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# The grade point average of one third of the classroom is 69; the grade

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Joined: 02 Sep 2009
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12 Jul 2016, 04:33
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25% (medium)

Question Stats:

78% (01:14) correct 22% (01:46) wrong based on 92 sessions

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The grade point average of one third of the classroom is 69; the grade point average of the rest is 60. What is the grade point average of the whole class?

A. 61.
B. 63.
C. 65.
D. 67.
E. It depends how many people are there in the class.

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12 Jul 2016, 05:14
Bunuel wrote:
The grade point average of one third of the classroom is 69; the grade point average of the rest is 60. What is the grade point average of the whole class?

A. 61.
B. 63.
C. 65.
D. 67.
E. It depends how many people are there in the class.

Let the number of students in class A be = X1 + X2 + ...... + A1 ( where A1 = remaining students )

Now the remaining avg of the students be A1 / T = 60

A1 = 60T ( we are not sure on the number of students , assuming it as T ).

A = X1 + X2 + ...... + A1 ( First set of students + remaining students).

One third of A students avg is 60.

A / 3 = 69

=> A = 207.

Now X1 + X2 + ...... + A1 = 207.
X1 + X2 + ...... = 207 - 60T.

We are not sure about the number of students in the remaining class + whole class and without that we can't solve this.

IMO E is correct option.

OA please...will correct if I missed anything.
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Updated on: 13 Jul 2016, 05:01
let n=total students in class
total points for 1/3 class=69n/3=23n
total points for 2/3 class=60*2n/3=40n
total points for whole class=23n+40n=63n
63n total class points/n total students=63 grade point average for total class

Originally posted by gracie on 12 Jul 2016, 21:01.
Last edited by gracie on 13 Jul 2016, 05:01, edited 1 time in total.
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12 Jul 2016, 21:59
Bunuel wrote:
The grade point average of one third of the classroom is 69; the grade point average of the rest is 60. What is the grade point average of the whole class?

A. 61.
B. 63.
C. 65.
D. 67.
E. It depends how many people are there in the class.

Bcz its given the 1/3 of class has 69 thus 2/3 of class has 60

Let x be the combined avg (ca)

60<ca<69

69-x/x-60 = 2/1

2x-120 = 69-x
3x=189
X=63

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10 Dec 2016, 10:41
Here is my take on this Question -->
Let the number of students be 3
hence one of them has a 69 and other two have a 60 each
So => Mean of the Group will be => 189/3 => 63

Hence B

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14 Dec 2016, 15:17
1
Using Algebra only method=>
Let the number of students be 3n
Sum(n)=> 69n
Sum(2n)=> 120n
Total = 189n
Hence mean = 189n/3n = 63

Hence B

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17 Dec 2018, 04:30
Solved this question by using "weighted average" method:

Let the total students be "x". As per prompt, 69(x/3) + 60(2x/3) / x = 567x/9x = 63.
Re: The grade point average of one third of the classroom is 69; the grade   [#permalink] 17 Dec 2018, 04:30
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