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The ratio of boys to girls in Class A is 3 to 4. The ratio

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by BTGmoderatorDC » Fri Mar 29, 2019 12:29 am

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Answers

A

B

C

D

E

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Difficulty—

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

OA E

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by GMATGuruNY » Fri Mar 29, 2019 3:40 am
BTGmoderatorDC wrote: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.
Since b:g = 3:4, the number of girls must be a multiple of 4.
Eliminate B, C and D.

Answer choice A: g = 8.
Since b:g = 3:4 = 6:8, b=6.
Since Class A has one more boy and two more girls than Class B, in Class B, b=5 and g=6.
Doesn't work: the required ratio in Class B is 4:5.
Eliminate A.

The correct answer is E.
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by Brent@GMATPrepNow » Fri Mar 29, 2019 5:13 am
BTGmoderatorDC wrote: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

OA E

Source: Manhattan Prep
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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- Intro to ratios: https://www.gmatprepnow.com/module/gmat ... video/1081
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by Scott@TargetTestPrep » Thu Apr 04, 2019 5:14 pm
BTGmoderatorDC wrote: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

OA E

Source: Manhattan Prep
We can create the ratios:

Class A:

Boys : girls = 3x : 4x

Class B:

Boys : girls = 4y : 5y

Combining, we have:

(3x + 4y)/(4x + 5y) = 17/22

22(3x + 4y) = 17(4x + 5y)

66x + 88y = 68x + 85y

3y = 2x

Also, we are given that class A has one more boy and two more girls than class B. So we have:

3x = 4y + 1 and 4x = 5y + 2

Since 3y = 2x, we know that 6y = 4x, and therefore we have:

6y = 5y + 2

y = 2

Since class A has 4x girls and 4x = 5y + 2, we have 5(2) + 2 = 12 girls in class A.

Answer: E

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