1)What is the smallest four-digit number that is the sum of three consecutive natural numbers? What are the three consecutive natural numbers that give this sum?

2)In a recent survey, men and women were asked where they primarily buy gifts. Do they shop in stores, shop online, or buy from catalogs? Based on the results of the survey, the following were found to be true:

  • The ratio of store shoppers to online shoppers is 3 to 4.
  • The ratio of women who shop in stores to men who shop in stores is 2 to 1.
  • The ration of men in the survey to women in the survey is 1 to 1.
  • The ratio of men who buy from catalogs to men who shop in stores is 4 to 3.
  • The ratio of women who shop in stores to women in the survey is 3 to 7.
  • Between 300 and 600 people participated in the survey.

Complete the table using the information listed above.

Participants / Shop in Stores / Shop Online / Buy from Catalogs / Total
Women
Men
Total

3)Yolanda’s Yummy Ice Cream Shoppe was giving away samples of new flavors: Yum-Yum Mint, Choco Chips, and Nutty Nosh. Forty-five people had mint, 56 had nosh and 63 had chips. Eighteen people sampled both mint and nosh, 26 tasted both chips and nosh, and 20 had both chips and mint. Eight very brave people sampled all three. How many people tried the new flavors?

4)Skydivers fall at 54 meters per second before their parachutes open. They fall at 6 meters per second after their parachutes open. If a skydiver jumped from a plane at 1452 meters high and reached the ground in 106 seconds, how high was she when she opened her chute?

5)Sharon has between 3 and 100 shells in her collection. If she counts her shells three at a time, she has two left over. If she counts them four at a time, she has two left over. If Sharon counts them five at a time, she still has two left over. How many shells does Sharon have in her collection?

6)A square measuring 10 centimeters on a side is divided by vertical and horizontal line segments into rectangles with areas of 12, 18, 28, and 42 square centimeters. Where should the vertical and horizontal lines be located? Draw a diagram.

7)Jim is shopping for Moose Tracks, which is his favorite flavor of ice cream. He notices that there are three different brands from which to choose. Super Dairy has a six-pint size for $6.15, Sweet Treat has a two-quart size for $3.95, and Grandma’s Ice Cream has a gallon size for $8.00. Which brand offers the best deal for Jim? Explain your reasoning.

8)Connor bought a bag of candy. He gave away 10 percent of the candy to his sister and then gave 3 pieces to his brother. He gave ¼ of what was left to his grandmother and then ate ½ of the remaining 18 pieces of candy. How many pieces of candy were originally in the bag?

9)Kyle rode his bike for 12 miles. During the first third of the trip, he traveled on level ground at an average rate of 10 miles per hour. During the second third of the trip, he traveled uphill at an average rate of 6 miles per hour. During his last third of the distance, Kyle traveled downhill at an average rate of 15 miles per hour. How long did Kyle’s 12-mile bike trip take?

10)A domino is a rectangular tile. The dots, called pips, represent the two numbers on the tile. The domino pictured on the right shows the pair 1– 5. A Double 6 set of dominoes consists of every possible pairing of numbers from 0 to 6 (0 – 0, 1 – 0, 1 – 1,…, 6 – 6). Sets are also available in double 9, double 12, Double 15, and Double 18. How many pips are on a Double 9 set of dominoes?