The grade point average of the entire class is 90. If the average of

Question

The grade point average of the entire class is 90. If the average of one third of the class is 96, what is the average of the rest?

A. 92.
B. 89.
C. 88.
D. 87.
E. 86.

14101992 · Answer

Let us take number of students on the class as 'x'.

avg grade point = sum of all grade points/x
sum of all grade points = avg grade point*x = 90x

average of one third of the class = 96 = sum of one third grade points of the class/(x/3)
sum of one third grade points of the class = 96*(x/3) = 32x

sum of rest two third grade points of the class = sum of all grade points - sum of one third grade points of the class
sum of rest two third grade points of the class = 90x-32x = 58x
avg of two third of the class = sum of rest two third grade points of the class/(x*2/3) = 58x/(2x/3) = 29*3 = 87.

Hence, answer is D.

-------------------------------

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Donnie84 · Answer

Let's say there are 3 students in the class.

If avg = 90 -> sum = 3*90 = 270.

Avg of 1/3 = 96. This implies that 1 student has 96 points.

Sum of points of other 2 students = 270 - 96 = 174.

Avg of points of those 2 students = 174/2 = 87.

Answer (D).

Alternate approach:

Once we see that units digit of the difference is 4, the average can either have 2 or 7 as its unit digit. There are 2 answer choices that qualify. However, since fewer students (1/3) have higher than average, the average of (2/3) will lie closer to the given average. Pick (D).

prady80 · Answer

Let x be the population of class

90x is the total marks
x/3 students have marks = 96 * x/3

Rest of the class is 2/3x
The marks of x/3 + marks of 2x/3 = marks of x

i.e. 96X/3 + 2/3*avg = 90X
2/3 marks = (90 - 96/3)X
marks = 58 *3 /2 X
avg = 87 
Ans D

Divyadisha · Answer

Let the average of 2/3 rd class = a

And, number of students in class= x

Total = number *average

Total points of whole class= total points of 1/3 class +total points of 2/3rd class
90x= 96 *1/3x + a* 2/3x
3/2x(90x-32x)= a
a= 87

D is the answer

gracie · Answer

equation1: t/n=90
equation2: (t-x)/(n/3)=96➡t/n-x/n=32
subtracting 2 from 1,
x/n=58
because ratio seems high and we know n is a multiple of 3,
assume n=3
then x=58*3=174
174/2=87=average of other 2 students

(checking: 90*3-174=96)

msk0657 · Answer

We can solve this question using mixtures type problem

90 is average of the entire class.

1/3 students avg 96 and the rest 2/3 avg is X ( let's assume this).

96 X

90

The ratio between the 2/1

=> 2/1 = 6 / 90 - X

=> 3 = 90 - X

X = 87.

IMO D is correct.

nipunjain14 · Answer

Bunuel, 
Can you please explain how come the ans is 88?

Bunuel · Answer

______________
Edited. Thank you.

abrakadabra21 · Answer

can be solved within 5 sec

96...............x
 ........90

1...............3
3..............6

90-3 =87

stonecold · Answer

Let the number of students =3
Hence one of them will have score of 96
and Sum(3)= 270
So Sum(2)=174
Hence Mean(2)=> 174/2 => 87

Hence D

bumpbot · Answer

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The grade point average of the entire class is 90. If the average of

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