Algebra and Number Problem (With Hint)

Problem-Solving and Selected Topics in Number Theory: In the Spirit of the Mathematical Olympiads

1. For every positive integers n ,

 divisible by 2000. Proof it.

Hint: 2000 = 125 x 16

2. If

 Find a x b x c x d

Hint: a is integer part of 57/17

Probability Problem

The Mathematical Olympiad Handbook: An Introduction to Problem Solving Based on the First 32 British Mathematical Olympiads 1965-1996 (Oxford Science Publications)

1. A survey of the non-healthy habits of 80 sophomore students of a certain seminary showed the following result.
45 drink alcoholic beverages
42 stay up late
40 smoke cigarettes
25 drink alcohol and smoke
19 stay up late and smoke
22 drink alcohol and stay up late
9 practice clean healthy living by not doing any of the 3

If a seminarian sophomore is randomly picked, what is the probability that he:
a. is just an insomniac (or just stay up late)
b. smokes and/or drinks but is a sleepyhead (or smokes and/or drinks but sleeps early)
c. he should be kicked out of the seminary (by doing all the three things)


2. What is the probability that a path from (0,0) to (8,6) pass through (5,4), assuming that all paths move along grid lines and that movement must be either the positive x or the positive y direction?

Math Olympiad Example Problem for Grade 6

Prentice Hall Mathematics California Grade 6 Math

Problems

1.  What are the possible dimensions of a rectangle with integer-valued side lengths in which the numerical value of the area is twice the perimeter?

2.  In celebration of her birthday, Claudine threw a big party. Every two persons shared a bowl of rice, every three persons shared a bowl of fruit salad, and every four persons shared a bowl of soup. There were 130 bowl used together. How many guests were present ?

3.  Calculate:

4.  The pages of the Math Book are numbered consecutively, starting with page 1. The book is bound in ten booklets, with equal number of pages in each booklet. If the sum of the numbers on the first page of every booklet is 4150, how many pages does each booklet have?

5.  Angela is fond of making a wish everytime her car’s odometer displays a number read the same forward and backward (palyndrome). At 10:18 am the odometer read 87978 km. Traveling continuosly the odometer displayed the next possible number that in palyndrome at 11:13 am. During this time, what was the car’s average speed in kilometers per hours ?
 

6.  Eight of the angles of an undecagon have measures whose sum is 1380˚. Of the remaining three angles, two are complementary to each other and two are supplementary to each other. Find the measure of the largest of these three angles.

7.  What is the sum of the numbers less than 200 that has exactly 3 divisors?

Math Olympiad Example Problem for K9

1.     ABC is a right triangle with <ACB= 74° and AM=MQ=QP. Find <QPB. 

math olympiad example problem

2.   How many positive integer n , if n-1 is the factor for 3n-6

3.   <A=60^o and the radius of big circle is 6. Find the radius of small circle.

math olympiad example problem

Canadian Math Olympiad

canadian math olympiad

Resource, problem and sample of solution for competitors see http://www.math.ca/Competitions/CMO/%20 .