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AMO 2027 Grades 2-3 SET 27 - Self-study

Question 1

An eraser costs 5 dollars less than a pencil. If 5 pencils and 5 erasers cost 40 dollars, what is the price of 2 pencils?

Question illustration

Choose one option.
  1. 6.50 dollars
  2. 1.50 dollars
  3. 130 dollars
  4. 13 dollars
  5. 65 dollars

Question 2

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

Question illustration

Enter one whole number, without units.

Question 3

Henry drives 2 km in the first 10 minutes. After every 10 minutes he increases his speed and travels 1 km farther in the next 10 minutes than in the preceding 10 minutes. How many kilometres does he travel in one hour?

Question illustration

Choose one option.
  1. 27
  2. 20
  3. 12
  4. 24
  5. 25

Question 4

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 5

Roy walks the first 10 m of his journey to school, then travels the remaining three-fourths of the whole journey by bus. How far is his school from his house?

Question illustration

Choose one option.
  1. 134 m
  2. 100 m
  3. 30 m
  4. 40 m
  5. 400 m

Question 6

Today is Monday, 13 September. What is the date of the fourth Monday after today? Count next Monday as the first; do not count today.

Question illustration

Choose one option.
  1. 12 October
  2. 12 November
  3. 11 November
  4. 11 October
  5. 9 October

Question 7

Find $48+498+4998+49998$.

Question illustration

Choose one option.
  1. 55548
  2. 55546
  3. 55564
  4. 55542
  5. 55562

Question 8

Tom scored one-third of his total score in English and two-fourths in Maths. His remaining 45 points were in French. What was his total score?

Question illustration

Enter one whole number, without units.

Question 9

When 10 is subtracted from a whole number greater than 10, the positive result is divisible by 2, 5 and 7. Find the smallest such original number.

Question illustration

Choose one option.
  1. 35
  2. 60
  3. 70
  4. 45
  5. 80

Question 10

What is the sum of the first 10 positive multiples of 6, starting with 6?

Question illustration

Enter one whole number, without units.

Question 11

A fruit vendor bought 4 dozen apples at 60 dollars per dozen and sold every apple for 6 dollars. How much was his gain, in dollars? Count only the stated buying and selling prices.

Question illustration

Enter one whole number, without units.

Question 12

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

Question illustration

Choose one option.
  1. 31
  2. 20
  3. 12
  4. 22
  5. 44

Question 13

Veena watches a movie on Netflix. She stops after watching one-third of it. If she had watched 12 minutes more, she would have watched half of the movie. How long is the movie, in minutes?

Question illustration

Enter one whole number, without units.

Question 14

Frank has more than 20 and fewer than 70 marbles. If he makes piles of 4, one marble is left over. If he makes piles of 7, three marbles are left over. How many marbles does he have?

Question illustration

Enter one whole number, without units.

Question 15

Each term of a sequence is found by subtracting the same number from the preceding term. The first term is 257 and the fifth is 209. What is the fifteenth term?

Question illustration

Enter one whole number, without units.