Train A and Train B travel towards each other from Town a and Town b
respectively, at a constant speed. The two towns are 1320km apart. After
the two trains meet, Train A takes 5 hours to reach Town b while Train B
takes 7.2 hours to reach Town a. How many km does Train A run per
𝑥 ∶ 5 = 7.2 ∶ 𝑥
𝑥2= 7.2 × 5 = _____
𝑥 = _____
Speed for A = 1320 ÷ 𝑥 + 5 = _____ km/h
In the figure below, in a right-angled triangle ACD, the area of shaded
region is 10 cm2. AD = 5 cm, AB = BC, DE = EC. Find the length of AB, in
Because DE = EC, ∆𝐵𝐸𝐷 = ∆𝐵𝐸𝐶 = 10 𝑐𝑚2
Because AB = BC and DE = EC, AD = 2 × BE
Since AD = 5cm, BE = 2.5 cm
× BE× BC = 10 cm2
× 2.5 × BC = 10 cm2
BC = 8 cm
AD = _____ cm
Answer: 8 cm
Eve said to her mother, “If I reverse the two-digits of my age, I will get your
age.” Her mother said, “Tomorrow is my birthday, and my age will then be
twice your age.” It is known that their birthdays are not on the same day. How
old is Eve?
If Eve’s age is 𝑎𝑏, her mother’s age is 𝑏𝑎.
𝑎 and 𝑏 is whole number between 1 and 9
And 𝑏𝑎 + 1 = 2 × 𝑎𝑏.
10𝑏 + 𝑎 + 1 = 2 × (10𝑎 + 𝑏)
8𝑏 = 19𝑎 − 1 ---- ①
Because all the multiples for 8 are even numbers, 19𝑎 must be odd number.
If 𝑏 is the biggest number 9, 8𝑏 = 72,
which mean 19𝑎 − 1 cannot be greater than 72, 19𝑎 cannot be greater than 73,
𝑎 cannot be greater than
which is 3
When 𝑎 = 1, cannot fulfill ①, so 𝑎 cannot be 1
When 𝑎 = 3, 𝑏 = ____
Answer: Eve is 37 years old
Balls of the same size and weight are placed in a container. There are 8
different colors and 90 balls in each color. What is the minimum number of
balls that must be drawn from the container in order to get balls of 4
different colors with at least 9 balls for each color?
** Note: Always treat this kind of question as finding worst case scenario, the
bad luck case **
Let’s find the largest number of balls we can drawn without achieving the
We may draw all 90 balls of each of 3 colors ⇒ 3 × 90 = 270
Then we may drawn 8 balls of each of the remaining colors ⇒ 5 × 8 = 40
If we draw one more ball, unavoidable the desired result will be met.
Therefore by drawing 270 + 40 + 1 = ___ balls, we are guaranteed to get at
least 9 balls of each of 4 colors.