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 hour?

Solution:

Speed for A = km/h

Answer:

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 cm.

Solution:

Because DE = EC, Because AB = BC and DE = EC, AD = 2BESince AD = 5cm, BE = 2.5 cm = BE BC = 10 cm2

2.5 BC = 10 cm2

BC = 8 cm AD = cm

Answer:

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?Solution:

If Eve’s age is , her mother’s age is . and is whole number between 1 and 9

And .

---- ①

Because all the multiples for 8 are even numbers, must be odd number.If is the biggest number 9, , which mean cannot be greater than , cannot be greater than ,cannot be greater than which is . When , cannot fulfill ①, so cannot be When ,

Answer: Eve is 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 desired result.

We may draw all 90 balls of each of 3 colors Then we may drawn 8 balls of each of the remaining colors If we draw one more ball, unavoidable the desired result will be met.

Therefore by drawing balls, we are guaranteed to get at least 9 balls of each of 4 colors.

Answer:

Solution: