Third World Youth Mathematics Inter-City Competition
Write your answer to each of the ten questions on the space provided. Solutions need not be shown. Each of
the questions carries 6 marks.
Question 1
Find a set of four consecutive positive integers such that the smallest is a multiple of 5, the second is a multiple of 7, the third is a multiple of 9, and the largest is a multiple of 11.
Answer:
________________________
Question 5
Between 5 and 6 o’clock a lady looked at her watch and mistook the hour hand for the minute hand. She thought the time was 57 minutes earlier than the correct time. What was the correct time?
Question 6
Determine all primes p for which the system
2
has integral solution(s).
Part II
Show your organized solution for each of the three questions in the space provided below. Each question carries 20 marks.
Prove that the following inequality holds:
(
)
Third World Youth Mathematics Inter-City Competition
Team Contest
Team Name _______________________________________________________________
Question 1
Third World Youth Mathematics Inter-City Competition
Team Contest
Team Name _______________________________________________________________
Question 2
Third World Youth Mathematics Inter-City Competition
Team Contest
Team Name _______________________________________________________________
Question 3
In the figure below AB = DE = EF = HA, BC = CD = FG = HG, ∠BCD = ∠FGH = 90°. Divide the given figure into 2 identical regions.
A B
C
D
E F
Third World Youth Mathematics Inter-City Competition
Team Contest
Team Name _______________________________________________________________
Question 4
If a 1 × 1 square is removed from a 8 × 8 square such that the remaining figure can be cut into 21 figures of
and can also be cut into 21 figures of . This 1 × 1 square is called a removable square. How many squares
