AMO 2027 Grades 2-3 SET 16 - Self-study

How many triangles do you see?

Pi had \(\text{\$200}\). He went to the grocery store and bought six gallons of ice cream for \(\text{\$5}\) each. Then he went to the farmer’s market and bought four dozen ears of corn for \(\text{\$7}\) dozen. How much money did Pi have left?

Self-study price clarification (editorial): the corn costs 7 dollars per dozen. Enter the remaining amount in dollars.

In a straight row, 12 trees are planted at equal distance. The distance between 1st and 12th trees is 33 meters. What is the distance between 3rd and 9th trees?

Self-study input (editorial): enter the distance in meters.

Cheryl forms a rectangle using 12 square tiles, each 1 inch by 1 inch. Which of the following, in inches, may not be the perimeter of the rectangle?

Self-study construction convention (editorial): use all twelve whole tiles, aligned edge to edge, without gaps or overlaps.

Two of my digits are even, but my ones digit is odd. The sum of my digits is 11. I’m between 256 and 299, and I am not 281. What am I?

In an increasing list of consecutive integers, the 3rd and 4th numbers in the list add to 11. What is the 26th number in the list?

Pi and Ksi got summer jobs at the ice cream shop and were supposed to work 15 hours per week each for 8 weeks. During that, Ksi was ill for one week and Pi took her shifts. How many hours did Pi work during the 8 weeks?

Chris is 15 years elder than Jordan. If 4 years ago, Chris was 3 times as old as Jordan, then find Chris’s present age.

Self-study age convention (editorial): ages may include fractional years; do not round to a whole number. Enter Chris’s present age in years as a plain decimal or a fraction written as numerator/denominator. Equivalent values are accepted exactly; do not enter units or a mixed number.

Find the area of the figure below which is made up of 7 identical rectangles of length 15 cm.



Self-study input (editorial): enter the area in square centimeters.

Rectangle X has a length of 17 meters and a width of 9 meters. Rectangle Y has a length of 17 meters and a width of 12 meters. You place both rectangles side-by-side to create a new rectangle, Rectangle Z. What is the perimeter of Rectangle Z?

Self-study construction clarification (editorial): join the full equal 17-meter sides without overlap or cutting. Enter the perimeter in meters.

There are 3 boxes, exactly one of which has a car. You can keep the car if you pick the correct box!

On each box there is a statement, exactly one of which is true.

• Box 1: The car is in this box.

• Box 2: The car is not in this box.

• Box 3: The car is not in box 1.

Which box has the car?

Self-study input (editorial): enter the number of the box containing the car.

Will bought a jumbo bag of Fruit-o candy. Before chowing down, he decided to see how many pieces of each flavor there were. Use his graph below to answer the questions.



a) How many pieces were banana?

b) What is the difference in the number of watermelon pieces and the number of strawberry pieces?

c) How many fewer watermelon pieces were there than banana pieces?

Self-study input convention (editorial): enter all three answers in order a;b;c, separated by semicolons.

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

A number is first subtracted by 11. The difference is then multiplied by 11. The product is then divided by 11. The final result is still 11. What is the number?

Self-study interpretation (editorial): the first operation subtracts 11 from the starting number.

According to the graph below, in which year was the ratio of the number of students enrolled at School B to the number of students enrolled at School A the greatest?

In the following, all different letters stand for different digits. Find the sum of T, A and T.