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

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14 Apr 2017, 16:14
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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

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Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B  [#permalink]

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16 Apr 2017, 22:23
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amathews 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

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

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

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Schools: Jones '21 (A$) GMAT 1: 710 Q48 V40 GPA: 3 Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B [#permalink] Show Tags 14 Apr 2017, 17:00 7 2 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 General Discussion Math Expert Joined: 02 Sep 2009 Posts: 56261 Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B [#permalink] Show Tags 15 Apr 2017, 02:48 1 amathews 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 Similar question to practice: https://gmatclub.com/forum/the-ratio-of ... 92242.html _________________ CEO Joined: 12 Sep 2015 Posts: 3848 Location: Canada Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B [#permalink] Show Tags 16 Apr 2017, 08:06 3 Top Contributor 4 amathews 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'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: RELATED VIDEO _________________ Test confidently with gmatprepnow.com e-GMAT Representative Joined: 04 Jan 2015 Posts: 2942 Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B [#permalink] Show Tags 16 Apr 2017, 22:32 2 3 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 _________________ Current Student Joined: 01 Dec 2016 Posts: 106 Concentration: Finance, Entrepreneurship GMAT 1: 650 Q47 V34 WE: Investment Banking (Investment Banking) Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B [#permalink] Show Tags 19 Apr 2017, 14:24 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 _________________ What was previously considered impossible is now obvious reality. In the past, people used to open doors with their hands. Today, doors open "by magic" when people approach them Current Student Joined: 01 Dec 2016 Posts: 106 Concentration: Finance, Entrepreneurship GMAT 1: 650 Q47 V34 WE: Investment Banking (Investment Banking) Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B [#permalink] Show Tags 19 Apr 2017, 14:25 1 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 _________________ What was previously considered impossible is now obvious reality. In the past, people used to open doors with their hands. Today, doors open "by magic" when people approach them Current Student Joined: 12 Oct 2015 Posts: 218 Location: Canada Concentration: Leadership, Accounting GMAT 1: 700 Q47 V39 GPA: 3 WE: Accounting (Accounting) Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B [#permalink] Show Tags 24 May 2017, 07:21 3 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. _________________ Winners dont make excuses. 350--> 700 https://gmatclub.com/forum/700-q47-v39-ir-7-awa-246682.html Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 6923 Location: United States (CA) Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B [#permalink] Show Tags 13 Dec 2017, 17:23 amathews 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 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 _________________ Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. VP Joined: 07 Dec 2014 Posts: 1206 The ratio of boys to girls in Class A is 1 to 4, and that in Class B [#permalink] Show Tags Updated on: 12 Aug 2018, 15:10 amathews 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 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 Originally posted by gracie on 15 Dec 2017, 14:07. Last edited by gracie on 12 Aug 2018, 15:10, edited 1 time in total. Intern Joined: 02 Nov 2017 Posts: 17 Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B [#permalink] Show Tags 17 Dec 2017, 02:50 Is there a way to do this sum through Alligation? EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14567 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B [#permalink] Show Tags 13 Jan 2018, 17:13 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: 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 *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B  [#permalink]

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19 Feb 2018, 03:21
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
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Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B  [#permalink]

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08 Aug 2018, 09:50
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.

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Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B  [#permalink]

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12 Aug 2018, 10:20
I wouldnt classify this question as "hard". Solved it in 20 seconds. I suggest changing it to a "medium" type of question.
Re: The ratio of boys to girls in Class A is 1 to 4, and that in Class B   [#permalink] 12 Aug 2018, 10:20
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