In a class of 20 students, a test was administered, scored only in whole numbers from 0 to 10. At least one student got every possible score, and the average was 7. Compare quantity A with quantity B (i.e. Quantity A is greater, less or equal to quantity B) given below:
- Quantity A: $4$
- Quantity B: The lowest score that two students could have received
Question: What does the wording "The lowest score that two students could have received" mean?
I solved this one as follows:
Total score of $20$ students $= 20*7= 140$
As at least one student got every possible score, so $11$ students get 55 in total. And rest of the students can get $140-55= 85$ in total.
Now, to minimize the score of $9th$ student, I have to maximize $8$ students score, which is $10$. so, their total = $8*10=80$, and the $9th$ student can get $5$.
So, I get lowest 2 scores of $2$ students are $0$ and $1$. In total $2$.
But, right answer I find in book is $5$. What am I missing?