Asia Pacific Mathematical Olympiad for Primary Schools 2004
7:13 PM
Muhammad Yusuf
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1. ABCD is a quadrilateral (4 sided figure).
AE and GC are perpendicular to BD. Given that BE = EF = FD, GF = FC and that the total area of ΔABE and ΔDFG is 12.9 cm2, find the area of the quadrilateral ABCD.
2. Teams X and Y work separately on two different projects.
On sunny days, team X can complete the work in 12 days while team Y needs 15 days.
On rainy days, team X’s efficiency decreases by 50% while team Y’s efficiency decreases by 25%.
Given that the two teams started and ended the projects at the same time, how many rainy days are there?
3. 2004 students arrange themselves in a row. In the first round of counting, they number themselves
1, 2, 3, 1, 2, 3, 1, 2, 3 … from left to right.
In the second round of counting, they number themselves
1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5,… from right to left.
Find the number of students whose sum of numbers in the first and second rounds of counting is 5.
4. Mrs Tan and Mrs Wong met each other at a park.
Mrs Tan : “Hi, how are you? How are your children?
You have three if I remember correctly.
But how old are they now?”
Mrs Wong : “Yes, I have three children.
The product of their ages is equal to 36.
The sum of their ages is equal to the number of chairs over there.”
Mrs Tan counted the number of chairs, thought for a while and said
“ I still can’t figure out the ages of your children.”
What are the possible ages of the three children?
(Assume whole number for ages.)
5. Tom walks up a staircase.
Each time he can either take one step or two steps.
How many ways are there for Tom to walk up a ten-step staircase?
6. Two points A and B are 1100 m apart.
Alice and Ben leave point A at the same time and travel to and fro along a straight road between A and B at uniform speeds. Alice and Ben travel at 60 m/min and 160 m/min respectively. They both stop after 40 minutes.
(i) At which meeting are they nearest to point B?
(ii) Find this nearest distance in metre.
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