AMO 2027 Grade 2 SET 3 - Self-study

A fan has three blades. How many blades are there on 150 such fans?



Choose one option.

Mahesh wrote the numbers from 31 to 80 in his notebook, including both 31 and 80. How many times did he write the digit 4 in any place?

Enter one whole number, without units.

The place cards shown are folded along the dotted line so that only a number or letter is visible. Chrissy enters the room and sees all five place cards, with at least 2 number cards being shown. The sum of the numbers she sees is less than 8. How many different sets of numbers are there?



Enter one whole number, without units.

Find P in the original boxes. Use the intended common rule: multiply the left and middle bottom numbers, then subtract the right bottom number to obtain the top number.



Enter one whole number, without units.

If $\overline{5A8}+\overline{B2}=600$, what is the largest possible difference between digit A and digit B? The bars indicate numbers made from digits, not products. Digits range from 0 to 9; B is nonzero because B2 has two digits. Difference means the larger digit minus the smaller.

The original choices are A. 7; B. 6; C. 5; D. 3; E. 1. For this self-study edition, enter a number rather than an option letter, whether or not it appears in that list.



Enter one whole number, without units.

Suzy has five children. Amy is older than Beth but younger than Carla. David is older than Erwin but younger than Beth. Who is the eldest?



Choose one option.

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.

Eleven lamps are installed at equal distances along a straight farm road 110 metres long, with one lamp at each end. What is the distance between two neighbouring lamps, in metres? The source phrase “any two lamps” is interpreted as neighbouring lamps.



Enter one whole number in metres, without units.

Nine lemons weigh the same as three peaches, and six peaches weigh the same as two mangoes. How many lemons weigh the same as five mangoes? Assume fruits of the same kind have equal weights.



Enter one whole 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.

Paul can jog 1 km in 4 minutes and 30 seconds. How many minutes will he take to jog 10 km? Assume he keeps the same pace for the whole distance.



Enter one whole number, without units.

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.



Enter one whole number, without units.

Ayer and Kumar tossed a coin. Ayer wins if it is a head while Kumar wins if it is a tail. The winner gets 3 marbles from the loser. Both had 20 marbles each in the beginning. They played 10 rounds and Ayer won 4 rounds. What is the total number of marbles Kumar had in the end?

Enter one whole number, without units.

Grace and Freddy each tossed a coin three times. Grace got a head on her first toss, and Freddy got a tail on his last toss. In how many different ways can they get the same outcome? “The same outcome” means that their three results match toss by toss, in the same order.



Choose one option.

Sarah’s birthday is on 6 September every year. Today is 27 July, a Sunday. On which day of the week will her birthday fall this year? Use the weekday given in this question; the self-study title does not specify the calendar year of the story.



Choose one option.