AMO 2027 Grades 2-3 SET 14 - Self-study

Wayne is 6 years older than Alice. Five years from now, the sum of their ages will be 52. How old are both of them?

Self-study input convention (editorial): enter the present ages in order Wayne;Alice, separated by a semicolon.

**Editorial input note:** Use no spaces before or after semicolons.

In the following alphabetic, all the different letters stand for different digits. Find the sum of A + L + L.

Jason has more money than Tom and less than Edison. Brandon has less money than Edison but more than Jason. Tom has less money than Edison but more than Alice. Who of them has the most amount of money?

A few years ago, there were 4 Saturdays and 4 Wednesdays in the month of March. On which day in that year was 10th of March?

Mary has several boxes. Each box has the same number of coins. If she has a total of 24 coins in 6 boxes, how many coins are there in her 12 boxes altogether?

Using the line graph shown below, answer the following question.



a) How many cars were sold in 5 days?

b) How many more cars were sold on Tuesday than on Monday?

Self-study input convention (editorial): enter two numbers in order a;b, separated by a semicolon.

**Editorial input note:** Use no spaces before or after semicolons.

A stack has 9 different number cards. The numbers are from 1 to 9. Alex, Benjamin, Carol, Danish each draws 2 cards. It is given that the sum of the cards drawn by Alex equals 10, the difference of the cards drawn by Benjamin is equal to 1, the product of the cards drawn by Carol equals 24, the quotient of the cards drawn by Danish is equal to 3. Which number card is still left in the stack?

Self-study convention (editorial): for a difference or quotient, put the larger card number first; each physical card can be drawn only once.

The sum of seven consecutive odd numbers is 49. Find the seven numbers.

Self-study input convention (editorial): enter all seven numbers in increasing order, separated by semicolons.

**Editorial input note:** Use no spaces before or after semicolons.

The sum of the digits in a 2-digit number is 12. If the tens digit is 2 less than the ones digit, find the number.

The figure below shows 9 cubes that are glued together. How many faces of small cubes are glued together?



Self-study counting clarification (editorial): count the individual faces of the small cubes. Each join glues two faces, one from each cube.

Alice earns \(\text{\$12}\) an hour for walking the neighbor's dog. Today she can only walk the dog for 45 minutes. How much will Alice make today?

Self-study input (editorial): use proportional payment at the stated hourly rate; enter the amount in dollars.

A glass of water has a mass of 180g. When one half of the water is poured away, the remaining glass of water has a mass of 120g. What is the mass of the glass?

Self-study input (editorial): enter the empty glass mass in grams.

Given △ × △ × △ = 27 and N × N × N = 64, then what is △ × N?

A website decided to reward the first user and every 15th user after the first user, with a free gift. How many rewards does the website give away before the 100th user visits the website?

Self-study spacing clarification (editorial): reward user 1, then add 15 to the rewarded user position each time. Count only positions strictly below 100.

Pi has a eighteen-dollar bill. He buys eight squirt guns for \(\text{\$2}\) each. How much money did Pi have left?

Self-study input (editorial): enter the remaining amount in dollars.