IKMC 2027 - Grades 5-6 - Self-study SET 17 - Thematic Batch 3

A tortoise cycles from the foot of a mountain to its summit at 20 metres per hour and returns at 40 metres per hour. The whole trip takes 3 hours. How long is the mountain route in metres?



Source-intended distance: the one-way mountain route; the full round trip is twice as long. The bilingual source unit discrepancy is documented in the solution.

In the table, equal letters stand for equal numbers and different letters for different numbers. Each number at the right is its row sum. What is X?

Rancho marks five points on paper and joins every pair by a straight segment. What is the largest number of triangles that the resulting drawing can contain?



Editorial consistency task: explain when the source answer 10 is correct, then prove the unrestricted visible-triangle maximum and identify whether any printed choice matches.

Original choices: A. 10; B. 20; C. 21; D. 12; E. 18

Linda has the illustrated pieces and a 4 × 4 square board. Which additional piece lets her cover the board completely? Pieces may be rotated or reflected.

Five weights consist of one 30 g weight, one 80 g weight and three 50 g weights. The balances compare them as drawn. Which weight is the lightest?

Four squirrels ate 1999 nuts altogether, each at least 100. One squirrel ate strictly more than each of the others. The second- and third-largest amounts total 1265. How many nuts did the largest eater consume?



Interpret the largest eater as eating more than each other squirrel individually.

Bin needs 9 kg of paint to cover all exterior faces of the solid 3 × 3 × 3 cube. How much paint is needed for the white interior faces of the cut-out cube?



The source’s left/right references are reversed; identify the solid and cut-out cubes by their drawings.

Bobby takes a 25-question test. A correct answer scores 5, a wrong answer loses 2, and a blank scores 0. He scores 80 and has at least one wrong answer. How many answers are correct?

Peter writes KANGAROO on a transparent pane as shown. He turns it through half a turn, then views it from the reverse side. Which image does he see?



Source-intended operations: an in-plane 180° turn, then viewing the reverse face.

A 60-page magazine is made from 15 nested folded sheets. Pages are numbered 1 to 60. If the sheet containing page 7 is lost, which other pages are lost?

A dance club has 39 boys and 23 girls. Each week 6 boys and 8 girls join. When the numbers of boys and girls become equal, how many members are there?

Molly, Dolly, Sally, Elly and Kelly sit in a row. Molly is not at the far right; Dolly is not at the far left; Sally is at neither end and is adjacent to neither Kelly nor Dolly; Elly is somewhere to Dolly’s right. Who sits at the far right?

Each player chooses a different three-digit number, every digit at most 4, with the hundreds digit equal to the sum of the other two. What is the maximum number of players?

Three basketball teams A, B, C play only one another. A plays 6 games, B 7 and C 11. How many games are between A and C?

Leni, Sarah, Hannes, Petra, Arno stand in that cyclic order. They repeatedly count KAN–GA–ROO–OUT–GOES–YOU, eliminating the person saying YOU and resuming at the next remaining person. Who should start for Arno to be the survivor?

All five diagrams use equal 3 × 3 square grids. Which has the largest shaded area?

Alex brings 8 identical food packets and Ben 7. They share all 15 equally with Charlie. Charlie pays them 30 units of money for what they contributed to his share. How much should Alex receive?

Maria was born on 5 April 2013. Her mother calls this a special date because all digits in its written form are distinct. How many days earlier was the most recent previous date with that property?



Editorial consistency task: use unpadded D/M/YYYY, examine the source’s preceding date, and determine the corrected gap. None of the printed choices is correct under that convention.

Original choices: A. 12; B. 9364; C. 196; D. 9436; E. 9281

At a party, 42 guests ate at least one cake, 33 at least two, 27 at least three, and 8 exactly four. Nobody ate more than four. How many cakes were eaten?

Julia has cards 1, 2, 3, 4, 5. She chooses two disjoint pairs so that the sum of one pair equals the product of the other. Which card is certainly left unused?



Editorial consistency task: test whether any card is necessarily unused, retaining the original choices and source construction.

Original choices: A. 1; B. 2; C. 3; D. 4; E. 5