AMO 2027 Grade 4 SET 3 - Self-study

Fill the $3\times3$ grid using each number from 1 to 9 exactly once. Every row and every column must sum to 15. Find the number in the cell marked *. Diagonals are not required to sum to 15.



Choose one option.

A boy sat an exam with 10 problems. He received 5 points for each correct answer and lost 2 points for each wrong or unanswered problem. His final score was 22. How many answers were correct?

Enter one whole number, without units.

There are 5 green, 9 orange, 6 red and 4 blue candies in a bag. At least how many candies must Sam take out without looking to ensure that he gets his first red candy? Candies are not put back.

Choose one option.

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

Choose one option.

What is $\frac12$ of $\frac23$ of $\frac69$ of 549?

Choose one option.

Paul can fill a pit in 4 hours. Renny can fill the same pit in 6 hours. If both work together, how many minutes will it take them to fill the pit? Assume each keeps a constant working rate and their work adds together.

Enter one whole number, without units.

In a leap year there were 53 Saturdays. What is the greatest possible number of Tuesdays in that year?

Choose one option.

Fill the grid with the numbers 1 to 9, using each exactly once, so that:
- first row sum = first column sum = 16;
- second row sum = second column sum = 15;
- third row sum = third column sum = 14.
Find $A\times B$.



Enter one whole number, without units.

A large rectangle is divided into five identical small rectangles as shown. Each small rectangle has width 8 cm. What is the perimeter of the large rectangle, in cm?



Enter one whole number, without units.

Sam filled up some boxes with sweets. If he put 5 sweets in each box, he would have left with 4 extra sweets. If he put 6 sweets in each box, the last box would have only 2 sweets. Find the number of sweets Sam had.

Use the same number of boxes in both arrangements.

Enter only the whole-number answer, without units.

In the pyramid below, each number is the sum of the two numbers immediately below it. For example, three 1s on the lowest layer give two 2s above, then one 4 above them. If a similar pyramid has five 1s on its lowest layer, what is the sum of the numbers on its topmost layer?



Choose one option.

What is the greatest 3-digit number divisible by both 5 and 11?

Choose one option.

The product of $k$ and 1260 is a square number. If $k$ is a whole number, what is its least possible value?

Here whole numbers mean 0, 1, 2, …, and a square number may be the square of any whole number. Enter one whole number.

Find the ones digit of $99\times101\times103\times105\times107-100\times102\times104\times106\times108$. For a negative result, use the ones digit of its absolute value (ignore the minus sign).

Enter one whole number, without units.

Anthony has at most 100 mathematics homework exercises to finish during his summer break. He finished two-fifths in the first week and three-sevenths in the second week, leaving 12 exercises unfinished. How many exercises were assigned?

Both fractions refer to the total number originally assigned. Choose one option.