In a college class, each student’s overall grade is calculated by aver

Question

In a college class, each student’s overall grade is calculated by averaging the student’s grades on t different exams. Up until the last exam, Wei had earned an average exam grade of 0.75g. After earning a grade of g on the last exam, Wei’s overall grade in the class was 0.8g. What is the value of t ?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

CareerGeek · Answer

0.75g*(t - 1) + g = t*0.8g
--> 0.75t - 0.75 + 1 = 0.8t
--> 0.05t = 0.25
--> 5t = 25
--> t = 5

Option D

jabhatta2 · Answer

Hi  chetan2u ,  VeritasKarishma ,  Bunuel ,  generis ,  MahmoudFawzy  - i Believe the OA is D on this

But i wanted to ask a question on my initial strategy which was incorrect

Why doesn't the following work

Up-till last exam average + New score
---------------------------------------------- = New average 
 T

0.75g + g 
 ------------------ = 0.8g 
 T

thus T is 2.1875 (this is obviously wrong but wondering why doesn't this strategy work)

KarishmaB · Answer

New Average = New Total / Total number of items

0.8g = (Old Total + g) / T

0.8g = (0.75g*(T - 1) + g) / T

Note that old total is 0.75g*(T - 1).
.75g is just the old average, not the old total. 
To get old total, you need to multiply it by (T - 1), the old number of items.

ScottTargetTestPrep · Answer

Using the formula sum = average x number, we see that the sum of Wei’s grades on the t - 1 exams is 0.75g(t - 1). With a grade of g on the last exam, the sum of the grades on t exams becomes 0.75g(t - 1) + g. We can create the equation:

/t = 0.8g

0.75g(t - 1) + g = 0.8gt

0.75gt - 0.75g + g = 0.8gt

0.25g = 0.05gt

t = 0.25g/0.05g = 5

Answer: D

randomguy2468 · Answer

Why can't you have T = 2 tests.
First Test=75, Second Test=75
Old Average= 150/2
Old Average=75

g=90
g is third test, where you score a 90
New sum=150+90
New sum=240
New Average=240/3
New Average=80

NEYR0N · Answer

My initial strategy was :

( g + 0.75g ) / ( t + 1) = 0.8g

But the problem seems to be testing the formula of arithmetic sequence: An = A1+ (n-1)*d

why can't I use * My initial strategy ?

thanks

Krunaal · Answer

Your initial strategy has the right thought process behind it, one small mistake - it will be (g +  0.75g(t-1) ) / t = 0.8g this is  Sum of grades of all tests / no. of tests = Overall grade

=> g + 0.75gt - 0.75g = 0.8gt
=> 0.25g = 0.05gt
=>  t = 5

Varun291 · Answer

I have the same question. Although t =3 not 2, but apart from that the numbers should work right?  Bunuel   karishma

Adit_ · Answer

Not an expert but he took g as 90.
0.75*90 will not give you 75 and 0.8*90 will not give you 80.
They will give you the respective numbers only if g=100.
But that does not work in case of 3 tests.

In a college class, each student’s overall grade is calculated by aver

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