4. 5/3 Goomats and Zignots Five goomats plus a zignot is 87. A goomat plus five zignots is 99. What is the sum of two goomats and two zignots? + = 87 + = 99
5. 5/6 Angles in a ClockWhat is the number of degrees theminute hand of a clock moves from6:04 pm and 6:21 pm?
6. 5/7 Wire WeightA wire of uniform diameter andcomposition that weighs 32 lb is cut intotwo pieces. One piece is 90 yd long andweighs 24 lb. What is the length, in yd,of the original wire?
7. 5/8 Shaded RegionsSquare WXYZ is partitioned into foursmaller congruent squares, and thenportions of those squares are shaded, asshown. What fractional part of the squareis shaded?
8. 5/10 Printing BusinessIf 45 business cards can be printedin 30 seconds, how long will it taketo print 555 business cards at thesame rate?
9. 5/13 Sums and ProductsWhat integer can be added to 13/12or multiplied by 13/12 to give thesame result?
10. 5/14 Find the NumberIf one-half of a number is eight lessthan two-thirds of the number, whatis the value of the number?
11. 5/15 Minimize the ProductFind the least possible product oftwo integers whose sum is 16? a + b = 16
12. 5/16 Simply Perfect!A perfect number is a number whoseproper factors add to equal the number.For example, 6 is a perfect numberbecause 1 + 2 + 3 = 6. Find anotherperfect number.
13. 5/17 How odd! What is the smallest odd integer with exactly six positive factors?
14. 5/20 Picture this! What is the minimum number of square tiles needed to exactly cover a rectangle whose length is 50% greater than its width?
15. 5/21 How Many Numbers?How many different four-digitnumbers can be formed if the digits2, 3, 4 and 5 must be used in eachof the integers? ___, ___ ___ ___
16. 5/23 Perimeter PuzzleA regular polygon has a total of 9 diagonals.If each side measures 2.5 inches, what is theperimeter of the polygon?
17. 5/24 Area: Holding SteadyThe length of a rectangle is three times itswidth. A new rectangle is created bydecreasing the length of the originalrectangle by half. By what factor must theoriginal width be multiplied, if the arearemains unchanged?
18. 5/27 Sweet Treats The Sachem singers earned $273 by selling a combined total of 440 brownies and cookies during their concert. If each brownie sold for $0.75 and each cookie sold for $0.50, how many brownies did they sell?
19. 5/28 Guess the NumberIf twice a number is equal to 6 morethan half the number, what is thenumber?
20. 5/29 Solve this one In the figure shown, the distance between adjacent dots in each row and column is 1 unit. Find the area of the shaded region in square units.
21. 5/30 Dollars to Dollars The ratio of John’s allowance to Bill’s allowance is 3:7. The ratio of John’s allowance to Mary’s allowance is 2:5. What is the ratio of Mary’s allowance to Bill’s allowance?
22. 5/31 Squares and Ratios ? The difference of the squares of two distinct positive numbers is equal to ? twice the square of their difference. What is the ratio of the smaller number to the larger?
23. Problems adapted from Math Counts School Sprint Round 2012