AMO 2027 Grades 4-5 SET 6 - Self-study

David is 2 years older than Sue. Tom is 47. Hector is 3 years younger than Tom and 1 year younger than Sue. How old is David?

Christine thought of a number. She added $\frac{1}{3}$ of this number and then multiplied the result by 5. Then she subtracted 4 and then divided the result by 8. She got 27 in the end. What was the original number?

The graph shows the number of minutes studied by both Asha (black bar) and Sasha(grey bar) in one week. On the average, how many more minutes per day did Sasha study than Asha?

David, Cindy and Tom were born in USA, Japan and China, but not necessarily in that order.

• David has never been to USA.

• Cindy was not born in China.

• Cindy was not born in USA.

Can you find out David’s place of birth?

Joan had twice as many marbles as Ann. After Christmas, Ann got 12 more marbles and Joan got 49 more marbles. Joan’s number of marbles is now three times that of Ann’s number of marbles. How many marbles did Ann have before?

Study the pattern below. In which row will you find the number 300?

Source table, read row by row (printed values retained):

| Row | First | Second | Third |
|---|---|---|---|
|A|1|8|15|
|B|7|14|21|
|C|2|9|16|
|D|6|13|20|
|E|3|10|17|
|F|5|13|19|
|G|4|11|18|

Which digit should replace X such that the 5-digit number $\overline{XX4XX}$ is divisible by 9?

The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds?

Benny spent 25% of her money on a handbag and $\frac{1}{5}$ of the remainder on transport. After spending 240 dollars on a television set, she had 10% of her original sum of money left. How much did she spend altogether?

Given a sequence

3, 3, 1, 9, 4, 3, 3, 1, 9, 4, 3, 3, 1, 9, 4, …

a) What is the 53rd number?

b) What is the sum of the first 102 terms?

Answer entry: enter (a); (b), separated by a semicolon.

**Editorial input note:** Use no spaces before or after semicolons.

Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?

In the following alphabetic, all different letters stand for different digits. Find the three-digit ABC.

$\overline{ABC}+\overline{ABC}=\overline{CDDB}$.

Roger spent 30% of his salary and Katie spent 2% of her salary. They had the same amount of money left. Find Katie’s salary if Roger’s salary was 2240 dollars.

Find how many three-digit numbers satisfy all the following conditions:

• if it is divided by 2, the remainder is 1,

• if it is divided by 3, the remainder is 2,

• if it is divided by 4, the remainder is 3,

• if it is divided by 5, the remainder is 4,

• if it is divided by 8, the remainder is 7.

How many sticks at length of 9 metres are placed end to end to make 81 metres?