IKMC 2027 - Grades 5-6 - Self-study SET 7 - Thematic Batch 3

Three monkeys start cycling around a closed track at the same time and from the same starting point. They take 4, 6 and 8 minutes respectively to complete a lap. How long after starting will all three first meet again at the starting point?

Carrie is drawing a cat’s face. She has completed the part shown and will add the remaining details. Which of the pictures below could be her completed drawing?

John draws two parallel lines x and y. He marks four distinct points on x and two distinct points on y. How many segments have two of these six points as endpoints and meet both x and y?



Convention: meeting either parallel line at an endpoint counts as intersecting it.

A 3×3×3 cube is built from 27 unit cubes. Of these, 26 can be seen from outside, while one is completely inside. How many unit cubes can be seen from outside when a 4×4×4 cube is built?

Tony overlaps three square pieces of side lengths 2 cm, 4 cm and 6 cm, with their edges parallel as shown. A vertex of the second square is at the centre of the first, and a vertex of the third is at the centre of the second. What is the area of the resulting shape, in square centimetres?

The diagram is a plan of Mr Brown’s plot of land. All corners are right-angled, and the measurements shown are in metres. What is the area of the plot, in square metres?

Anna, Bob and Chris find an old scale that only has markings above 50 kg. Each weighs less than 50 kg. Together they weigh 108 kg; Anna and Bob together weigh 75 kg. Further weighings show that Bob weighs 10 kg more than Chris. How much does Anna weigh?

The product of three consecutive positive integers is five times their sum. What is the smallest of the three integers?

Bob folds an intact square sheet, then pushes a nail once through the folded layers. When he unfolds the sheet, the holes are as shown. Which of the folding patterns below could produce that result?

Bill writes a natural number. Nick multiplies it by 5 or 6. John adds 5 or 6 to that result. Andrew then subtracts 5 or 6 and obtains 73. Which listed number could Bill have chosen?

Each die has the numbers 1 to 6 on its faces, with opposite faces summing to 7. Alice places three identical dice in a row as shown. What is the total number of dots on the faces touching one another?

Peter has a rectangular poster measuring 80 cm by 50 cm. He accidentally tears part of it, then cuts a square of side 20 cm from each corner. What is the perimeter of the remaining shape?



Diagram convention: calculate the final outline shown; the tear is assumed to lie within the removed corner material.

Bon has 16 cards, four of each suit ♡, ♢, ♣, ♠. He places them in a 4×4 grid so that each row and each column has exactly one card of each suit. Some cards are already placed as shown. Which suit belongs in the question-mark cell?

Look at the decorative pattern shown. Which of the shapes below does not occur in the pattern?



Interpretation: the regular polygon outlines in the choices must follow straight edges of the decorative pattern.

A square of side 6 cm is divided into six equal rectangular strips. A diagonal divides each strip into two parts, one black and one white as shown. What is the total black area, in square centimetres?

One of the three cats Tom, Butch and Spike ate the turkey. Tom and Spike each deny doing it. Butch says, “Spike ate it.” Exactly two cats are lying. Which statement below is true?

Jane cuts a sheet into 10 pieces. She then chooses one piece and cuts it into 10 smaller pieces. She repeats this operation two more times. How many pieces of all sizes does she have at the end?

Dragonflies and butterflies occupy more than half of the 11 flowers on a rose bush, with at most one insect per flower. There are three times as many butterflies as dragonflies. How many insects are there altogether?

Four friends have seats numbered 1 to 4 in one row. Lilly refuses the end seats 1 and 4. Riley wants a higher-numbered seat than Katy. How many seating arrangements satisfy both wishes?

At a party, five large pizzas are each cut into 12 pieces, initially one piece per guest. More guests arrive, so the waiter takes some uneaten pieces and cuts each into 12 smaller pieces. At the end everyone has eaten exactly one piece. Which total number of guests is possible?



Source-intended convention: all final pizza pieces are distributed and eaten, with no leftovers. Otherwise the number of guests need not equal the number of pieces, and other listed totals could be possible.