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 \(5\)

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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 \(A?\)

A. 8
B. 9
C. 10
D. 11
E. 12

Answer: E

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Gmat_mission wrote:
Fri Jan 28, 2022 11:58 am
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 \(A?\)

A. 8
B. 9
C. 10
D. 11
E. 12

Answer: E

Source: Manhattan GMAT
The ratio of boys to girls in Class A is 3 to 4.
Let B = number of boys in class A
Let G = number of girls in class A
We get: B/G = 3/4
Cross multiply to get: 4B = 3G

Class A has one more boy and two more girls than class B
So B - 1 = number of boys in class B
So G - 2 = number of girls in class B

The ratio of boys to girls in Class B is 4 to 5
We get: (B - 1)/(G - 2) = 4/5
Cross multiply to get: 5(B - 1) = 4(G - 2)
Expand: 5B - 5 = 4G - 8

So, we now have the following system to solve for G:
4B = 3G
5B - 5 = 4G - 8

Take 4B = 3G and solve for B to get: B = 3G/4

Take 5B - 5 = 4G - 8 and replace B with 3G/4
We get: 5(3G/4) - 5 = 4G - 8
Expand: 15G/4 - 5 = 4G - 8
Multiply both sides by 4 to get: 15G - 20 = 16G - 32
Solve to get: G = 12
Answer: E
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Gmat_mission wrote:
Fri Jan 28, 2022 11:58 am
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 \(A?\)

A. 8
B. 9
C. 10
D. 11
E. 12
We can PLUG IN THE ANSWERS, which represent the number of girls in Class A.
In Class A, the ratio of boys to girls is 3 to 4, implying that the number of girls in Class A must be a MULTIPLE OF 4.
Eliminate B, C and D.

Answer choice A: 8 girls in Class A
In this case:
Since the ratio of boys to girls in Class A = 3:4 = 6:8, Class A has 6 boys and 8 girls.
Since Class B has one less boy and two fewer girls, Class B has 5 boys and 6 girls.
Doesn't work:
In Class B, the ratio of boys to girls must be 4 to 5.
Eliminate A.

The correct answer is E.
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