abhasjha wrote:In a class of 100 students , the average age is 16 yrs. If the number of girls is increased by half of its previous number and the number of boys becomes 2/3 of its previous number,the total number of students remained unchanged.It was observed that the average age of boys and girls was not changed and the new total average was 15.Find the average age of girls?
(a) 18
(b) 19
(c) 13
(d) 12
When the number of girls increases by 1/2 and the number of boys decreases by 1/3. the total number of students does not change.
Thus, the increase in the number of girls must be EQUAL to the decrease in the number of boys:
(1/2)g = (1/3)b
3g = 2b
g/b = 2/3.
Since there are a total of 100 students, and g:b = 2:3 = 20:30 = 40:60, g=40 and b=60.
From here, we can plug in the answers for the average age of the girls.
An increase in the number of girls DECREASES the average age of the entire class.
Implication:
The average age of the girls must be LESS than the average age of the entire class -- explaining why adding more girls BRINGS DOWN the class average.
Eliminate A and B.
Before the change, the ORIGINAL sum of the ages = (number of students)(original average) = 100*16 = 1600.
After the change, the NEW sum of the ages = (number of students)((new average) = 100*15 = 1500.
Answer choice D: 12
Before the change:
Original sum of the girls' ages = (number of girls)(average age per girl) = 40*12 = 480.
Original sum of the boys' ages = (original sum for the class) - (original sum for the girls) = 1600-480 = 1120.
Average age of the boys = sum/number = 1120/60 = 112/6 = 56/3.
Not possible: on the GMAT, the average age must be an INTEGER VALUE.
Eliminate D.
The correct answer is
C.
Answer choice C: 13
Before the change:
Original sum of the girls's ages = (number of girls)(average age per girl) = 40*13 = 520.
Original sum of the boys' ages = (original sum for the class) - (original sum for the girls) = 1600-520 = 1080.
Average age of the boys = sum/number = 1080/60 = 18.
After the change:
When the number of girls increases by 1/2, the new number of girls = 40 + (1/2)40 = 60.
New sum for the girls = (new number)(average) = 60*13 = 780.
New sum for the boys = (new sum for the class) - (new sum for the girls) = 1500-780 = 720.
When the number of boys decreases by 1/3, the new number of boys = 60 - (1/3)60 = 40.
Average age of the boys = (new sum)/(new number) = 720/40 = 72/4 = 18.
Success!
Before the change and after the change, the average age of the boys is the same: 18.
Algebraic solution:
Let x = the average age of the girls and y = the average age of the boys.
Before the change:
Since there are 40 girls and 60 boys, and the sum of the ages is 1600, we get:
40x + 60y = 1600
2x + 3y = 80.
After the change:
Since there are 60 girls and 40 boys, and the sum of the age is 1500, we get:
60x + 40y = 1500
3x + 2y = 75.
Converting the equations so that y has the same coefficient in each case, we get:
2(2x + 3y = 80) --> 4x + 6y = 160
3(3x + 2y = 75) --> 9x + 6y = 225.
Subtracting the top equation from the bottom equation, we get:
(9x + 6y) - (4x + 6y) = 225-160
5x = 65
x = 13.
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