Question

Ansgar is writing a novel. He writes seven days a week. On each of those days, he writes for at least 4 hours but never more than 8 hours. Last week, he wrote for exactly 46 hours. What is the maximum number of days on which he could have written for 8 hours?
A) 2 days
B) 3 days
C) 4 days
D) 5 days
E) 6 days

Answer 1

Hint: First find the number of hours if Ansgar writes $4$ hours a day, then find the additional hours (18 hours) that he had worked in the last week. Now, divide these hours in the days so that the maximum number of hours per day is not more than 8.

Complete step-by-step answer:
It is given in the problem that Ansgar is writing a novel at least 4 hours a day and on each of those days, he writes at least $4$ hours but never more than $8$ hours.
If Ansgar writes at least $4$ hours per day for 7 days then
$ = 7 \times 4{\text{ hours}}$
$ = 7 \times 4{\text{ hours}}$
$ = 28{\text{ hours}}$
It means that if Ansgar writes at least $4$ hours per day, then he minimum writes $28$ hours in 7 days, but it is given that in the last week, Ansgar wrote for exactly $46$ hours. It means that Ansgar had written additionally more than 4 hours. These additional hours are:
$ = 46 - 28$
$ = 18$
Therefore, he had written 18 hours additional.
Now, a look at the table that defines the number of hours he could write in the last week.

As a result, he could have written for an additional 4 hours of no more than 4 different days.
Therefore the maximum number of days on which he could have written for 8 hours is 4 days.
Therefore option C is correct.
Note: When Ansgar writes 8 hours in fours a day and the total number of hours is $46$, then he has left 14 more hours. It means that in left three days he worked for 14 hours