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Boys and girls in a class are writing letters. [#permalink]

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20 Sep 2013, 16:49

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Boys and girls in a class are writing letters. There are twice as many girls as boys in the class, and each girl writes 3 more letters than each boy. If boys write 24 of the 90 total letters written by the class, how many letters does each boy write?

Re: Boys and girls in a class are writing letters. [#permalink]

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20 Sep 2013, 17:03

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jlgdr wrote:

Boys and girls in a class are writing letters. There are twice as many girls as boys in the class, and each girl writes 3 more letters than each boy. If boys write 24 of the 90 total letters written by the class, how many letters does each boy write?

There are twice as many girls as boys in the class --> g = 2b.

Each girl writes 3 more letters than each boy --> boys write x letters, girls write x+3 letters.

Boys and girls in a class are writing letters. [#permalink]

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26 Feb 2015, 21:59

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Hi GMAT01,

If you had included the 5 answer choices, then I could show you a really easy way to answer this question. However, since you have NOT included them, we're forced to do the Algebra (which will likely take longer). This question is based on "system" Algebra. With that approach, you have to create the necessary equations, then do all of the math needed to get to the solution.

Based on the prompt, here's what we know: 1) There are TWICE as many Girls as Boys in a class 2) Each Girl wrote 3 MORE letters than each Boy 3) Boys wrote 24 letters (out of 90 total letters)

We're asked for the number of letters that EACH BOY wrote.

Here are the equations that you can create from the above information....

G = number of girls B = number of boys X = number of letters written by each Boy (X+3) = number of letters written by each Girl

G = 2B (B)(X) = 24 (G)(X+3) = 66

Now we have 3 variables and 3 unique equations, so we CAN solve for the value of each variable. We're asked to solve for X....

From here, I'm going to let you try to do the Algebra. If you get stuck, then write back and I'll walk you through the math.

To answer your initial question though, this is an example of a 3-variable System question. They're relatively rare on Test Day, but if you're doing well in the Quant section, then there's a decent chance that you'll see one.

Re: Word Problem: Boys and girls in a class are writing letter. [#permalink]

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26 Feb 2015, 23:24

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Expert's post

GMAT01 wrote:

Boys and girls in a class are writing letter. There are twice as many girls as boys in the class, and each girl writes 3 more letter than each boy. If boys write 24 of the 90 total letter written by the class, how many does each boy write?

Is this difficulty level of word problem worth spending time on in your opinion? Haven't encountered these that often in the CAT exams I have taken.

Actually, there isn't much you need to do and no equations/variables you need to use if you just utilize what is given. The question is like a puzzle and certainly something GMAT could give:

Boys write total 24 letters Girls write total 90 - 24 = 66 letters

66 = 2*3*11 Number of girls must be an even number since it is twice of number of boys. The number of letters each writes should be more than 3. So number of girls can be 2 (which means 1 boy), or 6 (which means there are 3 boys) but not 22 (since then each girl would have written 3 letters)

If number of girls is 6, each writes 11 letters. In that case, number of boys is 3 and each writes 24/3 = 8 letters. Girls write 3 letters more than boys so it satisfies all our conditions. _________________

Re: Boys and girls in a class are writing letters. [#permalink]

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27 Feb 2015, 21:38

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jlgdr wrote:

Boys and girls in a class are writing letters. There are twice as many girls as boys in the class, and each girl writes 3 more letters than each boy. If boys write 24 of the 90 total letters written by the class, how many letters does each boy write?

A. 3 B. 4 C. 6 D. 8 E. 12

Given that B = 2G. Also, each girl writes 3 more letters than each boy. And, boys write 24 letters out of 90 => Girls write 66 letters.

Let us simply use the options to get the answer.

Option 1: If each boy writes 3 letters => 24/3 = 8 boys in the class => 16 girls in the class. Since each boy writes 3 letters => Each girl writes 6 letters. So, (8 boys * 3 letters) + (16 girls * 6 letters) = 120. This is NOT EQUAL to 90.

Option 2: If each boy writes 4 letters => 24/4 = 6 boys in the class => 12 girls in the class. Since each boy writes 4 letters => Each girl writes 7 letters. So, (6 boys * 4 letters) + (12 girls * 7 letters) = 108. This is NOT EQUAL to 90.

Option 3: If each boy writes 6 letters => 24/6 = 4 boys in the class => 8 girls in the class. Since each boy writes 6 letters => Each girl writes 9 letters. So, (4 boys * 6 letters) + (8 girls * 9 letters) = 96. This is NOT EQUAL to 90.

Option 4: If each boy writes 8 letters => 24/8 = 3 boys in the class => 6 girls in the class. Since each boy writes 8 letters => Each girl writes 11 letters. So, (3 boys * 8 letters) + (6 girls * 11 letters) = 90 Hence option D.

Re: Boys and girls in a class are writing letters. [#permalink]

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Word Problem: Boys and girls in a class are writing letter. [#permalink]

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26 Feb 2015, 19:42

Boys and girls in a class are writing letter. There are twice as many girls as boys in the class, and each girl writes 3 more letter than each boy. If boys write 24 of the 90 total letter written by the class, how many does each boy write?

Is this difficulty level of word problem worth spending time on in your opinion? Haven't encountered these that often in the CAT exams I have taken.

Re: Boys and girls in a class are writing letters. [#permalink]

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27 Feb 2015, 03:33

Expert's post

GMAT01 wrote:

Boys and girls in a class are writing letter. There are twice as many girls as boys in the class, and each girl writes 3 more letter than each boy. If boys write 24 of the 90 total letter written by the class, how many does each boy write?

Is this difficulty level of word problem worth spending time on in your opinion? Haven't encountered these that often in the CAT exams I have taken.

Re: Boys and girls in a class are writing letters. [#permalink]

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27 Feb 2015, 07:35

This is really easy to solve, but I feel as if most people get lost in the algebra here.

You know the sum of the letters 90, so the ratio of G:B must be able to produce a sum of 90, given the letter writing constraints.

Tip: start writing out the different ratios that satisfy the initial condition: ratio of boys to girls is 2:1. These are 2:1, 4:2, 6:3, 8:4, etc....writing these out will give you a great "feel" for the answer.

Working with what you're given:

If boys write 24 letters, you know the ratio of boys must be factor of 24. Looking through the ratios you listed out, all of these work, however oddly enough, 6:3 sums to 9, and the total number of letters is 90. Mmhhh, suspicious.

Using the 6:3 ratio, the multiple you have for boys is 8, which means the multiple used for girls is 11 (8+3). This leaves you with 90 total letters, 66 written by girls, 24 written by boys.

However, you don't need to solve for the ratio of letters written by girls, this information doesn't need to be solved for.

The crux of this problem is reading through and comprehending what is being stated/asked. My personal favorite approach to ratio problems is to just start writing down ratios that fit the given constraint. This gives me a great "feel" for the problem.

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