AMO 2027 Grades 4-5 SET 14 - Self-study

Using the same illustration, determine the perimeter of the plot of land.

How many dots are there in the figure?

The following bar graph represents the length (in letters) of the names of 19 people. What is the median length of these names?

Readable graph data: name length (letters) 3,4,5,6,7; frequency 7,3,1,4,4. Horizontal axis: name length. Vertical axis: frequency.

John and Anne each bought 12 ounces of coffee in a 16 ounce cup. John drank 2 ounces of his coffee and then added 2 ounces of cream. Anne added 2 ounces of cream, stirred the coffee well, and then drank 2 ounces. What is the resulting ratio of the amount of cream in John’s coffee to that in Anne's coffee?

Answer entry: simplest ratio John:Anne, for example 3:2.

Julian scored 284 marks out of 350 marks in his examination. Danny scored 68% of the total marks in the same examination. How many more marks than Danny did Julian score?

The Southeast Asian (SEA) Games is held once every two years, except in 1963 (i.e. it was held in 1961 and 1965, but not in 1963). Vietnam hosted the 22th SEA Games in 2003. When was the first SEA Games held (although it was known as South East Asian Peninsula Games at that time)?

In the following alphametic, all different letters stand for different digits. Find the two-digit sum $\overline{PI}$.

$\overline{IS}+\overline{IS}+\overline{IS}+\overline{IS}=\overline{PI}$.

Jack’s salary in June was 4000 dollars. He spent 40% of his salary on rent, 15% on transport, 20% on food and saved the rest. In July his salary was increased. The amount of money he spent on rent and transport for July remained the same. However, he spent 400 dollars more on food. If Jack saved the remaining 20% of his salary in July, find the percentage increase in his salary.

Answer entry: the percentage number only, using a decimal point if needed; omit the % sign.

A lion and a unicorn in a forest of forgetfulness are strange beings.

• The lion lies on Monday, Tuesday and Wednesday and tells the truth on the other days.

• The unicorn lies on Thursdays, Fridays and Saturdays and tells the truth on the other days.

One day, they talked to each other.

Lion: ”Yesterday I was lying.”

Unicorn: ”So was I.”

On which day did they say that?

What is the sum of all the digits of the page numbers of a 100- page book?

Town E and Town F were 240km apart. Jason left Town E at 9 : 00a.m. traveling at an average speed of 60km/h. Karen left Town E some time later than Jason and overtook him at 11a.m. Karen’s traveling speed was 90km/h.

(a) At what time did Karen leave Town E?

(b) How long had Karen rested when Jason finally reached Town F?

Journey convention used for the source answer: both travel at the stated constant speeds without intermediate stops, and Karen rests on arrival at F.

Answer entry: (a) morning time HH:MM;(b) rest in minutes, separated by a semicolon, for example 08:15;30.

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

In a test there were 40 questions. A candidate got 4 marks for each correct answer, and a negative marking of 2 marks for each wrong or no answer. If the total score of this candidate was 124 marks, how many correct answers did he have?

Here is a pattern of triangles. How many black triangles would there be in the next diagram of the sequence?

Today is Monday. Which day will it be after 61 days?

Amy, Bob and Chris each belong to one of the two tribes: truthtellers, people who always tell the truth and liars, people who always lie. Amy and Bob made the following the statements:

Amy: All of us are liars.

Bob: Exactly one of us is truthteller.

Which tribe does each of them belong to?