World Mathematics Invitational:.........Month:..........Year:...........

Total Core =

  • Question 1: Suppose ◇, □, and △ represent 3 different positive integers and satisfy the equations ◇+2=□– 2=△×2 .
    What is the smallest value for ◇+□+△?
  • Question 2: The figure on the right is a large square that is composed of 4 identical rectangles and one small square (no overlapping).
    If the perimeter of each small rectangle is 40 and their width is 5, find the area of the small square.
  • Image for question 2
  • Question 3: A bag of candies is distributed to certain number of people.
    If each person is given 5 candies, there are 10 candies left over.
    If the number of people is increased to 5 less than 3 times the original number and each person gets 2 candies, then there are 8 candies short.
    How many candies are in the bag?
  • Question 4: Among the 7 numbers 5, 17, 19, 37, 39, 46, and 66, at least how many numbers must be selected so that the sum of the selected numbers is 100?
  • Question 5: For making measurements, a certain balance scale uses standard weights of 1, 2, 4, 5, and 7 grams;
    the object to be weighed is placed on one side of the scale while
    combinations of standard weights are collected on the other until balance is achieved.
    One of these standard weights, however, is missing such that the balance scale cannot weigh something that is 10 grams.
    Which standard weight is missing?
  • Question 6: Divide a large rectangle into 16 small rectangles as shown in the figure below.
    If the sum of perimeters of all 16 small rectangles is 120, what is the perimeter of the large rectangle?.
  • Image for question 6
  • Question 7: Jeremy always walks from home to school. One day, when he is half way to
    school, he realizes that he will be late and decides to run the rest of the way.
    His running speed is 3 times his walking speed; that way, he is right on time
    when he gets to school such that the whole trip took him exactly 16 minutes. If
    he had continued at walking speed instead of running for that second half, how
    many minutes would he be late?
  • Question 8: The figure below is a three-ring pattern composed of 13
    shaded and 6 white tiles. If this pattern continues to expand
    to 100 rings, what is the difference between the number of
    shaded and white tiles?

  • Image for question 8
  • Question 9: A rope is used to measure the depth of a swimming pool. If the rope is folded
    in half, it is 60 centimeters longer than the depth of the pool. If the rope is
    folded in thirds, it is 40 centimeters short, find the depth of the pool.
  • Question 10: Today is August 6, 2015. Which digit should be inserted in □ so that the
    number 20150806□ is a multiple of 9.