Ratio Problem.......GMATPrep

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Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members; Thanked: 14 times

by Mo2men » Sun Apr 16, 2017 3:54 am

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

OA: C

Boys in class A = 1/5

Boys in Class B = 2/7

Let total boys in class A & B= X

1/5.....X.........2/7

I could not continue

How to use alligation method to solve problem above?

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Source: Beat The GMAT — Problem Solving | Sun Apr 16, 2017 3:54 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Apr 16, 2017 6:41 am

Mo2men wrote: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

Let M = the mixture of the two classes.
Alligation can be performed only with percentages or fractions.

Step 1: Convert the ratios to FRACTIONS.
A:
Since boys/girls = 1/4, and 1+4=5, boys/total = 1/5.
B:
Since boys/girls = 2/5, and 2+5=7, boys/total = 2/7.

Step 2: Put the fractions over a COMMON DENOMINATOR.
A = 1/5 = 7/35.
B = 2/7 = 10/35.

Step 3: Plot the fractions on a number line, with A and B on the ends and M in the middle.
A 7/35-----------M-----------10/35 B

Step 4: Calculate the distances between A, M and B.
This distances on the number of line are determined by the RECIPROCAL of the following ratio:
(number of students in A)/(number of students in B).
Since A has twice as many students as B, A/B = 2x/x.
Plotting the reciprocal of this ratio on the number line, we get:
A 7/35----x----M----2x----10/35 B

Step 5: Determine the value of x.
The number line indicates that the total distance (x+2x) is equal to the difference between 10/35 and 7/35:
x+2x = 10/35 - 7/35
3x = 3/35
x = 1/35.

Thus:
boys/total in M = 7/35 + x = 7/35 + 1/35 = 8/35.
Implication:
Of every 35 students in M, 8 are boys, implying that the remaining 27 students are girls.
Thus:
boys/girls in M = 8/27.

The correct answer is C.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Apr 16, 2017 7:02 am

Mo2men wrote: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

We can also solve the question using 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

For more information on weighted averages, you can watch this video: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Here are some additional practice questions related to weighted averages:
- https://www.beatthegmat.com/weighted-ave ... 17237.html
- https://www.beatthegmat.com/weighted-ave ... 14506.html
- https://www.beatthegmat.com/average-weig ... 57853.html
- https://www.beatthegmat.com/averages-que ... 87118.html

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Apr 16, 2017 11:23 am

Hi Mo2men,

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

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Rich

Contact Rich at [email protected]

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Sun Apr 16, 2017 10:44 pm

Mo2men wrote: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

OA: C

Boys in class A = 1/5

Boys in Class B = 2/7

Let total boys in class A & B= X

1/5.....X.........2/7

I could not continue

How to use alligation method to solve problem above?

Hi Mo2men,

A couple of nice approaches by experts... Here's my way.

On a ratio scale, the total number of students in the Class A = 1 + 4 = 5;

Similarly, on a ratio scale, the total number of students in the Class B = 2 + 5 = 7;

Say the total number of students in Class A = 5x and that in Class B = 7; where x is a constant of proportionality

We are given that the number of students in Class A = 2*the number of students in Class B

=> 5x = 2*7

=> x = 14/5

Ratio of total number of boys in both the classes to total number of girls in both the classes

=> [{(14/5)*1} + 2] : [{(14/5)*4} + 5]

=> (14/5 + 2) : (56/5 + 5)

=> 24 : 81

=>[spoiler] 8 : 27[/spoiler]

The correct answer: C

Hope this helps!

Relevant book: Manhattan Review GMAT Math Essentials Guide

-Jay
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Apr 18, 2017 4:49 am

Mo2men wrote: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

In A, boys/total = 1/5 = 7/35.
In B, boys/total = 2/7 = 10/35.

Since A has twice as many students as B, let A = 70 students and B = 35 students.

A:
Since boys constitute 1/5 of the total, boys = (1/5)(70) = 14, with the result that girls = 70-14 = 56.
B:
Since boys constitute 2/7 of the total, boys = (2/7)(35) = 10, with the result that girls = 35-10 = 25.
Resulting ratio for A+B:
(boys in A + boys in B)/(girls in A + girls in B) = (14+10)/(56+25) = 24/81 = 8/27.

The correct answer is C.

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