AMO 2027 Grade 4 SET 2 - Self-study

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

Enter one whole number, without units.

The picture shows a $4\times4$ grid. How many grid-aligned squares of any size contain the small square marked X? Count only squares whose sides follow grid lines.



Choose one option.

If all the numbers from 561 to 569 are added, what is their sum?

The source prints these choices: A. 5905; B. 5509; C. 5095; D. 5055; E. 5509. They are retained for source fidelity, but this edition uses numeric entry so that the computed sum can be entered even if no printed choice matches.

Enter one whole number, without units.

Scott, Emily and Jack chose a number. Emily said it was an even multiple of 13. Scott said it was divisible by 35. Jack said it was a four-digit number with digit sum 15. Find the number.

Enter one whole number, without units.

At a function, the valet charged 10 dollars for a motorbike and 25 dollars for a car. There were 150 vehicles and 360 tires in total. How much did the valet earn from cars only? Count two tires per motorbike and four per car, with no spare tires included.

Enter the number of dollars, without a currency symbol or units.

Find $25\times48+32\times25+25\times20$.

Choose one option.

The large rectangle below is made of 6 squares and 3 rectangles. How many times as large is the area of the largest square as the area of the smallest rectangle? For this edition, interpret the two narrow rectangles at the top left as having equal widths, as intended by the drawing.



Choose one option.

Josh drove from his house toward his aunt’s house, 15 km away. He travelled 3 km in the first hour, then drove at 2.5 km per hour. How far was he from his aunt’s house 4 hours after leaving home?

Choose one option.

When 500 chairs were distributed equally among 18 rooms, 14 chairs were left over. How many chairs were placed in each room?

Choose one option.

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

Choose one letter A–E.

What is the greatest two-digit number to be added to 95 so that it is divisible by 3?

“It” refers to the sum after adding the number to 95.

Choose one letter A–E.

A five-digit number satisfies all these conditions:
- It is a multiple of 3 and 5.
- Its third digit is half its first digit and one less than its second digit.
- The first three digits sum to 13 and the last three digits sum to 8.
- Its fourth digit is the second-largest digit in the number.
Find the sum of its digits.

Enter one whole number, without units.

Four friends Kevin, Larry, Pam and Sam had four bags of 30, 32, 35 and 38 marbles. Sam had more marbles than Pam but did not have the greatest number. Kevin had the least number. Which two friends have a total of 70 marbles?

Choose one option.

Sixteen trees stand in a straight row on one side of a road. Two cars are parked in every gap between consecutive trees. How many cars are there? Count only these gaps.

Enter one whole number, without units.

The mangoes remaining in a cart weigh 3 kg after 10 mangoes are removed. If only 8 mangoes are removed from the same original cart, the remaining mangoes weigh 3400 grams. How many mangoes were originally in the cart? Editorial assumption: all mangoes have equal mass, as required by the source solution; the cart itself is not included in either mass.

Enter one whole number, without units.