AMO 2027 Grades 4-5 SET 17 - Self-study

There are 21 trees planted along the road divider with trees planted at opposite ends. The trees are planted at regular intervals of 20 m. If some lamp posts are to be placed along the opposite side of the road at regular intervals of 10 m, how many lamp posts are required on the opposite side of the road if lamp posts are placed at opposite ends of the road?

Two trains travel in the same direction on parallel tracks close to each other. Both trains start moving at the same time, but train X is 40 km ahead of train Y. If train X travels at a speed of 70 km/h and train Y travels at a speed of 75 km/h throughout the journey, in how many hours will train Y catch up with train X?

Jane plans to go on a holiday from 22 July (first day) to 3 September (last day). How many days is she planning to spend on her holidays?

Evaluate:

(a) $975\times5-5\times123+648\times5$.

(b) $504\div3-126\div3+24\div3$.

(c) $22\times33+33\times44+44\times55+55\times66$.

Answer entry: three integer values in a;b;c order. Use semicolons between parts and no spaces.

A woman can row upstream at 16 km/hr and downstream at 26 km/hr. What is the speed of the stream?

Model convention: her rowing speed in still water and the stream speed are constant and the same in both directions.

A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floor?

Grid convention: the tiles form aligned rows and columns; count tiles whose interiors a diagonal crosses, not tiles touched only at a corner. A tile on both diagonals is counted once.

Mr. Wood and Mr. Smith each have two children below 9 years old. Below shows some information about their children.

• Mike is 3 years younger than his brother.

• Royston is the oldest among the four children.

• Sean’s age is half of Mr. Wood’s child’s age.

• Jack is 1 year older than Mr. Smith’s younger child.

• Each family had only one child three years ago.

If the ages of the children are different, can you list their ages and group them according to their family? Find the sum of the ages of Mr. Wood’s children.

Age convention for this practice item: ages are distinct positive whole years from 1 to 8. In each family the younger child is under 3; the older child is at least 3 and a child now aged 3 counts as already born three years ago. Either complete allocation satisfying these conditions is accepted. Enter seven semicolon-separated fields: Mike age;Royston age;Sean age;Jack age;Wood children;Smith children;Wood age sum. Use the exact names, alphabetical order within each family, a comma between the two names, and no spaces.

There are a total of 24 cows and chickens on a farm. Given that total number of legs on the farm is 78, find the number of cows.

John has 84 fewer pins than Pi. Holland has 295 more pins than the total number of pins John and Pi have. Holland has 752 more pins than John. How many pins do the three friends have altogether?

Which of the following is not a leap year, 1200, 2000, 700, or 800?

Calendar convention: apply the Gregorian leap-year arithmetic rule to all listed year numbers, including dates before that calendar was introduced.

The following figures are made up of squares and dots.

a) Calculate the number of dots in figure 10.

b) Calculate the number of dots in figure 100.

c) Which figure has 132 dots?

d) Which figure has 288 dots?

Pattern convention: continue adding adjacent squares in one row, with one dot above and below each square and one dot at each outer end.



Answer entry: four integer values in a;b;c;d order; enter only the figure numbers for c and d. Use semicolons between parts and no spaces.

In a group of seven friends, the mean (average) age of three of the friends is 12 years and 3 months and the mean age of the remaining four friends is 13 years and 5 months. In months, what is the mean age of all seven friends?

Loki had some bags of marbles. He kept $\frac14$ of the number of marbles for himself, gave 558 to Pi and the remaining $\frac3{10}$ to Ksi. If there were 40 marbles in each bag, how many bags of marbles did Loki have at first?

Fraction convention: both 1/4 and 3/10 refer to the original total number of marbles, as in the source worked solution.

There are 480 pupils in class 5A with 186 are boys. There are 54 boys and $\frac13$ of the girls can swim. Express the number of pupils who do not swim as a fraction of the total number of pupils in class 5A.

The bar graph below shows the number of seashells Melvin collected from Monday to Friday. Study it carefully and answer the question that follow.

a) How many seashells did Melvin collect from Monday to Wednesday?

b) How many fewer seashells did he collect on Thursday than on Tuesday?

c) The total number of seashells he collected on two of the days was the same as what he collected on Tuesday. Which were the two days?



Answer entry: a;b;day1,day2, using Mon for Monday, Tue for Tuesday, Wed for Wednesday, Thu for Thursday, Fri for Friday. Use semicolons between parts and no spaces.