IKMC 2027 - Grades 5-6 - Self-study SET 14 - Thematic Batch 3

Alila completes a 72-lap race at an average speed of 288 km/h. Each lap is 6 km long. How long does the race take?

Writing 1 March 2005 as 01-03-05 gives three consecutive positive odd numbers in increasing order. It is the first such date of the twenty-first century. Including it, how many dates in that century have this property?

The squares shown are formed by the 50 cm segment AB and the broken line AA₁A₂…A₁₀B. What is the sum of their perimeters?

A football competition begins with 32 teams. In each round, teams are divided into groups of four. Every pair in each group plays once, and the two best teams advance. When only two teams remain, they play one final. How many games are played altogether?

Emily attaches flowers to every interior grid intersection of a 15×10 rectangular grid of square cells, leaving all boundary intersections empty. How many flowers does she use?

In the diagram, the largest square has area 16 cm² and the smallest has area 4 cm². What is the area of the second-largest square?

MonMon knows the English alphabet, but now reverses its order: hearing A he writes Z, hearing B he writes Y, hearing C he writes X, and so on. What does he write when KANGAROO is spelled aloud?

Under a starry sky, Puppy the dog and Catty the cat set out simultaneously to visit each other, walking at constant speeds. Distracted by the stars, they do not notice when they pass. After passing, Puppy reaches Catty’s home in 9 minutes and Catty reaches Puppy’s home in 1 minute. Answer all three questions.

1. Let a be Catty’s speed divided by Puppy’s speed. Compare their speeds and determine whether a>1 or a<1.
2. How are their distances from home to the meeting point related to a?
3. Use their remaining distances and times to find a and each complete journey time.

Cathie has 49 red and white tulips. She divides them into more than one group, with equal numbers of flowers in every group and exactly 3 red tulips in each. How many white tulips does she have?

What fraction of the entire illustrated figure is shaded black?

Alibaba and forty thieves share 42 identical bags of gold equally. Each person receives one full bag and two extra gold coins. How many coins are in each bag?

Alice has 108 red balls and 180 blue balls. She divides all the balls into bags so that every bag contains the same number of red balls and the same number of blue balls. What is the greatest possible number of bags?

The source introduces ABRACADABRA with a historical story about an Assyrian deity and a European protective charm, then arranges its letters as shown. How many different adjacent-letter paths spell ABRACADABRA?



Count paths starting at the top A and moving to an adjacent letter in the next row, as intended by the source.

Emily makes the pictured triangular grid from equal sticks. What is the least number of sticks she must remove so that the remaining figure consists only of six small triangles?



Source solution convention: the remaining figure has only six small triangles, with no stray sticks or larger triangles. The erroneous source answer letter is corrected below.

Emily uses a special encoding rule. Her first diagram has value 14 and her second has value 123. Under her rule, what value corresponds to the third diagram?



Use the source-intended rule: loop depth 1, 2, 3, 4 gives units, tens, hundreds, thousands respectively.

A strip of cardboard is divided into equilateral triangles as shown. What shape results when it is folded along the dashed lines?

Peter has ten wooden sticks joined end to end by hinges as illustrated. Which listed shape cannot be formed from this chain?



Sticks may pivot at their original hinges; a drawing uses every stick once. Ends may meet; projected crossings or overlaps need not create new hinges.

Anna, Bin, Chila and David take the top four places in a chess tournament. Anna’s, Bin’s and David’s ranks sum to 6, as do Bin’s and Chila’s. Bin ranks above Anna. Who finishes first?

North Africa and West Asia together have 106 one-humped or two-humped camels. Seven elevenths of the North African camels have one hump, and seventeen twenty-firsts of the West Asian camels have two humps.

1. By what number must the North African total be divisible, and why?
2. By what number must the West Asian total be divisible, and why?
3. Find the number of camels in each region.

Bob picks apples on Sunday morning. He gives Anna 3 apples, then gives his grandparents one third of the remaining apples. He has 8 left. How many did he pick?



The one-third gift is taken from the apples remaining after giving Anna three.