Q.1
Hyram is helping his little sister write her integers from 1 to 50. He suggests that they take a break after she has written her 33rd digit. What was the last two-digit number that Hyram’s little sister wrote before they took the break? *

Q.2
Ten items have the following weights, in pounds: 2, 3, 5, 5, 6, 6, 8, 8, 8, 9. The items are then divided into three sets of 20 pounds each. How many sets contain an 8 pound weight? *

0508 math shells edited 1

Q.3
The population of Expotown is currently 54,000 people. If the population has increased by 200% in the past 30 years, what was the population 30 years ago? *

Q.4
An arithmetic series of positive integers has 8 terms and a sum of 2008. What is the smallest possible value of any member of the series? *

Q.5
The 660 students at Mandelbrot Middle School voted on their choice for favorite among six mathematicians. The table shows the results of the vote. Finn made a circle graph to represent the data in the table. In degrees, what is the measure of the central angle of the sector that represents votes for Gauss? *

0508 mathmeticians

Q.6
In a round-robin chess tournament every player plays one game with every other player. Five participants withdrew after playing two games each. None of these players played a game against each other. A total of 220 games were played in the tournament. Including those who withdrew, how many players participated? *

Q.7
The sum of the reciprocals of three consecutive positive integersis equal to 47 divided by the product of the integers. What is the smallest of the three integers? *

Q.8
A bag contains ten identical blue marbles and ten identical green marbles. In how many distinguishable ways can five of these marbles be put in a row if there are at least two blue marbles in the row and every blue marble is next to at least one other blue marble? *

0508 marbles

Q.9
The sum of five different positive integers is 80. What is the largest possible value of the second largest number? *

Q.10
From the time a shop opens at 10 a.m., one customer enters the shop every 15 minutes, until the shop closes at 7 p.m. There is a 1/3 chance that the salesman will convince the customer to buy a widget. The shop owner makes a profit of $6 on each widget sold. What is the most the shop owner can pay the salesman (in dollars per hour) to exactly break even? That is, what hourly rate will make the amount paid to the salesman equal the total amount of income from widget sales? *

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