stuck to simple numbers.) Then I verified the rest of the data against these numbers and got my answer easily as 40.

Algebra Solution
Say, if you do insist on algebra and do not want to rely on reasoning, try to work in a single variable.
Girls in A:Girls in B = 4:3
Girls in A = 4n, Girls in B = 3n
Since in A, girls are 40% and boys are 60%, number of boys is 6n.
Since in B, girls are 60% and boys are 40%, number of boys is 2n.

(6n - 20)/(2n + 20) = 5/3
You get n = 20

Boys at school A after transfer = 6*20 - 20 = 100
Boys are school B after transfer = 2*20 + 20 = 60
Difference = 40

_________________

Karishma
Veritas Prep GMAT Instructor

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1823
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

18 Mar 2014, 19:57
3
2
School A...................................................................... School B

Boys.............. Girls.......................................Boys................ Girls

$$\frac{60a}{100}............... \frac{40a}{100} ........................................... \frac{40b}{100} .................... \frac{60b}{100}$$

The ratio of the number of girls at school A to the number of girls at school B is 4:3

$$\frac{40a}{100} / \frac{60b}{100} = \frac{4}{3}$$

a = 2b

20 boys transferred from school A to school B

$$\frac{120b}{100} - 20 = \frac{6b-100}{5}$$ ............ (1)

$$\frac{40b}{100} + 20 = \frac{2b+100}{5}$$ ............. (2)

Ratio (1) : (2) = 5/3

$$\frac{6b-100}{2b+100} = \frac{5}{3}$$

Solving b = 100

We require to find $$\frac{6b-100}{5} - \frac{2b+100}{5}$$

= 100 - 60 = 40

_________________

Kindly press "+1 Kudos" to appreciate

##### General Discussion
Intern
Joined: 28 Dec 2012
Posts: 7
Re: School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

17 Nov 2013, 01:06
1
4
Assume the common variable for the ratio to be x.
As ratio of girls of school A (Ga) to girls of school B (Gb) is 4:3. Therefore, Ga/Gb = 4/3
i.e. there are Ga=4x, Gb=3x
Now, as school A has 40% girls,
Ga=40/100 * (Total students at school A)
Substuting Ga=4x.
Total students at school A = 10x
Similarly, Total students at school B = 5x

From this, we know that boys at school A (Ba) = 6x
boys at school B (Bb) = 2x

As 20 boys leave school A and join school B
new Ba = 6x - 20
new Bb = 2x + 20

It is also given that,
(new Ba)/(new Bb) = 5/3
i.e (6x - 20)/(2x + 20)=5/3
x=20

Hence difference between number of boys after transfer,
[6(20)-20] - 2(20)+20] = 40
Ans : B

Hope this helps
MBA Section Director
Affiliations: GMAT Club
Joined: 21 Feb 2012
Posts: 6001
City: Pune
Re: School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

18 Mar 2014, 23:38
2
2
VeritasPrepKarishma wrote:
registerincog 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

Sometimes, the question becomes very easy with a little bit of reasoning. People often ask - how do we go from Q48 to Q51? The difference often lies in utilization of this reasoning. Let me tell you my thought process when I saw this question.

School A - 40% girls
School B - 60% girls

"The ratio of the number of girls at school A to the number of girls at school B is 4:3"
When I read this line, I went back to the previous line with the % figures. I noticed that school A has more girls than school B (4:3) but its % of girls is lower (only 40% compared to 60% in B). This means that school A has more students than school B. Say something like school A has 200 students while school B has 100. So school A has 80 girls while school B has 60 girls. This gave me a ratio of 4:3. (If I had not got 4:3 on my first try, I might have tweaked the assumed numbers a bit but would have stuck to simple numbers.) Then I verified the rest of the data against these numbers and got my answer easily as 40.

Algebra Solution
Say, if you do insist on algebra and do not want to rely on reasoning, try to work in a single variable.
Girls in A:Girls in B = 4:3
Girls in A = 4n, Girls in B = 3n
Since in A, girls are 40% and boys are 60%, number of boys is 6n.
Since in B, girls are 60% and boys are 40%, number of boys is 2n.

(6n - 20)/(2n + 20) = 5/3
You get n = 20

Boys at school A after transfer = 6*20 - 20 = 100
Boys are school B after transfer = 2*20 + 20 = 60
Difference = 40

Great explanation, Karishma!! I mistakenly assumed that both the schools have same number of students. After realizing that I am on the wrong path, changed my approach and finally got the answer after 4.28 mins.

School A is 40% girls (means 60% boys) and school B is 60% girls (means 40% boys).

The ratio of the number of girls at school A to the number of girls at school B is 4:3 -------> Number of girls in School A is 4x and in School B, 3x

School A stats
Number of girls is 4x and percentage of girls is 40%. We also know that percentage of boys is 60%. So 40% is equivalent to 4x, then 60% is equivalent to 6x
Number of girls = 4x
Number of boys = 6x

School B stats
Number of girls is 3x and percentage of girls is 60%. We also know that percentage of boys is 40%. So 60% is equivalent to 3x, then 40% is equivalent to 2x
Number of girls = 3x
Number of boys = 2x

SO Ratio of boys in School A and School B is 6x/2x

After transferring 20 Boys from School A to School B, ratio of boys would be 5/3 --------> $$\frac{6x - 20}{2x + 20} = \frac{5}{3}$$ ---------------> x = 20

Number of boys in School A after transfer -----> 6x - 20 ----->100
Number of boys in School B after transfer -----> 2x + 20 ----->60

Difference = 40
_________________
Manager
Joined: 17 Jul 2013
Posts: 80
Re: School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

07 Jul 2014, 00:02
I am getting number of students in A as 200 so my answer reduces to 60 instead of 40.
My approach is as following :

.4A / .6B = 4/3 hence A = 2B where A and B are total number of students in A and B school respectively.
.6A - 20 / .4B + 20 = 5/3 the new ratio ... when I solve this equation I left with A= 200.

200 - 100 - 40 = 60

Can somebody please identify issue with my solution.
Thanks
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8803
Location: Pune, India
Re: School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

07 Jul 2014, 04:03
GmatDestroyer2013 wrote:
I am getting number of students in A as 200 so my answer reduces to 60 instead of 40.
My approach is as following :

.4A / .6B = 4/3 hence A = 2B where A and B are total number of students in A and B school respectively.
.6A - 20 / .4B + 20 = 5/3 the new ratio ... when I solve this equation I left with A= 200.

Till here, everything is fine. A = 200 and B = 100 (since A = 2B)
Number of boys in A = .6A = 120
Number of boys in B = .4B = 40

When 20 are transferred, number of boys in A = 100 and number of boys in B is 60.
Difference = 100 - 60 = 40
_________________

Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 23 Sep 2014
Posts: 34
Location: India
Concentration: Marketing, Finance
GMAT 1: 670 Q48 V34
School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

05 May 2015, 23:20
VeritasPrepKarishma wrote:
registerincog 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

Sometimes, the question becomes very easy with a little bit of reasoning. People often ask - how do we go from Q48 to Q51? The difference often lies in utilization of this reasoning. Let me tell you my thought process when I saw this question.

School A - 40% girls
School B - 60% girls

"The ratio of the number of girls at school A to the number of girls at school B is 4:3"
When I read this line, I went back to the previous line with the % figures. I noticed that school A has more girls than school B (4:3) but its % of girls is lower (only 40% compared to 60% in B). This means that school A has more students than school B. Say something like school A has 200 students while school B has 100. So school A has 80 girls while school B has 60 girls. This gave me a ratio of 4:3. (If I had not got 4:3 on my first try, I might have tweaked the assumed numbers a bit but would have stuck to simple numbers.) Then I verified the rest of the data against these numbers and got my answer easily as 40.

Algebra Solution
Say, if you do insist on algebra and do not want to rely on reasoning, try to work in a single variable.
Girls in A:Girls in B = 4:3
Girls in A = 4n, Girls in B = 3n
Since in A, girls are 40% and boys are 60%, number of boys is 6n.
Since in B, girls are 60% and boys are 40%, number of boys is 2n.

(6n - 20)/(2n + 20) = 5/3
You get n = 20

Boys at school A after transfer = 6*20 - 20 = 100
Boys are school B after transfer = 2*20 + 20 = 60
Difference = 40

Hi karishma,

Even I started of with the reasoning and using smart numbers.

I see the number of students that you initially took were 200 and 100.

I started of with 100 and 50 which did not work.

So in such cases should one go for the next set of smart numbers or should switch to the equation method??
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8803
Location: Pune, India
Re: School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

06 May 2015, 00:27
1
believer700 wrote:
VeritasPrepKarishma wrote:
registerincog 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

Sometimes, the question becomes very easy with a little bit of reasoning. People often ask - how do we go from Q48 to Q51? The difference often lies in utilization of this reasoning. Let me tell you my thought process when I saw this question.

School A - 40% girls
School B - 60% girls

"The ratio of the number of girls at school A to the number of girls at school B is 4:3"
When I read this line, I went back to the previous line with the % figures. I noticed that school A has more girls than school B (4:3) but its % of girls is lower (only 40% compared to 60% in B). This means that school A has more students than school B. Say something like school A has 200 students while school B has 100. So school A has 80 girls while school B has 60 girls. This gave me a ratio of 4:3. (If I had not got 4:3 on my first try, I might have tweaked the assumed numbers a bit but would have stuck to simple numbers.) Then I verified the rest of the data against these numbers and got my answer easily as 40.

Algebra Solution
Say, if you do insist on algebra and do not want to rely on reasoning, try to work in a single variable.
Girls in A:Girls in B = 4:3
Girls in A = 4n, Girls in B = 3n
Since in A, girls are 40% and boys are 60%, number of boys is 6n.
Since in B, girls are 60% and boys are 40%, number of boys is 2n.

(6n - 20)/(2n + 20) = 5/3
You get n = 20

Boys at school A after transfer = 6*20 - 20 = 100
Boys are school B after transfer = 2*20 + 20 = 60
Difference = 40

Hi karishma,

Even I started of with the reasoning and using smart numbers.

I see the number of students that you initially took were 200 and 100.

I started of with 100 and 50 which did not work.

So in such cases should one go for the next set of smart numbers or should switch to the equation method??

During practice, always start with the more intuitive method. Stick to it for a while. Even if you spend a few mins and are unable to get the answer, you can later switch to algebra. With practice, these instances of "not getting the answer" will reduce. You will automatically zero in on the right numbers with some tweaking (for example, is your answer greater than or smaller than what is required? Adjust the assumed numbers accordingly etc).

In the actual exam, know where you stand. If, during recent practice, you were able to get most answers without algebra, then go ahead and use the intuitive methods. Even if you have to rely on algebra in some questions after wasting 2-3 mins on it, you will have plenty and more extra time. If you were almost always forced to resort to algebra during practice, then might as well stick with algebra in the actual exam.
_________________

Karishma
Veritas Prep GMAT Instructor

Manager
Joined: 16 Feb 2016
Posts: 52
Concentration: Other, Other
Re: School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

23 Feb 2016, 07:08
Looking at the answers they are in multiples of 20.

So I will use substitution on this one:

Girls
School A to School B
4:3
Multiply y 20
School A= 80 girls
School B = 60 girls

From the difference of percentages we can calculate the number of boys
School A: 60% is 120
School B: 40% is 40

So if 20 are transferred from A to B then we will have 100 in School A and 60 in School B.

Difference is 100-60=40.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8803
Location: Pune, India
Re: School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

22 Aug 2016, 04:12
VeritasPrepKarishma wrote:
registerincog 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

Algebra Solution
Say, if you do insist on algebra and do not want to rely on reasoning, try to work in a single variable.
Girls in A:Girls in B = 4:3
Girls in A = 4n, Girls in B = 3n
Since in A, girls are 40% and boys are 60%, number of boys is 6n.
Since in B, girls are 60% and boys are 40%, number of boys is 2n.

(6n - 20)/(2n + 20) = 5/3
You get n = 20

Boys at school A after transfer = 6*20 - 20 = 100
Boys are school B after transfer = 2*20 + 20 = 60
Difference = 40

Responding to a pm:
Quote:
Since in A, girls are 40% and boys are 60%, number of boys is 6n.
Since in B, girls are 60% and boys are 40%, number of boys is 2n

Why is it that you didn't represent boys in school b as 4n? You simplified it 60/40 to get 3/2. However, in A you left the boys as 6n, you did not reduce the ratio as you did in B.

Your help would be greatly appreeciated.

Girls in A:Girls in B = 4:3
Assume actual numbers with a variable:
Girls in A = 4n, Girls in B = 3n

Since in school A, girls are 40% and boys are 60%,
40% of Total students in A = 4n
Total students in A = 4n *100/40 = 10n
So number of boys in school A = 10n - 4n = 6n

Using the same logic for school B, since in school B, girls are 60%,
60% of Total students in B = 3n
Total students in = 3n * 100/60 = 5n
So the number of boys in school B = 5n - 3n = 2n

I hope you understand from where I got 6n and 2n. I did this so that a single variable represents all the relevant quantities.
_________________

Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 02 Nov 2015
Posts: 21
Re: School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

09 Sep 2016, 10:30
Hi All,

Why can't we go backwards in such type of questions where two ratios are given and final answer really depends on the final ratio.

Let us start with taking final Boys ratio of 5:3, for school A & B respectively. We know that no. of students in school A is significantly greater than B, so, we can take final numbers of boys in A & B to be 100 & 60 (5:3), also 100 sounds better and is easy for calculation purposes.

now Boys(A original)= 100 +20= 120 & Boys (B original)= 60-20=40). These new numbers of 120 & 40 are original percentage of boys in schools A & B respectively (60% & 40%). So, the number of girls in school A & B are 80 & 60 respectively (40% & 60%), which matches with the original ratio 4:3.

I prefer "picking numbers method" in such question more useful as it will eliminate any silly mistakes we may commit while solving algebraic equations and eventually get stuck in getting/marking the right answer.

Experts let me know, if you also suggest to pick numbers in such question types.

Regards
Yash
Director
Joined: 13 Mar 2017
Posts: 699
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

23 Oct 2017, 01:09
registerincog 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

A : Girls = 0.4 A, Boys = 0.6 A
B: Girls = 0.6 B, Boys = 0.4 B

Now, 0.4A/0.6B = 4/3 -> A = 2B

So,
A= 2B : Girls = 0.8B, Boys = 1.2B
B: Girls = 0.6 B, Boys = 0.4 B

After transfer of 20 boys from A to B
A= 2B : Girls = 0.8B, Boys = 1.2B-20
B: Girls = 0.6 B, Boys = 0.4 B+20

(1.2B-20)/(0.4B+20) = 5/3 -> B = 100

Difference in no. of boys between Class A and B after transfer = (1.2B-20)-(0.4B+20) = 0.8B -40 = 0.8*100 - 40 = 40

_________________

CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

Director
Joined: 13 Mar 2017
Posts: 699
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

23 Oct 2017, 02:04
1
Yash26 wrote:
Hi All,

Why can't we go backwards in such type of questions where two ratios are given and final answer really depends on the final ratio.

Let us start with taking final Boys ratio of 5:3, for school A & B respectively. We know that no. of students in school A is significantly greater than B, so, we can take final numbers of boys in A & B to be 100 & 60 (5:3), also 100 sounds better and is easy for calculation purposes.

now Boys(A original)= 100 +20= 120 & Boys (B original)= 60-20=40). These new numbers of 120 & 40 are original percentage of boys in schools A & B respectively (60% & 40%). So, the number of girls in school A & B are 80 & 60 respectively (40% & 60%), which matches with the original ratio 4:3.

I prefer "picking numbers method" in such question more useful as it will eliminate any silly mistakes we may commit while solving algebraic equations and eventually get stuck in getting/marking the right answer.

Experts let me know, if you also suggest to pick numbers in such question types.

Regards
Yash

Yes back solving also works most of the times, unless data is very complex..
For GMAT problems is a very good way to solve the problems.
_________________

CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

26 Oct 2017, 14:27
registerincog 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

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.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13361
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

11 Feb 2018, 12:34
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

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

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

VP
Joined: 07 Dec 2014
Posts: 1152
School A is 40% girls and school B is 60% girls. The ratio  [#permalink]

### Show Tags

11 Feb 2018, 15:45
registerincog 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

let a and b=total students at A and B respectively
.4a/.6b=4/3
b=a/2
substituting,
(.6a-20)/(.4a/2+20)=5/3
a=200; b=100
.6*200=120 boys originally at A
120-20=100 boys remaining at A
.4*100=40 boys originally at B
40+20=60 boys currently at B
100-60=40 boys difference between A and B
B
School A is 40% girls and school B is 60% girls. The ratio &nbs [#permalink] 11 Feb 2018, 15:45
Display posts from previous: Sort by