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Ratio 2 and combined

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by karthikpandian19 » Mon Jan 09, 2012 6:37 pm
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?

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by Anurag@Gurome » Mon Jan 09, 2012 7:30 pm
karthikpandian19 wrote: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?

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Given: In Class A, B : G = 3 : 4
In Class B, B : G = 4 : 5
In combined class, B : G = 17 : 22

Let the # of boys in class A = b and # of girls = g
Then in class B, # of boys = b - 1 and # of girls = g - 2
b : g = 3 : 4 implies 4b = 3g implies b = 3g/4
(b - 1) : (g - 2) = 4 : 5
5b - 5 = 4g - 8
5(3g/4) - 5 = 4g - 8
15g - 20 = 16g - 32
g = 12

The correct answer is E.

Please note that the ratio of boys and girls for combined class is irrelevant in this question.
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by karthikpandian19 » Mon Jan 09, 2012 7:33 pm
Does these kind of irrelevant information comes in GMAT? becoz i have wasted more time to solve this problem wrong.
Anurag@Gurome wrote:
karthikpandian19 wrote: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?

8
9
10
11
12
Given: In Class A, B : G = 3 : 4
In Class B, B : G = 4 : 5
In combined class, B : G = 17 : 22

Let the # of boys in class A = b and # of girls = g
Then in class B, # of boys = b - 1 and # of girls = g - 2
b : g = 3 : 4 implies 4b = 3g implies b = 3g/4
(b - 1) : (g - 2) = 4 : 5
5b - 5 = 4g - 8
5(3g/4) - 5 = 4g - 8
15g - 20 = 16g - 32
g = 12

The correct answer is E.

Please note that the ratio of boys and girls for combined class is irrelevant in this question.
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by Anurag@Gurome » Mon Jan 09, 2012 7:38 pm
karthikpandian19 wrote:Does these kind of irrelevant information comes in GMAT? becoz i have wasted more time to solve this problem wrong.
Such type of questions with irrelevant information are quite rare on GMAT.
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by GMATGuruNY » Tue Jan 10, 2012 4:42 am
karthikpandian19 wrote: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?

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ALWAYS LOOK AT THE ANSWER CHOICES.

The answers choices represent the number of girls in Class A.
Since b:g = 3:4, the number of girls must be a multiple of 4.
Eliminate B, C and D.

Answer choice A: g = 8.
Since b:g = 3:4 = 6:8, b=6.
Since Class A has one more boy and two more girls than Class B, in Class B, b=5 and g=6.
Doesn't work: the required ratio in Class B is 4:5.
Eliminate A.

The correct answer is E.

Note that we had to try ONLY ONE ANSWER CHOICE and perform only SIMPLE ARITHMETIC to determine the correct answer -- a very efficient way to solve the problem.
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by karthikpandian19 » Tue Jan 10, 2012 5:01 am
Thts really a short way to solve a problem less than a minute....Thanks
GMATGuruNY wrote:
karthikpandian19 wrote: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?

8
9
10
11
12
ALWAYS LOOK AT THE ANSWER CHOICES.

The answers choices represent the number of girls in Class A.
Since b:g = 3:4, the number of girls must be a multiple of 4.
Eliminate B, C and D.

Answer choice A: g = 8.
Since b:g = 3:4 = 6:8, b=6.
Since Class A has one more boy and two more girls than Class B, in Class B, b=5 and g=6.
Doesn't work: the required ratio in Class B is 4:5.
Eliminate A.

The correct answer is E.

Note that we had to try ONLY ONE ANSWER CHOICE and perform only SIMPLE ARITHMETIC to determine the correct answer -- a very efficient way to solve the problem.
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by LalaB » Tue Jan 10, 2012 11:06 am
karthikpandian19 wrote:Does these kind of irrelevant information comes in GMAT? becoz i have wasted more time to solve this problem wrong.
in case if u are still interested in so- called "irrelevant info", please see below

in class A girls/total=4/7
in class B girls/total=5/9

in A+B =22/39 (so called irrelevant info)

in a q.stem it is said "Class A has one more boy and two more girls than class B". it means total of B=total of A minus 3 (one boy and 2 girls)

so, now we have the following equation -

4/7*A+5/9(A-3)=22/39(A+A-3)

A=21

Girls in A is 4/7*21=12

now we see,that everything depends on ur imagination. u can use any piece of info to solve a q.
in some cases the method above is good.
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by ronnie1985 » Thu Jan 12, 2012 11:39 pm
(D)
Make a table:-

Class Boys Girls
A 3x 4x
B 4y 5y
Comb 17k 22k

Also
3x = 4y+1
4x = 5y+2 and
hence, 8y+1 = 22k and 10y+2 = 22k. As first iteration k = 1, we get y = 2 and then we get Girls = 12
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by ArunangsuSahu » Fri Jan 13, 2012 12:44 pm
Better to Plug in the answer Choices.

Lot Quicker

Girls in Class A=12
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by [email protected] » Sun Nov 11, 2012 1:20 pm
I solved it like this but then I get x=2 instead of 3

4/5 = 3x-1/4x-2
x=2

Can someone please explain why I get the wrong answer?

Manhattan does it like this:

3/4 = 4x+1/5x+2
x=3


Thanks!!
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by jkaustubh » Mon Nov 12, 2012 1:42 am
[email protected] wrote:I solved it like this but then I get x=2 instead of 3

4/5 = 3x-1/4x-2
x=2

Can someone please explain why I get the wrong answer?

Manhattan does it like this:

3/4 = 4x+1/5x+2
x=3


Thanks!!
Manhattan does it like this:

3/4 = 4x+1/5x+2
x=3

what I get is x=2
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by [email protected] » Thu Nov 15, 2012 7:08 am
Thanks, so it has to be an error from manhattan gmat....
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by GaneshMalkar » Fri Nov 16, 2012 6:43 am
I dont think it is a manhattan error....

You got x = 3 for Class A and x = 2 for Class B which both are correct...
To explain it further....Class A ratio B/G = 3x/4x and x = 3 so Boys = 9 and girls = 12

Class B ratio B/G = 4x/5x and x = 2 which is Boys = 8 and Girls = 10

which satisfy both of our condition
1. Combined ratio of Class A and Class B = (8+9)/(10+12) = 17/22
2. Class A has one more boy and 2 more girls


Hope this helps....

[email protected] wrote:I solved it like this but then I get x=2 instead of 3

4/5 = 3x-1/4x-2
x=2

Can someone please explain why I get the wrong answer?

Manhattan does it like this:

3/4 = 4x+1/5x+2
x=3


Thanks!!
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by [email protected] » Fri Nov 16, 2012 7:42 am
You are absolutely right, I just plugged x in the wrong ratio!

Thanks
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