Katherine wants to finish her accounting class with an average test

Question

Katherine wants to finish her accounting class with an average test grade of 85%. On her previous 3 tests she scored 77%, 84% and 92%. If there is one test left and all 4 tests are weighted equally, what is the lowest grade she could earn on the last test and still meet her goal?

A. 80%
B. 85%
C. 87%
D. 90%
E. 92%

A. 80%
B. 85%
C. 87%
D. 90%
E. 92%

acegmat123 · Answer

77+ 84 + 92 + x = 85*4

x=87

C

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Manofsteel · Answer

The way i did it is a method you can use to do it mentally - 
The average of 4 is 85 so the sum of the difference of all 4 nos from the average should be 0 :
77-85 = -8
84-85 = -1
92-85 = 7
Adding all of those differences = -8 - 1 + 7 =-2
Thus inorder for the sum of the differences of all 4 nos to be zero , x-85 = 2
x-85 = 2 (x is the lowest grade she needs to earn in her last test to meet her goal)
x = 87

Thus ans is C

Note - The principle is : The sum of the difference of all 4 nos from the average (in this case 85) should be = 0

Hope it helps.

Abhishek009 · Answer

Since weightage is same for all the tests , let marks for each test be 100

So, Total score in 4*100 = 400

She wants to score 85% of 400 = 340

Marks scored so, far = 77+84+92 => 253

Marks she needs to score in the last test = 340 - 253 => 87
 
Hence, Lowest grade she needs to earn in the last test is 87% , answer will be (C)

Mo2men · Answer

Another way based on unit digit:

Sum of grades /4 =85 ..........sum of grades= 4& 85 = --0 (a number with unit digit 0)

Sum of grades = 77 + 84 +92 + X = --3 +x (Do not sum all numbers, just unit digit)

So we need two numbers when sum up gives 0. so we need number that starts with 7.

the answer is 87

Answer: C

Vinayak Shenoy · Answer

IMO C
77+84+92+x=85*4
x=87%

stonecold · Answer

Nice Question. Here is what i did in this one -> Sum(3)=> 253 Sum(4)=> 340 Hence she must get 87 atleast to make her average of 85. Anything above will be bonus :twisted: