AMO 2027 Grade 2 SET 6 - Self-study

Sheila has to write 48 pages. She has finished only one-fourth of them. How many pages remain to be written?



Choose one option.

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?



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.

How many times altogether do the hour hand and minute hand cross an even-numbered mark on a clock from 1 a.m. to 1 p.m.? Count each hand separately, even if both cross at the same instant. Count crossings after the starting time and up to and including the ending time. The source clock is an illustration of the face, not a picture of the stated starting time.



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On a number table from 1 to 100, we start at a number, add 72 and then subtract 36 to reach 50. What was the original number?



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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.

If the letters of the alphabet are represented by numbers starting with $A=1$, $B=2$, $C=3$, and so on, find the sum of the digits represented by the word SMART. (Note: DOG is written as 4157.)

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A basket contains 30 red balls. Karla takes 5 red balls and replaces them with 6 green balls. She continues to exchange the balls in the same way until all the red balls are replaced by green balls. How many balls are there in the basket now?

Enter one whole number, without units.

In the following addition, different letters represent different digits. What is the sum of A, B and D? The addends are 7A, 3B5, 1C70 and D209; their sum is 8026.



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Two players were playing a dice game. Each player rolled a die 3 times and recorded the numbers. The first player got a sum of 13, with the product of the three numbers as large as possible. What is the sum of the numbers he got? Use a standard die numbered 1 to 6.

Enter one whole number, without units.

If the last day of May is a Friday, what day is the 1st of April in that same year?



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A total of 400 points were scored by 5 players. The top two players scored 100 each. The other two players scored 88 and 76. How much did the 5th player score?

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A 1-litre bottle is being filled using a 150-ml jug and a 50-ml jug. Each full jug is poured three times into the initially empty bottle. How much more liquid is needed to fill it to the brim?



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What number has 2 hundreds, 5 more tens than 20, and 1 less than 7? Use the source meaning: the tens contribution is 20 plus five tens, and the ones contribution is 7 minus 1.



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Each letter represents a number in the sequence $A,7,9,B,C,D$. The sum of any three neighbouring numbers is 19. What is the value of the letter $D$?



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