WorksheetsG6 Math Olympiad Part B
Total questions: 15
Worksheet time: 36mins
The 7-digit numbers 74A52B1 and 326AB4C are multiples of 3. Which one of the following is the value of C?
1
2
3
5
8
A tournament had six players. Each player played every other player only once, with no ties. If Helen won 4 games, Ines won 3 games, Janet won 2 games, Kendra won 2 games and Lara won 2 games, how many games did Monica win?
0
1
2
3
4
What is the number of shortest paths from A to B?
4
5
6
8
None of the above.
Sam has two identical wooden pyramids, each with a square base. He glues the two bases together to make a new bigger wooden shape. How many vertices are there in the new bigger shape?
6
7
8
9
10
When you multiply Sophie’s age and Sony’s age, you get 36. If you add their ages together, you get 15. Sophie is older than Sony. How old is Sony?
12
3
4
5
None of the above
Students from Mrs. Hein’s class are standing in a circle. They are evenly spaced and consecutively numbered starting with 1. The student with number 3 is standing directly across from the student with number 17. How many students are there in Ms. Hein’s class?
28
29
30
31
None of the abouve
A "leap year" is a year which has 366 days including February 29 as an additional day. Any year that is divisible by 4 is a leap year, but a year that is divisible by 100 is a leap year only if it is also divisible by 400. How many leap years are there from 2000 to 2017?
3
4
5
6
None of the above
Jessica is an avid reader. She bought a copy of the best seller book Math is Beautiful. On the first day, Jessica read 51 of the pages plus 12 more,
and on the second day she read 41 of the remaining pages plus 15 pages. On the third day, she read 31 of the remaining pages plus 18 pages. She then realized that there were only 62 pages left to read, which she read the next day. How many pages are in this book?
120
180
240
300
360
Reverse the digits of 1746 and we get 6471, the new number is larger than the original number by 4725. How many four-digit numbers satisfy such condition?
16
17
20
21
None of the above
Every day at school, Jo climbs a flight of 6 stairs. Jo can climb using 1, 2 or 3 steps or a combination of any of them. How many ways can Jo climb the flight of 6 stairs?
13
18
20
22
24
Let the operation ∗ be defined by 𝑎 ∗ 𝑏 = 𝑎𝑏 − 𝑎 − 𝑏 + 2. If 7 ∗ 𝑏 = 13, what is the value of b?
(a)
A game consists of black and white pieces. The number of black pieces is 5 more than 3 times the white pieces. Seven white and 15 black pieces are removed each round. After several rounds, there are 3 white and 56 black pieces left. How many pieces were there in the beginning?
(a)
As shown in the figure, the area of △ABC is 42. Points D and E divide the side AB into 3 equal parts, while F and G divide AC into 3 equal parts. CD intersects BF and BG at M and N, respectively. CE intersects BF and BG at P and Q, respectively. What is the area of the quadrilateral EPMD?
(a)
Four players compete in a tournament. Each player plays exactly two games against every other player. In each game, the winning player earns 2 points and the losing player earns 0 points; if the game results in a draw (tie), each player earns 1 point. What is the minimum possible number of points that a player needs to earn in order to guarantee that he/she will be the champion (i.e. he/she has more points than every other player)?
(a)
Let us call a whole number "lucky" if its digits can be divided into two groups so that the sum of the digits in each group is the same. For example, 34175 is lucky because 3 + 7 = 4 + 1 + 5. Find the smallest 4- digit lucky number, whose neighbour is also a lucky number (i.e. the whole number next to it is a lucky number as well).
(a)
