HKIMO Reviewer

LOGICAL THINKING: Given that S: T = 4: 10 , T:U = 5: 12 , U: V: W = 8: 3: 7 and S + T + U + V + W = 476. What is the value of W−(T + V) ?.

LOGICAL THINKING: Two cars are travelling starting from the same point. The speed of car A is 120 km/h, and car B is 20 km/h slower than the speed of car A. Car A overtakes Car B, 5 hours after start. How many hours has car B been travelling when the overtake happened?.

LOGICAL THINKING: There are 15 black, 26 red and 37 blue pens in a bag. Robert randomly picks pens from the bag. At least how many pen(s) need/s to be picked to ensure there are at least 11 pens of each color picked?.

LOGICAL THINKING: Jundel drives straight toward Elen’s home. He first drives at 100 km/hour for 3.5 hours and then drives at 70 km/h for 4 hours. What is the average travelling speed of Jundel in km/min?.

LOGICAL THINKING: Find the number of positive integers that are smaller than 100, and the sum of digits of the number is a multiple of 6.

LOGICAL THINKING: Joshua walks 39m northeast, runs 10m northwest, runs 31m southwest, and walks another 5m northwest. How far in meters is he now from the original position?.

ALGEBRA: If the sum of squares of 5 positive consecutive odd numbers is equal to 1485, find the largest number among them.

ALGEBRA: Find the value of x if (79 + x) − (34 − 4x) = 65.

ALGEBRA: Find the value of 1 + 5 + 25 + ... + 3125 + 15625 + 78125.

ALGEBRA: Find the value of 1234 x 4567 - 1233 x 4568.

ALGEBRA: Find the value of 1 x 2 + 2 x 3 + 3 x 4 + ... + 20 x 21.

ALGEBRA:

NUMBER THEORY: Find the sum of all positive factors of 756.

NUMBER THEORY: Find the value of the last digit of 5^1999 + 23^2000 + 7^2001.

NUMBER THEORY: A 3-digit number has a remainder 4 when it is divided by 6, has a remainder 6 when it is divided by 7, and has a remainder 7 when divided by 11. What is the maximum value of this 3-digit number?.

NUMBER THEORY:

NUMBER THEORY: The sum of the positive integers m and n is 44, and their LCM is x . Find the difference of the greatest and the least possible value of x.

NUMBER THEORY: It is known that the ratio of the sum, the difference and the product of two positive integers are 10 : 4 :105 . Find the value of the greater number.

GEOMETRY: A triangle has sides with lengths 15cm, 20cm and 25cm. Find the area of the triangle in cm^2.

GEOMETRY: A square and a right-angled triangle overlap. The base of the triangle is the same as the side length of the square and the height of the triangle is twice the side length of the square. If the length of the diagonal of the square is 30, find the area of the triangle.

GEOMETRY: If the sum of all interior angles of a n-sided polygon is 1800° , find the value of n.

GEOMETRY: A solid cuboid is formed by merging 448 cubes with side length 1. Find the minimum value of the total surface area of the cuboid.

GEOMETRY: The perimeter of the base of a square pyramid is 60cm. If the value of the area of the base of the pyramid is thrice the value of the height of the pyramid, find the volume of the square pyramid in cubic centimeters.

GEOMETRY: There is a regular hexagon with side length 12. Find the area of an inscribed circle of the hexagon. (Answer in π.).

COMBINATORICS: Choosing from numbers 1,3,5,7 and 9 as digits, how many positive integers less than 10000 can be formed? (Each number cannot be used more than once).

COMBINATORICS: Suppose 3 cards are randomly drawn from an ordinary poker deck of 52 playing cards one by one without replacement. Find the probability that the three cards share the same suit.

COMBINATORICS: How many different way(s) is/are there to line up 8 identical yellow pens, 4 identical white pens and 3 identical green pens in a row from left to right?.

COMBINATORICS: A flight of stairs has 15 steps. Zeri can go up for 1 step, 2 steps, or 3 steps each time. The 4th, 8th and 12th step cannot be stepped on as they are broken. How many way(s) are there for Zeri to go up the stairs?.

COMBINATORICS: Find the number of 3-digit positive integers such that the product of its digits is 36 or 54.

COMBINATORICS: Find the number of positive square numbers that are less than 2024 and are divisible by 11.