AMO 2027 Grades 2-3 SET 22 - Self-study

Josh thought of a two-digit number and then added a zero at the end of that number to make it a three-digit number. He then added the three-digit number to his original number and the result was 726. What was his two-digit number?

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If $\frac25$ of a jug of juice is poured into one glass and 10 such glasses need to be filled, how many jugs of juice are needed?

Enter one whole number, without units.

A total of 400 points were scored by 5 players. The top two players scored 100 each. The other two players scored 88 and 76. How much did the 5th player score?

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If the letters of the alphabet are represented by numbers starting with $A=1$, $B=2$, $C=3$, and so on, find the sum of the digits represented by the word SMART. (Note: DOG is written as 4157.)

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How many rectangles of any size are there in the picture?



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If there are 8 roses for every 5 daffodils in the garden bed, how many daffodils are there if there are 96 roses?

Enter one whole number, without units.

Mahesh wrote the numbers from 31 to 80 in his notebook, including both 31 and 80. How many times did he write the digit 4 in any place?

Enter one whole number, without units.

Harry wrote $1,2,3,11,22,33,111,222,333,\ldots$ until he got 17 numbers. What is the sum of the digits of the last number he wrote?

Enter one whole number, without units.

A 5-digit number is a palindrome, meaning it reads the same forward and backward. It satisfies these conditions:
- The sum of the first three digits is 14.
- The third digit is half of the second digit.
- The sum of the second, third and fourth digits is 15.
Find the number.

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Count the triangles in the picture.



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How many non-negative whole numbers have the same quotient and remainder when divided by 12? Include zero among the numbers being considered.

Enter one whole number, without units.

Two players were playing a dice game. Each player rolled a die 3 times and recorded the numbers. The first player got a sum of 13, with the product of the three numbers as large as possible. What is the sum of the numbers he got? Use a standard die numbered 1 to 6.

Enter one whole number, without units.

If 300 digits were used to print the page numbers of a book, how many pages does the book have? Assume its pages are numbered consecutively from 1, with every page number printed once.

Enter one whole number, without units.

A four-digit number lock was installed at Tim's door. The tens digit is the sum of the hundreds and thousands digits. The ones digit is one-third of the tens digit. If the sum of all the digits is 21, find the tens digit.

Enter one whole number, without units.

Find the product of the triangle, circle and square values in these equations.



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