At a certain elementary school, 10 percent of the fifth-grade students

Question

At a certain elementary school, 10 percent of the fifth-grade students are members of the school band. If 12 percent of the fifth-grade boys and 8 percent of the fifth-grade girls are members of the band, what percent of the fifth-grade students at the school are boys?

A. 10%
B. 12%
C. 20%
D. 30%
E. 50%

A. 10% 
B. 12% 
C. 20% 
D. 30% 
E. 50%

gmatlover12 · Answer

If there are b boys and g girls, then, rewriting the question mathematically, 
0.1 (b + g) = 0.12b + 0.08g ==> 0.02b = 0.02g ==> b = g, thus boys are 50%

CAMANISHPARMAR · Answer

The equation developed is 0.12B + 0.08G = 0.10 (B + G) 
Which implies 12B + 8G = 10B + 10G
or  \frac{G}{B} =1
Add 1 to both sides to get  \frac{Total students}{Total Boys}  = 2 or flipping the ratio we get  \frac{Total Boys}{Total students}  =  \frac{1}{2}  or 50%

saraheja · Answer

0.12B + 0.08G = 0.10 (B + G)

G/B = 1

Adding total no. of boys :

G+B/2B = Total Students/Boys = 2 , Required is 1/2

ScottTargetTestPrep · Answer

We can let the total number of 5th grade students be 1000.

So 100 5th graders are in the band.

Now let b = the number of boys in 5th grade of the school, so 1000 - b = the number of girls in 5th grade. We can create the equation:

0.12b + 0.08(1000 - b) = 100

0.12b + 80 - 0.08b = 100

0.04b = 20

b = 20/0.04 = 2000/4 = 500

So the number of boys in 5th grade is 500/1000 = 1/2 = 50% of all 5th graders at the school.

Answer: E

zishu912 · Answer

Lets assume that there are 100 students in the fifth grade
10 % of the 100 are in school band = 10

number of boys = x and number of girls = 100 - x

According to question,

12 % of x + 8 % of (100 - x )= 10
12x/100 + 800/100 - 8x/100 = 10
12x + 800 -8x = 1000
4x = 200
x = 50

therefore number of boys = 50 and number of girls = 50 in a class of 100 students

hence the percentage of boys in fifth grade student is = 50/100 * 100 = 50%

Abhishek009 · Answer

b + g = 100 ------------>(I)

10 = \frac{12b}{100} + \frac{8g}{100}

Or,  250 = 3b + 2g ------------>(II)

(I)x3 =>  3b + 3g = 300 ------------>(III)

(III) - (II) is  g = 50

Hence boys must be 50, and percent of the fifth-grade students at the school are boys is 50% , Answer must be (E)

CrackverbalGMAT · Answer

At a certain elementary school, 10 percent of the fifth-grade students are members of the school band. If 12 percent of the fifth-grade boys and 8 percent of the fifth-grade girls are members of the band, what percent of the fifth-grade students at the school are boys?

A. 10%
B. 12%
C. 20%
D. 30%
E. 50%

Let's say, the no of boys in 5 th grade = B

No of girls in 5 th grade = G

So Total no of students in 5 th grade = B+ G

It's given that,

12 % of B + 8% of G = 10 % of (B+G)

12 % of B + 8% of G = 10 % of B + 10% of G
2% of B = 2 % of G
B=G . i.e No of boys in 5th grade is equal to no of girls in 5th grade

what percent of the fifth-grade students at the school are boys? 
 50 % ,Since boys and girls are equal in number.

Ans:  Option E.

Hope it helps!
  Clifin J Francis,
GMAT SME

At a certain elementary school, 10 percent of the fifth-grade students

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At a certain elementary school, 10 percent of the fifth-grade students

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