Official Solution: Bunuel
For each of the following statements, select Yes if, according to the information provided, the statement is true. Otherwise select No.
Let us look at the info provided.
(I) Auditorium:
Max capacity - 1000,
Number of events - three(music, dance and art), with concert dance every Sunday.
First day of month was Sunday, so 5 Sundays in the week.
Music was on at least five days.
(II) Seating:
Every day of 30 days, all 1000 seats filled
Men higher on 15 days and women higher on remaining 15 days.
Entire month - Average of women = 600, Average of men = 400
Sundays - Average of women = 700, Average of men = 300
______________________
Question 2:
(a) The highest number of female attendees on any day was on a Sunday.
We know that average per day on Sundays was greater than the other days, but we also know that for exactly 15 days, the women outnumbered men.
What the strength was on any of these 15 days cannot be found from given information. So, the highest number of female attendees on any day could be on any of these 15 days....NO
(b) The total number of men attendees was less than the total number of female attendees in the month.
The average of men was 400, while that of female was 600. So, surely women were more in number. No need to calculate, as higher average means higher total...YES
(c) Given that the auditorium has been booked completely for each of the 30 days of the next month and the average of the female attendees will increase by exactly 10%, the average number of male attendees will decrease by more than 10%.
The average number of women next month would be 600*1.1 = 660, so average of men next month will be 1000-640 or 340.
So decrease in average number of men \(=\frac{60}{400}*100\) or 15%...YES
Correct answer: The highest number of female attendees on any single day occurred on a Sunday
"No" The total number of male attendees was less than the total number of female attendees for the month.
"Yes" Given that the auditorium is fully booked for each of the 30 days of the next month, and the average number of female attendees will increase by exactly 10%, the average number of male attendees will decrease by more than 10%.
"Yes"