Grade 5
1997 Team Round 1
Team Rounds in the Math Masters Competitions are timed (15 minutes), and calculators are allowed.
Note: Test Preparation Packets containing hundreds of problems (fact drills,
individual and team) from previous years' competitions can be ordered
from Math Masters of Minnesota.
1. The number 15 has four divisors: 1, 3, 5, and 15.
If a number has exactly six divisors, we will call that number "smart".
Which of the following numbers would we call "smart"?
2. Meredith's pet turtle walks 1 foot 3 inches in 3 minutes. At this same rate, how long would it take the turtle to walk 5 feet?
3. If the sum of the odd divisors of 56 is subtracted from the sum of the even factors of 56, what is the result?
4. The digits 3, 4, 5, and 7 are placed in the following squares to give the multiplication problem with the smallest answer possible. What is the smallest answer?
5. On January 1, 1994, Leo traded in his old car that averaged 24 miles a gallon for a newer car that averages 32 miles per gallon. Leo drove 12,000 miles in 1994. How many fewer gallons of gas did Leo use by driving his newer car in 1994?
6. On the first day of school, Principal Larson challenged all the classes in school to help collect 1 million pop tabs. If each class accepting the challenge could collect an average of 300 pop tabs per school day, which is the best estimate of how many classes are needed to collect 1 million pop tabs in one year?
Note: Consider 5 days per week and 36 weeks per school year.
| a) 2 classes | b) 5 classes | c) 19 classes | d) 25 classes |
7. The dimensions of a shoe box are 4 inches by 6 inches by 12 inches. What is the greatest number of cubes, 2 inches per edge, that can be stacked inside this shoe box?
8. I am thinking of three odd numbers, each less than 20.
I multiplied tham all together, and then added 7.
Which one of the following could be my answer?
9. A taxi company charges $1.55 for the first half-mile and $0.35 for each quarter-mile after that. Shawn rode a taxi and paid a fare of $4.70. What was the distance that Shawn traveled in the taxi? Give answer as a mixed number.
10. The diameter of a circle is 14 cm. Which of the following gives the best approximation for the area of the circle?
a) 22 square cm
b) 42 square cm
c) 44 square cm
d) 154 square cm
e) 616 square cm
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