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Class B has 50%

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by BTGmoderatorDC » Sun Dec 03, 2017 3:03 am
Class B has 50% more students than class A. Number of girls in class A is equal to number of boys in class B. The percentage of girls is the same in both classes. What percentage of the student group are boys?
A. 25 %
B. 33 %
C. 40 %
D. 50 %
E. 60 %

How will i solve this the proper way?

OA C
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boys and girls

by GMATGuruNY » Sun Dec 03, 2017 5:34 am
Generally, percentages on the GMAT convert to common fractions.
For this reason, I suspect that option B is intended to be 33 1/3%, which converts to 1/3.
lheiannie07 wrote:Class B has 50% more students than class A. Number of girls in class A is equal to number of boys in class B. The percentage of girls is the same in both classes. What percentage of the student group are boys?
A. 25 %
B. 33 1/3 %
C. 40 %
D. 50 %
E. 60 %
Since the percentage of girls is the same for each class, so is the percentage of boys.
We can PLUG IN THE ANSWERS, which represent the percentage of boys in each class.
Since option B implies that 1/3 are boys, and option D implies that 1/2 are boys, let the number of students in Class A = a nice round multiple of 3 and 2 = 60 students.
Since Class B has 50% more students, Class B = 60 + (50% of 60) = 60 + 30 = 90 students.
When the correct answer choice is plugged in, the number of girls in Class A will be equal to the number of boys in Class B.

B: 33 1/3 %
Boys in Class A = (1/3)(60) = 20, implying that girls in Class A = 60-20 = 40.
Boys in Class B = (1/3)(90) = 30.
Here, the number of girls in Class A (40) is GREATER than the number of boys in Class B (30).

D: 50 %
Boys in Class A = (1/2)(60) = 30, implying that girls in Class A = 60-30 = 30.
Boys in Class B = (1/2)(90) = 45.
Here, the number of girls in Class A (30) is LESS than the number of boys in Class B (45).

Since option B makes the number of girls in Class A GREATER than the number of boys in Class B, and option D makes the number of girls in Class A LESS than the number of boys in Class B, the correct answer must be BETWEEN options B and D.

The correct answer is C.

C: 40%
Boys in Class A = (40/100)(60) = 24, implying that girls in Class A = 60-24 = 36.
Boys in Class B = (40/100)(90) = 36.
Success!
The number of girls in Class A (36) is equal to the number of boys in Class B (36).
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by Brent@GMATPrepNow » Sun Dec 03, 2017 9:17 am
lheiannie07 wrote:Class B has 50% more students than class A. Number of girls in class A is equal to number of boys in class B. The percentage of girls is the same in both classes. What percentage of the student group are boys?
A. 25 %
B. 33 %
C. 40 %
D. 50 %
E. 60 %
Class B has 50% more students than class A.
Let's choose some nice values that work with this information. How about:
TOTAL number of students in class A = 100
TOTAL number of students in class B = 150

Number of girls in class A is equal to number of boys in class B.
Let x = number of girls in class A
So, x = number of boys in class B

This ALSO means that 100-x = number of boys in class B
And 150-x = number of girls in class B

The percentage of girls is the same in both classes.
In other words, the proportion of girls is the same in both classes.
In class A, the proportion of girls to the TOTAL class A population = x/100
In class B, the proportion of girls to the TOTAL class B population = (150-x)/150
So, we can write: x/100 = (150-x)/150
Cross multiply: 150x = 100(150-x)
Simplify: 150x = 15000 - 200x
Add 200 x to both sides: 250x = 15000
Solve: x = 60

So, there are 60 girls in class A and 60 boys in class B
We can also conclude that there are 40 boys in class A

What percentage of the student group are boys?
Total number of boys = 60 + 40 = 100
Total population = 100 + 150 = 250

So the PROPORTION of boys = 100/250 = 2/5
2/5 = 40%

Answer: C
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boys and girls

by GMATGuruNY » Sun Dec 03, 2017 2:30 pm
lheiannie07 wrote:Class B has 50% more students than class A. Number of girls in class A is equal to number of boys in class B. The percentage of girls is the same in both classes. What percentage of the student group are boys?
A. 25 %
B. 33 %
C. 40 %
D. 50 %
E. 60 %
One more approach:

Since the percentage of girls is the same for each class, the RATIO of girls to boys is the same for each class.

Class A:
Let g = girls and b = boys, implying that the ratio of girls to boys = g:b and that the total number of students = g+b.

Class B:
Since Class B has the same ratio of girls to boys but 50% more students, the number of boys and the number of girls in Class B must each be 50% greater than their counterparts in Class A:
Girls in Class B = g + (50% of g) = g + (1/2)g = (3/2)g.
Boys in Class B = b + (50% of b) = b + (1/2)b = (3/2)b.

Class A, revisted:
Since the number of girls in Class A is equal to the number of boys in Class B, the blue values above are equal:
g = (3/2)b.
Substituting g = (3/2)b into total students = g+b, we get:
Total students = (3/2)b + b = (5/2)b.
Thus:
(boys)/(total students) = b / (5/2)b = 1/(5/2) = 2/5 = 40%.

Since boys constitute 40% of Class A -- and Class B has the same ratio of girls to boys -- boys must also constitute 40% of Class B.
Thus:
40% of the students are boys.

The correct answer is C.
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by Scott@TargetTestPrep » Fri Dec 15, 2017 6:51 am
lheiannie07 wrote:Class B has 50% more students than class A. Number of girls in class A is equal to number of boys in class B. The percentage of girls is the same in both classes. What percentage of the student group are boys?
A. 25 %
B. 33 %
C. 40 %
D. 50 %
E. 60 %
Let the number of students in class A be 2x. Since the number of students in class B is 50% more, it is (1.5)2x = 3x.

Denote the number of boys in class B by y. Since the number of girls in class A is the same as the number of boys in class B, it is also y. Since there are 2x students in class A and y of them are girls, there are 2x - y boys in class A. Thus, in class A and B, there are (2x - y) + y = 2x boys. Therefore, the percentage of boys in the two classes combined is 2x/5x = 2/5 = 40%.

Answer: C

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by GMATWisdom » Fri Dec 15, 2017 8:27 am
lheiannie07 wrote:Class B has 50% more students than class A. Number of girls in class A is equal to number of boys in class B. The percentage of girls is the same in both classes. What percentage of the student group are boys?
A. 25 %
B. 33 %
C. 40 %
D. 50 %
E. 60 %

How will i solve this the proper way?

OA C
If srtudents in class A = 100 then students in class B =150
If there are X% boys in each class then
number of boys in Class A = X and in class B = 1.5X
number of girls in class A = 100-X = number of boys in class B = 1.5 X
= > 100-X =1.5X or 2.5X = 100 or X= 40
hence option C
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