AMO 2019 – Primary 4 (Grade 4)

A shirt and a tie cost 300 dollars altogether. The tie costs 60 dollars less than the shirt. Find the cost of the tie.

Find the sum of all integers from 561 to 569, inclusive.

A town has 10905 residents. There are 2500 more male voters than female voters. If 911 residents are not allowed to vote, how many female voters are there?

What is the largest three-digit number divisible by both 11 and 5?

If $\overline{EAT}+\overline{EAT}+\overline{EAT}=444$, find $E\times A\times T$. Here $E,A,T$ are the digits of the three-digit number.

The five-digit number $\overline{83m24}$ is divisible by 3 and 4. What is the smallest possible digit $m$?

In the pattern $15,17,21,A,35,45,B,\ldots$, find $A+B$.

How many times does the digit 5 appear in a book with 350 pages? Clarification: count occurrences in the page numbers 1 through 350.

Find the sum of the digits of $5\times8\times15$.

Three fruit vendors make 3 fruit baskets in 3 minutes. How many baskets can 10 vendors make in 15 minutes? Assume all vendors work independently at the same constant rate.

Anthony has at most 100 mathematics exercises for the summer. He completes $2/5$ in the first week and $3/7$ in the second week, leaving 12 exercises unfinished. How many exercises were assigned? Both fractions refer to the original total.

What is the greatest number smaller than 425 whose digits sum to 11?

Each entry of the pyramid is the sum of the two entries immediately below it. The example has three 1s at the bottom, then two 2s, then 4. If a similar pyramid has five 1s in its bottom layer, what is the sum of the numbers in its topmost layer?

How many triangles are in the figure?

A box contains only balls and bats. Three-sevenths of the items are balls, and there are 32 bats. How many items are in the box?

What is the greatest three-digit multiple of 19 divisible by 3?

In a book of 100 pages, all the pages with digits that are factors of 5 are torn out. How many pages remain? Clarification: remove each numbered page from 1 to 100 whose number contains at least one digit 1 or 5; count page numbers independently, not the two sides of a physical sheet.

Fill the grid with the numbers 1 to 9, each exactly once. The first row and first column each sum to 16; the second row and second column each sum to 15; the third row and third column each sum to 14. Find $A\times B$.

A festival requires 3500 chairs. Each batch contains 85 chairs. What is the minimum number of batches that must be ordered?

On Monday, $5/6$ of a class is present. All absent students are girls. Of those present, $2/3$ are boys and 15 are girls. How many students are in the class?