AMO 2027 Grades 6-7 SET 2 - Self-study

If the four-digit number 19N6 is divisible by 14, find N.

A “stair-step” figure is made of alternating black and white squares in each row. Rows 1 through 4 are shown. All rows begin and end with a white square. How many black squares are there in the 37th row?

Alice, Ben and Charles are going to enroll for the following clubs: Mathematics, Creative Writing, Arts and Crafts, Concert Band. If each of them is allowed to enroll for only one club, how many different combinations are there?

The chart below provides information on how bonuses of certain amounts were distributed among the employees of a business:

| Bonus paid to an employee (dollars) | Number of employees |
|---|---|
| 50 | 7 |
| 100 | 37 |
| 150 | 4 |
| 200 | 2 |

a) What was the average bonus per employee?

b) If the median bonus is m dollars, the average bonus a dollars, and the mode bonus is p dollars, which of the must be true?

A. $m < a < p$.

B. $m < a = p$.

C. $m = p < a$.

D. $m < p < a$.

A mixture, weighing 100kg is made up of 2 chemicals A and B in the ratio 7 : 3. When some volume of Chemical A evaporates, the content of Chemical A is reduced to 60% of the new mixture. What is the mass of the mixture now?

A train moves from Bangkok to Chiang Mai. After 1 hour 40 minutes, another train moves from Chiang Mai to Bangkok whose speed is 5 km/h more than the first train. The trains meet each other at a station that is 300 km away from Chiang Mai. Given that the distance between Bangkok and Chiang Mai is 645 km, find the velocity of the first train.

Alex has 84 fewer pins than Ryan. Helen has 295 more pins than the total number of pins Alex and Ryan have. Helen has 752 more pins than Alex. How many pins do the three friends have altogether?

When 3 metal balls were placed in the water, the water level rose by 4.5cm. Find the volume of 8 such metal balls.

A cyclist rides 30 km at an average speed of 9 km/h. At what rate must the cyclist cover the next 10 km in order to bring the overall average speed up to 10 km/h?

There are 6 points on a circle. How many quadrilaterals can be formed by joining any of the 4 points on the circle?

A fruiterer has a certain number of apples. If he arranges them in groups of 2, 3, 4, 5, 6, 7, 8 or 9, he will always have one left over for each group. What is the least number of apples he can possibly have?

The integers 1 to 32 are spaced evenly and in order around the outside of a circle. Straight lines that pass through the centre of the circle join these numbers in pairs. Which number is paired with 12?

William has 130 model cars in total. If the number of convertibles is four times the number of cars which are not convertibles. How many convertibles model cars does William have?

James had some local and foreign stamps in the ratio 8 : 9. After he gave 88 local stamps to his brother, the ratio of the number of local stamps to the number of foreign stamps became 2 : 5. How many local stamps did he have at first?

The total length of a rope, string and wire is 26.3 m. The rope is 1.8 m longer than the string and 3.4 m longer than the wire. Find the length of the rope and wire.