AMO 2027 Grades 2-3 SET 21 - Self-study

If the cells are added in the same pattern, which row will have the number 25?

**Editorial note:** Keep the printed fifth row exactly as shown. For this exercise, continue after 35 with 34, 33, 32, …, and put one more cell in each new row. Count the top row as row 1. Choose one option.

Jack and his father’s weight add up to 100 kg. If Jack loses 4 kg, he will be exactly half of his father’s weight. What is the difference between their weights, in kg?

**Editorial note:** Find the difference before Jack loses weight; his father’s weight stays unchanged. Choose one option.

Solve: $$100+90-80-70+60+50-40-30+20+10$$

**Editorial note:** Choose one option.

The product of $58\times24$ is

**Editorial note:** Choose one option.

A basket contains an equal number of balls and pebbles. They are either white or black. The number of white balls is 30 and the total number of black items is 30. If the difference between the number of black and white balls is 20, find the number of white pebbles.

**Editorial note:** Enter only the number, without units.

If 5 postmen deliver 200 letters in 2 days. How many postmen will be needed to deliver 600 letters in 3 days?

**Editorial note:** Assume every postman works at the same constant rate for the same amount of time each day. Choose one option.

A box of apples can be shared equally between 3, 4, 5 or 6 classes. What is the smallest possible number of apples in the box if it had more than 200 but less than 500 apples?

**Editorial note:** Share whole apples with no remainder. Enter only the number, without units.

Suppose today is 15th August, Friday. How many Sundays will there be as of 30th October?

**Editorial note:** Use the stated hypothetical calendar, not the actual 2027 calendar. Count Sundays after 15 August through 30 October inclusive. Choose one option.

Chloe’s current age is a multiple of 6. Next year, her age will be a multiple of 5. She is more than 30 years old and less than 70 years old. Find her age 4 years from now.

**Editorial note:** Choose one option.

Brian takes a day off from work every 4th day and David takes a day off on every 5th day. If they have a day off today and their next day off falls on a Monday, what day is today?

**Editorial note:** Interpret “their next day off” as their next shared day off after today. Today is day 0; Brian’s future days off are 4, 8, 12, … and David’s are 5, 10, 15, … days later. Choose one option.

Garry left his house for the park which is 10 minutes away on foot. He then played football for 45 minutes and was back after chatting with his friends for 15 minutes. If he got back home by 7.00 pm, then what time did he leave his house?

**Editorial note:** For the source’s intended answer, take the arrival as exactly 7.00 pm. The return walk also takes 10 minutes, and the listed activities happen consecutively with no extra delay. Choose one option.

Find the sum of $A+B+C$ if different letters stand for different digits.

**Editorial note:** A8 and BCC are ordinary base-ten numbers; A and B are nonzero leading digits. Choose one option.

How many 3-digit numbers have the sum of the digits less than 5?

Original printed choices: A. 4; B. 8; C. 12; D. 15; E. 19.

**Editorial note:** The printed choices contain a source error. Enter the corrected count rather than an option letter. Three-digit numbers range from 100 to 999. Enter only the number, without units.

Zack, Tom and Jim each draw 3 cards from 9 cards numbered 1, 2, 3, …, 9.

Zack: The product of all my numbers is 35.

Tom: The product of all my numbers is 96.

Jim: The sum of my numbers is 16.

What is the second largest number of Jim?

**Editorial note:** The nine distinct cards are shared without replacement: each card goes to exactly one boy. Enter only the number, without units.

If $a\infty b=a\times5-b\times2$, what is the value of $8\infty9$?

**Editorial note:** Choose one option.