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- Brenda multiplies a number by 3, adds 3, divides by 3, adds 6, subtracts 3 from the result to get 9. What is six times of the original number?
A. 5
B. 3
C. 30
D. 54
E. 126 - 2021 is the sum of at least how many positive two-digit numbers?
A. 20
B. 21
C. 202
D. 203
E. 1011 - Which of the following is true?
A. If a circle and a regular octagon have the same area, the length of the radius of the circle will be equal to the distance between the centre of any vertex of the octagon.
B. The difference between the number of sides of an octagon and a trapezium is a prime number.
C. All regular quadrilaterals have sides of equal length.
D. Four more than the sides of a decagon is the same value as the total number of sides of two heptagons stuck to each other.
E. The area of only right triangles is given by (𝑏 × ℎ) ÷ 2 - Natural numbers are also called counting numbers and they are positive integers starting from 1. For example, 1, 2, 3, 4, … are natural numbers. The average of the sum of the first 4 natural numbers and the first 5 even numbers is:
A. 10
B. 20
C. 30
D. 40
E. 4.5 - One-fifth of all apples in a crate is rotten. Three-fourths are ordinary. The remaining are considered excellent. If there were 200 apples in a crate, how many excellent apples did it have?
A. 10
B. 40
C. 160
D. 190 - Amanda’s score was twice Brian’s score. Cassie scored 5 points less than Brian. Dora scored 10 points more than Amanda. Dora’s score was 6 times as much as Cassie’s. Whose score was 10?
A. Amanda
B. Brian
C. Cassie
D. Dora - The largest natural number formed by the digits 4, 5, 0, 3 and the smallest number formed by using all of those digits exactly once, are subtracted. Assume that a valid number does not start with 0 unless it is 0 itself (which we shall consider to be a 1- digit number.) What is the number formed by the first two digits of the result?
A. 23
B. 85
C. 50
D. 57 - Observe the two shapes. Find the total volume of the shapes, if all have equal unit sides of 3 cm. Assume it is a packed figure where the invisible areas also are packed with cubes of similar sizes and that the figures fit flush into the corner of the rectangular walls of a room.
A. 12 $\text{cm}^3$
B. 27 $\text{cm}^3$
C. 567 $\text{cm}^3$
D. 81 $\text{cm}^3$
E. 48 $\text{cm}^3$ - What is the size of the problem space (i.e. if you count all the possible values, how many such values are there) of the following experiment: “Guessing a 4 digit ATM pin”. (Assume that each digit of the pin can have values from 0—9)
A. 10,000
B. 256
C. 40
D. 6561
E. 10 - Dr. Hazma, Dr. Tan and Dr. Gupta created vaccines in their labs. Dr. Hazma’s vaccine showed 98% effectiveness. Dr. Tan’s was 92% effective. Dr. Gupta’s was 93% effective. What was the probability that all three were simultaneously effective? Assume they are independent trials.
A. Not possible
B. 83.85%
C. 16.15%
D. 12%
E. Not possible to determine - Three pentagons are stuck together as shown below. All sides are equal and measure 3 cm. What is the difference between the total perimeter of the three individual pentagons and the final figure?
A. 12 cm
B. 6 cm
C. 45 cm
D. 33 cm - What is the 2021st number in the sequence below? $$7, 9, 11, 13, …$$
A. 2028
B. 4041
C. 4047
D. 4050
E. 4042 - Which of the following numbers has an odd number of even prime factors?
A. 182
B. 442
C. 128
D. 100
E. 400 - Azma took part in a gymnastics competition where many people participated. When the rank list arrived, it turned out that no one was disqualified. She was the 3rd place ahead of the first of the lower half of the contestants. She was 3rd place behind the bronze medalist. The first prize is a gold medal, the second prize is a silver medal and the third prize is a bronze medal. How many people competed in all?
A. 12
B. 13
C. 15
D. 16
E. 17 - A number 𝑝 is 1.5 times another number 𝑞. If 𝑝 is 18 bigger than 𝑞, then what is 𝑝 + 𝑞?
A. 18
B. 36
C. 54
D. 108
E. None of the above - A dancer is allowed to step only on one of the following tiles. One is coloured blue, 1 is coloured green, 2 are coloured red, 2 are coloured orange, and 3 are coloured grey. The grey ones are sticky and they cause the dancer to stop dancing. If the chance that the dancer will get stuck on the first step itself is $\frac{𝑚}{𝑛}$, find 𝑚 + 𝑛.
- Five natural numbers are chosen from 1 to 45. These add up to 45. If we call the biggest of these five numbers ‘𝐵’, what is the largest possible value of 𝐵 across all such sets of five numbers?
- Raziya started with the following structure. It is a fully packed box all the way to the back of the top stairs. She added similar unit cubes to build it up to a packed staircase. She has unit cubes that fill a box 3 × 11 × 10 $\text{cm}^3$ in dimensions. (A unit cube is 1 cm × 1 cm × 1 cm in size.). The final staircase she made was 10 steps high. What was the length (width) of each step in her structure?
- In the weighing scale below, the rectangle weighs 2 kg more than the triangle. The oval weighs 3 kg less than the triangle. What is the weight of the rectangle, in kg?
- A five-digit number is formed such that it satisfies the following conditions:
- It is a multiple of 3 and 5.
- The third digit is half of the first digit and one less than the second digit.
- The sum of the first three digits is 13 and the sum of the last three digits is 8.
- The fourth digit is the second-largest digit of that number.
Find the sum of digits of that number. - Find the perimeter of each small rectangle within (assume they are all the same dimensions), given that the total area of the shape shown is 60 $\text{cm}^2$.
- A train travelling at 54 km/h passes a platform. A man is standing on the platform, and he sees the train pass him in 20 seconds. Find the length of the train, in meters.
- How many ways can we go from the dark square at the top to the dark square at the bottom of the grid moving only right or down and only along the grid lines? No backtracking is allowed. No moving through the same section more than once.
- A 4-digit number in the form 𝑎𝑎𝑏𝑏 is a perfect square. What is the square root of 𝑎𝑎𝑏𝑏?
- Read this sentence carefully: “If you take the GCD (or HCF) of two numbers, you are left with numbers that are co-prime.”. For example, if the numbers are 50 and 70, their underlying co-primes are 5 and 7. You get that by dividing both the numbers by their GCD, which is 10.
Now read the following problem and use the above sentence to solve it. Two numbers add to 1085. Their GCD is 35. What is the average of the underlying coprime numbers, rounded off to the nearest whole number?
Posted : 19/06/2026 3:30 am
