AMO 2027 Grades 4-5 SET 11 - Self-study

John is 10 years old. His brother, Johnny, is 14 years old. How old will each boy be when the sum of their ages is 50?

Answer entry: enter John;Johnny, in years, separated by semicolons.

**Editorial input note:** Use no spaces before or after semicolons.

A train can hold 78 passengers. The train starts out empty and pick up 1 passenger at the first stop, 2 passengers at the second stop, 3 passengers at the third stop, and so forth. Given that no one leaves the train during the trip after how many stops will the train be full?

A number has a remainder of 2 when it is divided by 3. It also has a remainder of 2 when it is divided by 4. Find the sum of two such numbers that are greater than 20 but smaller than 40.

Three regular hexagons are put together to make a larger shape. The perimeter of one of the regular hexagons is 18cm. Find the perimeter of the larger shape.

There are 200 pieces of 5 dollars and 2 dollars notes. Their total value is 640 dollars. How many pieces of 5 dollars notes are there?

3187 pupils were at a theatre. There were 345 more girls than boys. If 435 girls did not wear spectacles, how many girls wear spectacles?

The table below shows the distribution of ages of the 20 students enrolled in a college class. Which of the following gives the correct order of the mean, median, and mode of the ages?

Ages of 20 Students Enrolled in a College Class

| Age | Frequency |
|---|---:|
|18|6|
|19|5|
|20|4|
|21|2|
|22|1|
|23|1|
|30|1|

Given $A=1+2+3+4+\cdots+97+98+99+100$, find the sum of all digits of $A$.

Mr. Garcia asked the members of his health class how many days last week they exercised for at least 30 minutes. The results are summarized in the following bar graph, where the heights of the bars represent the number of students.
What was the mean number of days of exercise last week, rounded to the nearest hundredth, reported by the students in Mr. Garcia’s class?

Readable graph data: days of exercise 1,2,3,4,5,6,7; corresponding numbers of students 1,3,2,6,8,3,2.



Answer entry: use a decimal point, for example 12.3.

In the figure below, ABCG and CDEF are 2 squares, BD = 63cm, GF = 9cm. Find the area of the shaded part.



Answer entry: use a decimal point, for example 12.3.

John has 25% less stamps than Elaine. Esther has 45% more stamps than Elaine. John and Esther have a total of 264 stamps. How many stamps do the 3 children have altogether?

How many pieces of string, each $\frac23$ m long, can be cut from a piece of string 90 m long?

Find the value of $T+E+N$ if

$\overline{ONE}+\overline{ONE}+\overline{ONE}+\overline{ONE}=\overline{TEN}$.

Sage has a walking speed of 300 feet per minute. On the way to gate 14C at the airport, Sage has the option of using a moving sidewalk. By simply standing on the sidewalk, it would take 4 minutes to get to the gate that is 800 feet away.

a) How much time will it take Sage to walk the distance to the gate without using the moving sidewalk?

b) How much time will it take Sage to get to the gate by walking on the moving sidewalk?

c) After traveling 200 feet (by standing on the sidewalk), Sage notices a Moonbucks, and turns around on the moving sidewalk. How long will it take Sage to get back to the beginning of the moving sidewalk, walking in the opposite direction? Assume the sidewalk is empty of other travelers.

Answer entry: enter (a);(b);(c), all in seconds, separated by semicolons.

**Editorial input note:** Use no spaces before or after semicolons.

Four children take turns to weight themselves in pairs. All the six readings of the total weight of every two children are recorded as follow:

39 34 38 38 42 37

What is the average weight of the four children?