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A Contest For You...A Dare!

Try these problems from an old Atlantic-Pacific Mathematics League contest? This particular version was aimed at students in grades 5-9. You have 30 minutes to complete all six questions.

  1. A strip of paper 1 cm wide by 50 cms long is marked off at intervals of 1 cm in order to cut off a series of 1 cm squares. In seconds, how long will it take to cut the 50 square cms if each cut takes 4/5 of a second and the paper must not be folded?
  2. The sum of a set of 12 numbers is 186. If each of the numbers is tripled and 4 is then subtracted from each product, what is the sum of the new set of 12 numbers?
  3. It is understood that (x)(y) means the product of a and y. If (1)(2)(3)(4)(5)(6)(A)(B)(C)(10)(11) = N, then in terms of N find the value of (12)(11)(10)(C)(B)(A)(6)(5).
  4. If 4x + 2(7-x) = 6, then find the value of x/3 + 3.
  5. If the average of two numbers is AB and one of the numbers is A, then what is the other number?
  6. A cube of ice, 2 ft to an edge and weighing 456 lbs, is left sitting in the hot sun. After several hours, while it is still a cube, it only measures 1 ft to an edge. How much weight has it lost?


Source: Atlantic-Pacific Mathematics League, April 10, 1985

Hint: It's a contest...no hints allowed! Plus, time is passing...


Solution Commentary: Rather than provide solutions, I will provide only some comments:

  1. To create 50 squares, how many cuts are needed?
  2. In each case you have 3y-4, twelve times...so, using the dristibutive property...
  3. (3)(4) = 12...thus...
  4. Some straight forward algebra...little thinking unfortunately.
  5. What fraction of its volume has been lost...can you determine this visually?