Ten Points Each. Total 150 Points.
1. For her birthday birthday,, Lucy received a jigsaw puzzle puzzle which is a picture picture that consists consists 600 pieces. pieces.
From the picture shown shown on on the cover, cover, the finished picture is a
nearly square in shape and each piece is also nearly square in shape. Lucy decides to complete the border first. How many border pieces does this puzzle have? 2. One particular particular chapter chapter in a book consists of 6 pages. pages. Each Each page has a page number and when the page numbers n umbers for this chapter are summed, the total is 507. What is the page number for the first page of this chapter? 3. Consider a certain 2-digit number. number.
If a 4-digit number is created from this
2-digit number by appending the number '1' both to the left of the first digit and to the right of the second digit, the value of this new 4-digit number is 1190 more than that that of the original 2-digit number. number.
What is that that original number?
4. If a teacher divides the students in in his class into 4 groups, he will have have 2 students left over over. left over. over.
If he divides them them into 5 groups, there there would would be 1 student
Suppose this class class has has 15 girl students and the number of boy
students is a little less than the number nu mber of girl students. How many boy students are in that class? 5. A teacher is is providing her students students with 4 special lessons which which are Child Psychology Psycholo gy,, Education Theory, Civic, and Child Development. Developmen t. has exactly exactly 3 participants, participants, lesson together. together.
(a) Each lesson
(b) Any two two students students must must attend attend at least one special special
According to these these two conditions, what is the maximum
number of students who can join these special lessons? 6. Paul had discovered that there is a 2–digit number number in which which if it is multiplied by itself, the last two digits of the product is the same as the original 2–digit number. What is the sum of all 2–digit numbers that satisfy this condition? 2015 Final
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7. What is the largest odd number less than 1000 that has a remainder of 4 when it is divided by 5 and a remainder of 2 when it is divided by 3? 8. Find a 2–digit number such that the sum of its tens digit and the square of its unit digit will yield the original number again. 9. Suppose the first digit on the left of a 6–digit number is 1 and this digit is moved to behind the last digit on the right. If this new 6–digit number is 3 times the original number, what are the last three digits on the right of the original 6–digit number? 10. Bob has two children, John and Sandy. The sum of the ages of all three persons is 49 and John's age is three times larger than Sandy's age. Five years from now, Bob's age will be 3 times John's age. What is the product of all three ages now? 11. Let W, X, Y , and T represent four distinct numbers selected from the nine numbers 1, 2, 3, 4, 5, 6, 7, 8, 9.
Find
W – X + Y – T when
X W
+
T Y
is at
minimum. 12. Among all 4–digit numbers, how many will require occur some "carry" when they are added to 6574?
(For example, 1234 + 6574 = 7808 has one carry but
1225 + 6574 = 7799 has no carry.) 13. Select 3 numbers from a group of 6 numbers 5, 8, 11, 7, 9, and 12. the selected numbers and multiply the sum by the third number.
Add two of
Among all the
different selections, what would be the smallest product? 14. As shown in the figure on the right, there are 12 small squares in the rectangle. of 4.
Each square has a side length
If AB, AC , and BC are all straight lines, what is
the area of triangle ABC ? 15. On a circular track, A and B start from the same place and same time but run opposite directions. the race. track.
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2015 Final
After 18 seconds, A and B meet for the first time after start
A knows that he needs 30 seconds to complete one full lap of the
How many seconds would it take B to complete one lap?
