Ten Points Each. Total 150 Points.
1. 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? 2. Jeremy always walks from home to school.
One day, day, when he is half way to
school, he realizes that he will be late and decides to run the rest of the way. way. His running speed is 3 times his walking speed; that way, way, he is right on time when he gets to school such that that the whole trip took him exactly 16 minutes.
If
he had continued at walking speed instead of running for that second half, h alf, how many minutes would he be late? 3. The figure below below is 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? 4. A rope is used to measure the depth of a swimming pool.
If the rope is folded
in half, it is 60 centimeters centimeters longer than than the depth of the pool. pool.
If the rope is
folded in thirds, it is 40 centimeters centimeters short, find the depth of the pool. 5. Today is August 6, 2015. Which Which digit should be inserted in □ so that the number 2015 201508 0806 06□ is a multi ultipl plee of 9. 6. There is a total of 24 cars and motorcycles in a parking lot.
Each car has 4
wheels and each motorcycle has 3 wheels. If there is a total of 86 wheels among all the cars and motorcycles, how many motorcycles are in the t he parking lot? 7. The rectangle on the right is divided into into 4 parts, each having the same area. If the length of rectangle a is twice its width, how many times longer is the th e length of rectangle b than its width? 2015 Final
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8. Let n be a 4–digit number. If 9 times n is exactly equal to the reversed order number of n (For example, the reversed order number for 123 is 321), what is n? 9. Use 5 different digits to write the largest 5–digit number that is divisible by 18. 10. Given a fraction in which the sum of its numerator and denominator is 122. If both its numerator and its denominator are subtracted by 19 and the simplified 1 resulting fraction is , what is the absolute difference between the original 5 numerator and denominator? 11. Suppose the average weight of A, B, and C is 60 kilograms.
If the average
weight of A and B is 3 kilograms more than the weight of C and A is also 3 kilograms heavier than C, find the weight of B in kilograms. 12. If the sum of two numbers is 64 and 4875 is divisible by their product, what is the absolute difference between these two numbers? 13. According to the figure below, what is
A＋ B＋C ＋ D＋ E ＝?
(Assume each
letter represents a different digit)
14. Kelly found a bottle with a note inside.
The note said, "There is a chest of
treasure buried nearby, the key to which is a 3–digit number
abc
where
a < b
< c, with its digits written in the form of electronic digits just like the ones shown below.
If you can find this number, the treasure is yours. You can find
this number by using the following two rules. (1) Use 15 pieces of identical small sticks to arrange this 3–digit number, (2) No digit is permitted to use either 5 or 6 sticks." Can you help Kelly to find that 3–digit number?
15. If the product of 3 consecutive odd numbers is a 4–digit number that ends with 7 as its units digit, find the largest such 4–digit number. 2
2015 Final
