AMO 2027 Grades 2-3 SET 28 - Self-study

One stack contains 8 coins. The stacks are arranged with 1 stack in the first layer, 2 in the second, and so on. How many coins are needed for 5 layers?



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Each letter represents a number in the sequence $A,7,9,B,C,D$. The sum of any three neighbouring numbers is 19. What is the value of the letter $D$?



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Find the sum: $2+8+12+18+22+\cdots+92+98$. Continue the shown pattern: the increments alternate between 6 and 4.



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The sum of three consecutive even numbers is 78. Find the largest number.



Enter one whole number, without units.

A prime number is a whole number with exactly two positive factors: 1 and itself. For example, 2 and 7 are prime numbers. Two prime numbers sum to 55. Find their product.



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Sarah’s birthday is on 6 September every year. Today is 27 July, a Sunday. On which day of the week will her birthday fall this year? Use the weekday given in this question; the self-study title does not specify the calendar year of the story.



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Five years ago, the sum of a couple’s ages was 76. Fifteen years later, the man will be 4 years older than the woman. What will their total age be 30 years later? Here “later” means from the present time, as in the source solution.



Enter one whole number, without units.

A two-digit number is doubled, then 25 is added. The result is three times the original number. What is the original number?



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A 1-litre bottle is being filled using a 150-ml jug and a 50-ml jug. Each full jug is poured three times into the initially empty bottle. How much more liquid is needed to fill it to the brim?



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Eight notebooks and 10 pens cost 480 dollars. One pen costs 15 dollars less than one notebook. Find the price of 5 notebooks.



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A car travels 44 km using 4 litres of petrol. Tom starts with 6 litres and uses one-third of it on Monday. He travels another 22 km on Tuesday. How many kilometres can the car travel with the petrol left? Assume the same fuel use per kilometre throughout and no extra petrol is added.



Enter one whole number, without units.

Cards are numbered 1 to 100. The first child gets card 1, the second gets cards 2 and 3, the third gets cards 4, 5 and 6, and so on. Which child gets card 50?



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A number pyramid continues as shown. What is the 10th number from the left in the 12th row? Each row has one more entry than the row above, and the counting numbers continue from left to right.



Enter one whole number, without units.

Two identical squares, each with side length 16 cm, are joined along one whole side to make a rectangle. What is the perimeter of the rectangle, in centimetres?



Enter one whole number, without units.

A fan has three blades. How many blades are there on 150 such fans?



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