AMO 2027 Grade 4 SET 1 - Self-study

If the five-digit number $83m24$ is divisible by both 3 and 4, what is the smallest possible value of the digit $m$?

Choose one option.

How many triangles are in the figure? Count triangles of every size whose complete straight sides follow drawn line segments.



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In a book of 100 pages, all the pages with digits that are factors of 5 are torn. How many pages are left now?

Number the pages 1 to 100 inclusive. Remove each numbered page independently if its number contains at least one digit that is a positive factor of 5. Enter one whole number.

Ann read a book with 1000 pages. How many digits were used to print its page numbers? Assume pages are numbered 1 through 1000, each number printed once without leading zeros.

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If $A+B=28$, $B+C=40$ and $A+C=36$, what is $5\times A+5\times B+5\times C$?

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$(A-15)$ is an even number. What is the 10th odd number after it when $A=21$?

Enter one whole number, without units.

In a town of 10 905 residents, there are 2500 more male voters than female voters. If 911 residents are not allowed to vote, how many female voters are there? Here voters means residents eligible to vote.

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How many whole numbers from 1 to 100, inclusive, are divisible by neither 5 nor 7?

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Find the value of $A5B+C9$ in the subtraction shown.

$A5B$ and $C9$ are base-ten whole numbers formed by concatenating their digits; $A,C$ are nonzero digits and $B$ is a digit.



Choose one letter A–E.

Mangoes were bought and placed into baskets to be distributed in an orphanage. If each basket was filled with 13 mangoes, 54 mangoes were left. But when 16 mangoes were put in each basket, there was a shortage of 27 mangoes. How many mangoes were bought?

Enter one whole number, without units.

Calculate $450\times3+450\times17-45\times190$.

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Among Jack, Jade and James, one is a painter, one is a lawyer and one is a firefighter. Jack is older than the firefighter, while the lawyer is younger than James. Jade and the lawyer are not the same age. Who is the firefighter? Use Jack = 1, Jade = 2, James = 3.

Enter the person’s code: 1, 2 or 3.

Five years from now, Derrick and Stacy will have combined age 37. Three years ago, Derrick was twice as old as Stacy. How old is Derrick now?

Choose one option.

Count the number of triangles in the following figure.



Choose one letter A–E.

What is the greatest whole number smaller than 425 whose digits have sum 11?

Choose one option.