1. Find the smallest natural number which when multiplied by 123 will yield a product that ends in 2004
Solution:
Assume 𝒙 is the smallest natural number
𝟏𝟐𝟑𝒙= 𝑨 × 𝟏𝟎 𝟒 +𝟐𝟎𝟎𝟒 ---- ①
When 𝑨=𝟎, 𝟐𝟎𝟎𝟒 is not divisible by 123
When 𝑨=𝟏, 𝟏𝟐𝟎𝟎𝟒 is not divisible by 123
When 𝑨=𝟐, 𝟐𝟐𝟎𝟎𝟒 is not divisible by 123
When 𝑨=𝟑, 𝟑𝟐𝟎𝟎𝟒 is not divisible by 123
When 𝑨=𝟒, 𝟒𝟐𝟎𝟎𝟒 is not divisible by 123
When 𝑨=𝟓, 𝟓𝟐𝟎𝟎𝟒 is not divisible by 123
When 𝑨=𝟔, 𝟔𝟐𝟎𝟎𝟒 is not divisible by 123
When 𝑨=𝟕, 𝟕𝟐𝟎𝟎𝟒 is not divisible by 123
When 𝑨=𝟖, 𝟖𝟐𝟎𝟎𝟒 is not divisible by 123
When 𝑨=𝟗, 9𝟐𝟎𝟎𝟒 ÷𝟏𝟐𝟑=𝟕𝟒𝟖
Answer :𝒙 = _____

2. In the following figure, if CA = CE, what is the value of 𝑥 ?
Solution:
6𝟖°
6𝟖° 𝒙°
32°
36°
∠𝑪𝑬𝑨=∠𝑬𝑪𝑫+∠𝑬𝑫𝑪 = _____°
𝑪𝑨=𝑪𝑬 ⇒ ∠𝑪𝑨𝑬=∠𝑪𝑬𝑨 = _____°
Answer :𝒙° =𝟏𝟖𝟎° −𝟔𝟖° −𝟔𝟖°= _____°

3. Compute: − − …− −
Solution:
The above question can be re-written as:
− − …− −
We know that
𝑎 2 − 𝑏 2 = 𝑎+𝑏 (𝑎 −𝑏)
= − − … −
= …
= ×2005 2
Sum of sequence with common difference:
𝑙𝑎𝑠𝑡 𝑡𝑒𝑟𝑚+𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚 ×𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑒𝑟𝑚𝑠 2
Answer:

4. City P is 625 kilometers from City Q. M departed from City P at 5
City P is 625 kilometers from City Q. M departed from City P at 5.30am travelling at 100 kilometers per hour, and arrived at City Q. Fifteen minutes after M left, N departed from City Q and arrived at City P travelling at 80 kilometers per hour. At what time did M and N meet together?
Solution:
After 15 minutes, which is 5:45am
M has travelled = 100 × =___ 𝑘𝑚
The distance between M and N = 625 − ___ 𝑘𝑚 ---- ①
The time needed to meet = ① = hours
∴ The time they meet is 5:45am hours
Answer: ________________________________