AMO 2027 Grades 2-3 SET 30 - Self-study

Eleven lamps are installed at equal distances along a straight farm road 110 metres long, with one lamp at each end. What is the distance between two neighbouring lamps, in metres? The source phrase “any two lamps” is interpreted as neighbouring lamps.



Enter one whole number in metres, without units.

Count the triangles in the picture. Editorial interpretation for this imperfect drawing: treat the two very close left vertical strokes as one line, and the nearly coincident bottom strokes as one straight baseline. Ignore line thickness and small printing offsets. The left triangle ends before the rectangle’s right side, as shown; do not extend its sloping side.



Choose one option.

Alice started her homework at 7:20 p.m. She finished it at 8:05 p.m. How long did she take to do her homework?

Ksi has tomato plants in his backyard. This year the plants grew 120 tomatoes. Birds had eaten 29 of the tomatoes. 13 tomatoes had been ruined by bugs. He picked the rest. How many tomatoes did Ksi pick?

Alice had an activity book with lots of activities, there were 22 pages of mazes. It took Alice 5 minutes to finish a page. How many pages of maze were left after she spent 45 minutes doing the maze?

There were 42 mangoes in each crate. 7 such crates of mangoes were delivered to a factory. 4 mangoes were rotten and had to be thrown away. The remaining mangoes were packed into boxes of 10 mangoes each. How many boxes of mangoes were there?

Self-study clarification (editorial): the four rotten mangoes are four in the entire delivery, not four per crate. Enter the number of full boxes, without units.

Ksi had three boxes of pencils with sixteen pencils in each box. He gave nine pencils to his brother. How many pencils did Ksi have left?

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?

What is the largest 2-digit number that can be divided by both 3 and 5?

The sum of the digits in a 2-digit number is 12. If the tens digit is 2 less than the ones digit, find the number.

The directions on an exam allow 2 hours and 30 minutes to answer 50 questions. If you want to spend an equal amount of on each of the 50 questions, about how much should you allow for each one?

Self-study input (editorial): enter the time per question in minutes.

Evaluate
2 + 4 + 6 + 8 + 10 + 20 + 40 + 60 + 80 + 100.

Melissa, Frank and Shelly are going to meet for a picnic. Melissa has 5 berries while Frank has 9 berries. How many berries should Shelly bring so that they can share and have 8 berries each?

There are 100 third-graders at SMEC School. 44 on them are girls. On Friday, 5 third-grade girls and 7 third-grade boys were absent. How many third-grade boys were at SMEC School on Friday?

Pi walks to school. He leaves each morning at 7:32 A.M and arrives at school fifteen minutes later. If he travels at a steady rate of 4 miles per hour, what is the distance between his home and the school? (Distance = rate x time.)

Self-study input (editorial): enter the distance in miles, without units.