IKMC 2027 - Grades 3-4 - Self-study SET 14 - Thematic Batch 3

Zita has four candles, each of which burns for exactly three hours. She lights two candles. After 30 minutes a gust blows out one; one hour later another gust blows out the other. She then lights all four together. How long from that moment until all the candles have gone out?

Owl’s class has three kittens, four ducks, two geese and some sheep. The students have 44 legs altogether. How many sheep are in the class?

A rectangular piece of cardboard measures 15 cm by 9 cm. A square of side 3 cm is cut out of each corner. What is the perimeter of the remaining shape?

The rectangular solid below consists of two cubes. Each cube has the numbers 1,2,3,4,5,6, one on each face, and opposite faces sum to 7. The two touching faces carry the same number. Some numbers are shown. Which listed number could be on the face marked “?”?

Before a snowball fight John received some snowballs. During the fight he threw 21 and received 13 new ones. He had seven left at the end. How many did he receive before the fight?

Which value should replace the black triangle in the calculation diagram?

A maze is shown below. Each square contains a piece of cheese. Ron enters and leaves in the arrow directions and wants to eat as much cheese as possible without entering any square twice. What is the greatest number he can eat?

Josip has four toys: a car, a doll, a ball and a boat. He wants to place them in a row on a shelf with both the boat and the doll immediately next to the car. How many arrangements are possible?

Which of the solids below is different from the others?

Peter cycles in the park shown, starting at S in the arrow direction. At the first junction he turns right, then left, then right, and finally left. Which labelled point does he not pass?

When it is 10 a.m. in London, it is 11 a.m. in Madrid and 2 a.m. in San Francisco. Ann went to bed in San Francisco at 9 p.m. yesterday. What time was it then in Madrid?

Editorial task: calculate the time and date, then compare the wording of B and E.



Original source options (retained):
(A) 6 a.m. yesterday; (B) 6 a.m. the next day; (C) noon yesterday; (D) midnight yesterday; (E) 6 a.m. today

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

Jimmy buys the heart-shaped chocolate shown for his mother. Each small square of chocolate weighs 10 grams. How many grams does the whole chocolate weigh?

A square is repeatedly subdivided into 4, 7 and 10 separate squares, as shown. How many separate squares are in the tenth figure?

One pan of a balance contains six oranges, and the other contains two watermelons. Adding one watermelon to the orange pan balances the scale. One watermelon weighs as much as how many oranges?

Three ropes lie on the floor as shown. You can join them into one longer rope. Which joining pattern below should you use?

Gregor makes two three-digit numbers using each of 1,2,3,4,5,6 exactly once, then adds them. What is the greatest possible sum?

Mai colours an umbrella divided into 16 sectors using blue, red, purple and yellow. Each sector has one colour, every colour is used, and adjacent sectors have different colours. What is the greatest possible number of red sectors?

Find the number that belongs in the circle containing the question mark.

Two gears mesh as shown. The smaller gear winds a rope connected to a water bucket.
1. If the large gear turns clockwise, which way does the small gear turn, and does the bucket rise or fall?
2. How many teeth does each gear have? If the large gear turns once, how many turns does the small gear make?

The first four figures of a pattern are shown. How many green triangles will the fifth figure contain?