Question: 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?

1. 8
2. 9
3. 10
4. 11
5. 12

Answer: D
Solution and Explanation:
Approach Solution 1:
To solve this GMAT problem-solving question, you must use the information given in the question. The problems in this group come from many different areas of mathematics. This one has a lot to do with algebra.
The options are set up in a way that makes it hard to pick the best one. The candidates must know the right way to get the response they need. Only one of the five choices given is correct.
Given in the question that
There are 3 to 4 more boys than girls in Class A. For some positive integer multiple x, the number of boys is 3 and the number of girls is 4;
Boys outnumber girls in Class B by a ratio of 4 to 5: For some positive integer multiple y, the number of boys is 4 and the number of girls is 5;
In comparison to class B, class A has one extra boy and two more girls (3x = 4y+1 and 4x = 5y+2). Since we now have a system of two separate linear equations and two unknowns, we can solve it. When we solve for x, we obtain x=3. There are 4*3=12 girls since there are 4x as many girls in Class A.
Response: E.
As you can see, you did everything correctly; nonetheless, solving the system of equations would have been preferable to using a substitute.

Approach Solution 2:
To solve this GMAT problem-solving question, you must use the information given in the question. The problems in this group come from many different areas of mathematics. This one has a lot to do with algebra.
The options are set up in a way that makes it hard to pick the best one. The candidates must know the right way to get the response they need. Only one of the five choices given is correct.
As stated in the question,
If Class A boys are x and girls are y, then
Therefore, for class B, boys equal x-1 and girls equal y-1.
(x-1)/(y-2) = 4/5 and x/y = 3/4.
Adding the value of x to the second equation yields y = 12.
The only options are 8 and 12, as x must be an integer and y must be a multiple of 4 (since x must be an integer). For y = 8 and 12, we substitute 6 and 9 for x in the second equation to satisfy. Since (x-1)/(y-2) = (6-1)/(8-2)
is not equal to 4/5, the answer is 12.
E is the correct choice.

Approach Solution 3:
To solve this GMAT problem-solving question, you must use the information given in the question. The problems in this group come from many different areas of mathematics. This one has a lot to do with algebra.
The options are set up in a way that makes it hard to pick the best one. The candidates must know the right way to get the response they need. Only one of the five choices given is correct.
The ratios Ba (boys in A) to Ga (girls in A) and Bb (boys in B) to Gb can be established (girls in B).
Bb/Gb = 4/5 Ba/Ga = ¾
We want our ultimate ratio to be 17/22 when combined. Several multiples of each of the original ratios can be written out.
Ba/Ga = 3/4, 6/8, 9/12…
Bb/Gb = 4/5, 8/10, 12/15…
It is clear that choosing 9/12 for option A and 8/10 for option B will result in a combined ratio of 17/22. Thus, group A will consist of 12 girls.
E is the correct choice.

“The ratio of boys to girls in Class A is 3 to 4. The ratio of boys tol" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.
To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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