AMO 2027 Grade 3 SET 6 - Self-study

Study the original table and find the missing value in column D. Use the intended row rule $D=A+B-C$.



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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.

In the original row below, every four consecutive cells have sum 20. Find $X+Y$.



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

**Editorial note:** Choose one option.

Tom’s clock loses 5 minutes for every hour of real time. He sets it correctly at 12:00 pm (noon). What time does it show when the real time is 2:00 am the next morning?



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There are 5 pairs of different colours of socks in a drawer. What is the least number of socks Jeena must take out without looking to be sure that she has a pair of the same colour?

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Find the ones digit of $100\times102\times104\times106\times108$ minus $99\times101\times103\times105\times107$.



Enter one whole number, without units.

What is the 11th term in the pattern 17, 20, 25, 32, 41, …? Continue the source’s intended rule: successive increases are consecutive odd numbers, beginning with 3.



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What is the digit in the hundreds place of $6969+9696+6996+9669$?



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

**Editorial note:** Choose one option.

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.

What is the smallest four-digit number divisible by both 7 and 5?



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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.

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.