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AMO 2027 Grade 3 SET 2 - Self-study

Question 1

Three 5-Star bars, two Kit Kat bars and one Perk bar cost 145 dollars. Two Kit Kat bars, one 5-Star bar and three Perk bars cost 135 dollars. Find the combined price, in dollars, of one bar of each kind.

Question illustration

Enter one whole number, without units.

Question 2

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

Question illustration

Choose one option.
  1. 210
  2. 21
  3. 300
  4. 30
  5. 60

Question 3

Radha has to cut small strips of ribbon of 5 cm each. But after every 3 strips of 5 cm, she cuts a strip of 4 cm mistakenly. If a total roll of 100 cm was cut into small ribbons, how many 5 cm ribbon strips are there?

Choose one option.
  1. 15
  2. 16
  3. 14
  4. 19
  5. 20

Question 4

Harry brought a few marbles to school. He distributed one-third of the marbles among his friends on the bus. He then gave 20 marbles to his classmates. Now he is left with only one-fourth of his marbles. How many marbles did he have at first?

Both fractions refer to his original number of marbles.

Choose one option.
  1. 24
  2. 36
  3. 48
  4. 40
  5. 42

Question 5

Find the value of the digit in the ones place of the following expression: $99\times101\times103\times105\times107-100\times102\times104\times106\times108$.

Enter one whole number, without units.

Question 6

How many consecutive zeros are there at the end of the following product? $25\times25\times6\times6\times36$.

Enter one whole number, without units.

Question 7

A number is multiplied by 3 and then 5 is added. The final result is 26. What is the number?

The original options are A. 19; B. 20; C. 18; D. 21; E. 17. This edition keeps the stated result 26. Enter a number rather than an option letter, whether or not it appears among the original options.

Question illustration

Enter one whole number, without units.

Question 8

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.
  1. 62
  2. 59
  3. 60
  4. 61
  5. 58

Question 9

Sara’s birthday falls on Friday, 15 August this year. On which day will her birthday fall next year if next year is a leap year? Use the hypothetical year described, not the 2027 edition year.

Question illustration

Choose one option.
  1. Tuesday
  2. Thursday
  3. Sunday
  4. Monday
  5. Saturday

Question 10

A rectangle is formed by placing two squares of the same size next to each other. If the perimeter of each square is 60 cm, find the area of the rectangle in square centimetres.

Question illustration

Choose one option.
  1. 288
  2. 450
  3. 354
  4. 360
  5. 225

Question 11

Two years from now John will be twice as old as he was two years ago. How old will he be ten years from now?

Question illustration

Enter one whole number, without units.

Question 12

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.

Question 13

One stack contains 8 coins. The stacks are arranged with 1 stack in the first layer, 2 in the second, and so on. How many coins are needed for 5 layers?

Question illustration

Choose one option.
  1. 120
  2. 150
  3. 210
  4. 48
  5. 75

Question 14

Given that $k\times726$ equals the square of 66, find $k$. Here the square of 66 means $66\times66$.

Question illustration

Enter one whole number, without units.

Question 15

What is the hundreds digit of $40444+44044+44404+44440$?

Question illustration

Choose one option.
  1. 0
  2. 4
  3. 8
  4. 2
  5. 3