IKMC 2027 - Grades 3-4 - Self-study SET 19 - Thematic Batch 3

Betty replaces the stars in 1 ∗ 2 ∗ 3 ∗ 4 ∗ 5 with exactly two plus signs and two minus signs. She also inserts one pair of parentheses. What is the largest value she can obtain?

Rabbit carries a clock that loses exactly one minute for every real hour. He resets it at 10 p.m. every night before bed, but forgot last night. This morning it shows 9:15 a.m., as pictured. About how many minutes remain until his 10 a.m. tea party?

Basil is exactly one year and one day older than Pete. Basil was born on 1 January 2002. On what date was Pete born?

The calculation shown has three covered signs. Tom inserts +, − and ×, using each sign once, to make the value as large as possible. In what order does he insert the signs?

The Paddler family, consisting of the father, mother and their son Benjamin, rents a boat with seats for three people. In how many ways can they sit in the boat?

Both scales shown are balanced. The weight of two triangles equals the weight of how many circles?

A two-digit natural number has digits whose product is 15. What is the sum of its digits?

Four brothers eat 11 cookies. Each eats at least one cookie, and two of them eat the same number. Three of them eat 9 cookies altogether, and one brother eats exactly 3. How many cookies does the brother who eats the most eat?

Editorial task: test whether the wording determines a unique answer. Give all possible largest counts and state an extra assumption that would justify the source answer.



Original source options (retained):
(A) 3; (B) 4; (C) 5; (D) 6; (E) 7

Editorial format note: this essay examines the source wording and its assumptions. The original choices are retained for comparison.

The Ant Kingdom’s guard contains big ants and fire ants in the ratio 4:3. Then 24 big ants are transferred out and 6 fire ants join. The new ratio is 2:3. How many ants are in the guard after these changes?

Mary has the pictured sheet with kangaroos. How many times must she fold along the drawn lines so that only one kangaroo remains visible?

Ann starts moving in the direction of the arrow shown. She turns right, left, left, right and left, in that order. At which pictured place does she stop?

Jack makes the pictured cube using 27 small black and white cubes. No two face-adjacent small cubes have the same colour. How many white cubes does he use?

Linda folds a blue square sheet in half twice, then punches two round holes as shown. Which picture does she obtain when she opens the sheet?

Two meshing gears carry kangaroo pictures. The fixed large gear has 14 teeth; the small gear above it has 7. The small gear rolls around the outside of the large gear to the bottom position shown. What do the two gears look like then?

An older brother is 10 years old when his younger brother is 3. How many years later will the older brother be twice as old as the younger?

At the trainer’s first signal, the monkeys form 6 rows with 4 monkeys in each. At the second signal they form 8 equal rows. How many monkeys are in each row then?

A path surrounds a rectangular garden as shown. Its outer boundary is 8 metres longer than the garden’s perimeter. How wide is the path?

Bob folds a square sheet several times and punches one hole through it. After opening it, he sees the pictured four holes. How did he fold the sheet?

Mary is a girl with 3 brothers and 2 sisters. How many brothers and sisters does her brother Michael have?

Dolly breaks her favourite mirror. How many of the resulting pieces are quadrilaterals?