Challenge-averages

[Night reader]

On six consecutive vocabulary quizzes, Kelvin's lowest score was 70. Was his average (arithmetic mean) quiz score for the six quizzes less than 80?

(1) The average of Kelvin's three lowest quiz scores was 72.
(2) The average of Kelvin's three highest quiz scores was 92.

[Rahul@gurome]

Solution
Let his scores in ascending order be a1, a2, a3, a4, a5 and a6.
Since lowest score is 70, a1 = 70.
We need to know whether (a1+a2+a3+a4+a5+a6)/6 < 80 or not.
Or whether (a1+a2+a3+a4+a5+a6) < 480 or not.
Or whether a2+a3+a4+a5+a6 < 410 or not.
Consider first (1) alone.
It means (a1+a2+a3)/3 = 72.
Or (a1+a2+a3)=216
Or (a2+a3)=146.
So we need to know whether a4+a5+a6<{410 - 146=264} or not .
Since a1 = 70 is the lowest score we can only say that a4>70, a5>70, a6>70 or (a4+a5+a6)>210.
But we cannot say whether (a4+a5+a6) < 264 or not.
So (1) alone is not sufficient.
Next consider (2) alone.
It means (a4+a5+a6)/3 = 92.
Or (a4+a5+a6) = 276.
So we need to know whether (a2+a3) < {(410-276) = 134} or not.
Now a2 > (a1=70) and a3 > (a1=70).
So a2+a3>140.
Or a2+a3 is definitely not < 134.
So from (2) we can say that average of 6 quizzes is not less than 80.
Hence (2) alone is sufficient to answer the question.
The correct answer is (B).

[Night reader]

As usually, Rahul is perfect.