Mary and three other students took a math test. Each of their scores was a non-negative integer. The teacher announced that the average score (of the 4 students) was 20. Mary immediately knew that all of the other three students scored below average. What is the minimum score that Mary could have gotten to be certain of the above situation?
A. 40
B. 41
C. 60
D. 61
E. 80
Let set variables. We have Mary, student a, student b and student c
No one student a,b and c can get more than 20 each
a + b + c < 20
a+b+c = 30
So, 2 possibilities exist:
1.Student a gets 10
b gets 10
c gets 10
10+10+10=30
2. a gets 28
b gets 1
c gets 1
28+1+1=30
As we know Mary doesn't know the results of the 3 other students, but she knows that not one of them get more than 20.
So, a + b + c < 20
Next we calculate Mary's result:
We know that
a+b+c = 19
(19+M)/4 = 20
M = 61
D
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