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?
8
9
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12
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mevicks
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Class A:nakul17 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?
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B/G = 3/4
Class B:
B/G = 4/5
For class B adding 1 to the numerator and 2 to the denominator to their multiples should yield a ratio of class A ie (3/4)
(4/5) *(2/2) => 8/10 => Add 1 to the numerator and 2 to teh denominator => 9/12 = 3/4
Thus the Number of girls in [spoiler]A = 12[/spoiler]
Regards,
Vivek
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mevicks
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Algebraic Approach:nakul17 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?
8
9
10
11
12
Class A:
B/G = 3/4
B = 3x
G = 4x
Class B:
B/G = 4/5
B = 4y
G = 5y
Class A has one more boy and two more girls than class B:
3x = 4y + 1 ... (i)
4x = 5y + 2 ... (ii)
Multiply (i) by 5 and (ii) by 4:
15x = 20y + 5
16x = 20y + 8
Subtract (i) from (ii):
16x = 20y + 8
-15x = -20y - 5
x = 3
[spoiler]4x = 12 = Number of girls in A[/spoiler]
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Hi nakul17,
Ratio questions that have numerical answers often provide a Number Property shortcut that you can take advantage of.
Here, we're told that the ratio of boys to girls in Class A is 3:4...and some other ratio data (which we'll get to in a moment). We're asked for the number of girls in Class A. Since we have a ratio of 3:4, then the number of boys in Class A MUST be a multiple of 3 and the number of girls MUST be a multiple of 4. You can immediately eliminate B, C and D because they're not multiples of 4.
Now, we just have to "check" answer A and E against the rest of the question; whichever answer matches all of the facts is the answer:
The ratio of boys to girls in Class B is 4:5, so the number of boys MUST be a multiple of 4 and the number of girls MUST be a multiple of 5. We're also told that Class A has 1 more boy and 2 more girls than class B.
Answer A
Room A
Boys = 6
Girls = 8
Room B
Since Room A has 1 more boy....
Boys = 5
BUT the number of boys MUST be a multiple of 4. This DOES NOT MATCH the info, so answer A is incorrect.
Answer E
Room A
Boys = 9
Girls = 12
Room B
Since room A has 1 more boy and 2 more girls....
Boys = 8
Girls = 10
This MATCHES the ratio of 4:5
Total for both rooms:
Boys: 17
Girls: 22
This MATCHES the total ratio of 17:22
Final Answer:E
GMAT assassins aren't born, they're made,
Rich
Ratio questions that have numerical answers often provide a Number Property shortcut that you can take advantage of.
Here, we're told that the ratio of boys to girls in Class A is 3:4...and some other ratio data (which we'll get to in a moment). We're asked for the number of girls in Class A. Since we have a ratio of 3:4, then the number of boys in Class A MUST be a multiple of 3 and the number of girls MUST be a multiple of 4. You can immediately eliminate B, C and D because they're not multiples of 4.
Now, we just have to "check" answer A and E against the rest of the question; whichever answer matches all of the facts is the answer:
The ratio of boys to girls in Class B is 4:5, so the number of boys MUST be a multiple of 4 and the number of girls MUST be a multiple of 5. We're also told that Class A has 1 more boy and 2 more girls than class B.
Answer A
Room A
Boys = 6
Girls = 8
Room B
Since Room A has 1 more boy....
Boys = 5
BUT the number of boys MUST be a multiple of 4. This DOES NOT MATCH the info, so answer A is incorrect.
Answer E
Room A
Boys = 9
Girls = 12
Room B
Since room A has 1 more boy and 2 more girls....
Boys = 8
Girls = 10
This MATCHES the ratio of 4:5
Total for both rooms:
Boys: 17
Girls: 22
This MATCHES the total ratio of 17:22
Final Answer:E
GMAT assassins aren't born, they're made,
Rich
