1. Find the sum of all the prime factors of 𝑁 if: $$\log_3 \log_5 (\frac{N}{2})=6$$
   A. 6
   B. 5
   C. 7
   D. 3
   E. 2
2. If 𝑁 = 5! 8! 9! then find the number of factors of N which are square integers.
   A. 144
   B. 24
   C. 72
   D. 128
   E. 180
3. Find the value of: $$X = \cos (57) \cos (27) + \sin (57) \sin (27)$$ If $\cos (57) = 0.5446, \cos (27) = 0.8910$ and all values in side sin and cos are in degrees.
   A. 0.1045
   B. 0.5
   C. $\frac{\sqrt{3}}{2}$
   D. $\frac{1}{\sqrt{2}}$
   E. 1
4. If $x+\frac{1}{x}=\sqrt{3}$ then find the value of $x^3+\frac{1}{x^3}$.
   A. 1
   B. $3\sqrt{3}$
   C. $-\sqrt{3}$
   D. 0
   E. 3
5. Find the following sum if 𝑖 = $\sqrt{−1}$: $$𝑆 = 𝑖 + 2𝑖^2 + 3𝑖^3 + ⋯ + 2020𝑖^{2020} + 2021𝑖^{2021}$$
   A. 1011 + 1010𝑖
   B. 1010 + 1011𝑖
   C. 1010 − 1010𝑖
   D. 2020 + 2021𝑖
   E. −1011 − 1011𝑖
6. If $a>b>1$ and $\frac{1}{\log_a b}+\frac{1}{\log_b a}=\sqrt{293}$, then find the value of: $$\frac{1}{\log_{ab} b}-\frac{1}{\log_{ab} a}$$
   A. 18
   B. 17
   C. 1
   D. 29
   E. 19
7. A tower 40m tall, has an elevation of 45 degrees from a point B on the ground, and 53 degrees from a point C on the ground. If point A lies on the base of the tower 40m tall, then what is the distance between point B and C on the ground if ∠𝐵𝐴𝐶 = 90° (Given sin(37) = $\frac{3}{4}$).
   A. 50m
   B. 40m
   C. 40$\sqrt{2}$m
   D. 25$\sqrt{3}$m
   E. 37m
8. In the adjoining figure, 4 semi-circles are constructed and the area of overlap between any 2 semi-circles is shaded purple. Find the area of the shaded region if the side of the square is 10.
   
   A. 50𝜋 − 50
   B. 100 − 25𝜋
   C. 25𝜋 − 50
   D. 50𝜋 − 100
   E. 100𝜋 − 100
9. A quadratic equation of the form $𝑓(𝑥) = 𝑥^2 + 𝑏𝑥 + 𝑐$ opens upwards and has its vertex 5 units above the x-axis and 7 units to the right of the $y$-axis. If a linear equation 𝑔(𝑥) = 𝑚𝑥 + 10 were added to the original equation to give ℎ(𝑥) = 𝑓(𝑥) + 𝑔(𝑥). Find the x coordinate of the vertex if the graph of h(x) just touches the positive $x$ axis.
   A. 7
   B. 5
   C. 6
   D. 10
   E. 8
10. In a class of 40 students, 20 boys and 20 girls, when given a choice to play either football or chess 5 girls and 12 boys preferred football with the rest choosing chess. What is the probability that the winner of the chess tournament held between the students who choose chess is a girl if all students are equally likely to win?
    A. $\frac{3}{8}$
    B. $\frac{1}{2}$
    C. $\frac{15}{23}$
    D. $\frac{12}{17}$
    E. $\frac{4}{5}$
11. If $\frac{1}{x+1}+\frac{12}{y+12}+\frac{144}{z+144}=1$, then find the value of $\frac{x^2}{x^2+x}+\frac{y^2}{y^2+12y}+\frac{z^2}{z^2+144z}$.
    A. 3
    B. 12
    C. 157
    D. 2
    E. 11
12. Find the product of all integers 𝑛 ≥ 1 such that $\frac{n^3+9}{n^2+13}$ is an integer:
    A. 2
    B. 13
    C. 65
    D. 22
    E. 26
13. In the adjoining figure, if value of the larger 2 circles is 72 and 18 then find the radius of the smallest circle. It is known that all circles are tangent to each other and the common ray B.
    
    A. 4.5
    B. 14.4
    C. 8
    D. 6
    E. 7.2
14. A person invests $\$$100 every month in a Recurring deposit which compounds monthly promising a 10% increase, in the principal invested, every year. Find the total value to the recurring deposit after 4 years or after the 48th instalment is paid. (Given $1.1^{\frac{1}{12}}$ = 1.00797)
    A. $\$$582.3
    B. $\$$766
    C. $\$$7660
    D. $\$$5823
    E. $\$$4800
15. If 𝑎, 𝑏, 𝑐 ∈ 𝑅, 𝑎 + 𝑏 + 𝑐 = 36, $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=39$ find: $$\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{a}{c}+\frac{c}{b}+\frac{b}{a}$$
16. Find $abc$ if $a, b, c$ are distinct prime numbers, and the following is given: $$𝑎 + 𝑏 + 𝑐 = 92 $\text{ and } 𝑎𝑏 + 𝑏𝑐 + 𝑐𝑎 = 2201$$
17. If $a$ and $b$ are relatively prime positive integers, then find the value of $a + b$ if: $$\frac{a^3-b^3}{(a-b)^3}=\frac{133}{3}$$
18. In the adjoining figure, line segments DE is constructed perpendicular to the diameter BC of the circle intersecting BC at point P. Find the length of the line segment if the radius of the circle is 10 and PB = 2.
    
19. 10 lines are drawn on a plane. Find the maximum number of unique line segments that can be identified from these 10 lines on the plane. Note: the line segment identified must be between 2 points that already lies on one of the 10 lines and AB is equivalent to BA.
20. In the adjoining figure area of the regions are mentioned in the figure (not to scale). Find the value of $m + n$, if $\frac{𝑚}{𝑛}$ is the unknown area $x$, of the quadrilateral, in the lowest terms.
    
21. Find the maximum value of the following expression. $$\sqrt{781-X}+\sqrt{X-59}$$
22. Find the ordered set of 4-tuples, of positive integers, such that: $$𝑤 + 𝑥 + 𝑦 + 𝑧 = 21$$
23. If the following is true: $$\frac{3+\cot 78\times\cot 18}{\cot 78+\cot 18}=\frac{\tan n+\sin m}{\cos m}$$ Where $n$ and $m$ are in degrees and are acute angles, find the product $mn$.
24. Find the value of: $$X=\sum_{n=1}^{7}\tan^2 \frac{n\pi}{16}$$

1. Rationalise the denominator of the following fraction. $$\frac{1}{\sqrt{6}-\sqrt{3}+\sqrt{2}+1}$$
   A. $\frac{\sqrt{6}+\sqrt{3}-\sqrt{2}+1}{2}$
   B. $\frac{\sqrt{6}-\sqrt{3}+\sqrt{2}+1}{2}$
   C. $\sqrt{6}-\sqrt{3}+\sqrt{2}+1$
   D. $\sqrt{6}+\sqrt{3}-\sqrt{2}+1$
   E. $\sqrt{6}-\sqrt{3}-\sqrt{2}+1$
2. If adding 1 to the numerator and adding 5 to the denominator of a fraction is the same as subtracting 5 from the numerator and subtracting 1 from the denominator of the same fraction, then find the fraction if its decimal expansion is 1.5.
   A. $\frac{6}{5}$
   B. $\frac{12}{8}$
   C. $\frac{4}{12}$
   D. $\frac{12}{6}$
   E. $\frac{10}{8}$
3. Two vectors in the 3-D Euclidian space are given $$4\hat{i}+ 9\hat{j}− 13\hat{k} \text{ and } 7\hat{i}+ 6\hat{k} + 5\hat{j}$$ Find the dot product of the 2 vectors.
   A. 17
   B. 147
   C. 5
   D. 151
   E. None of these
4. Find 𝑀𝑁 − 𝑀 − 𝑁 in the rational equation below. $$\frac{52x+73}{14x^2+83x+33}=\frac{M}{7x+3}+\frac{N}{2x+11}$$
   A. 19
   B. 13
   C. 16
   D. -22
   E. 7
5. In the adjoining figure, 𝐴𝐵 is the diameter of the circle and 𝐶, 𝐷 lie on the same side of the diameter. If ∠𝐴𝐵𝐶 = 75° and ∠𝐷𝐴𝐶 = 33°, then find the measurement of ∠𝐷𝐶𝐴, in degrees.
   
   A. 33
   B. 24
   C. 72
   D. 42
   E. 27
6. In the adjoining figure Δ𝐴𝐵𝐶, point 𝐷 is on 𝐴𝐵 such that 𝐵𝐷 = 3𝐴𝐷, 𝐸 is a point on 𝐴𝐶 such that 𝐷𝐸||𝐵𝐶, 𝐹 is a point on the line 𝐷𝐸 such that 𝐴𝐵||𝐶𝐹 Find the length of 𝐸𝐹 if 𝐵𝐶 = 16.
   
   A. 12
   B. $\frac{32}{3}$
   C. 4
   D. 8
   E. Not uniquely determined
7. A tangential quadrilateral 𝐴𝐵𝐶𝐷 is a convex quadrilateral whose sides are tangent to a circle. Given that 𝐴𝐷 = 16, 𝐵𝐶 = 8 and the radius of the circle is 4, find the area of the quadrilateral.
   A. 48
   B. 24
   C. 144
   D. 96
   E. 192
8. In the diagram, 𝐴𝐵𝐶𝐷 is a square, 𝐴𝐻𝐷 and 𝐵𝐶𝐺 are equilateral triangles. Points 𝐼 and 𝐽 are intersection points of the sides of the triangles as shown. Given the length of a side of the square is 6, find the area of the rhombus 𝐼𝐺𝐽𝐻.
   
   A. 24$\sqrt{3}$ − 36
   B. 6
   C. 48 − 24$\sqrt{3}$
   D. 12
   E. 3$\sqrt{3}$
9. What is the greatest number of regions can 7 lines divide a circle into?
   A. 14
   B. 28
   C. 29
   D. 15
   E. 35
10. If ℎ(𝑥) = 2 + $\sqrt{x}$ and 𝑓(ℎ(𝑥)) = 7 + 5$\sqrt{x}$ + 𝑥 then find 𝑓(3).
    A. 13
    B. 10 + 5$\sqrt{3}$
    C. 8
    D. 10
    E. 12
11. In a sequence of numbers, each subsequent term is the sum of cubes of digits of the previous term. If one such sequence starts with the number 457, find the 2021st term in it.
    A. 352
    B. 160
    C. 217
    D. 153
    E. 371
12. The first 5 terms of a sequence are: $$5, 9, 16, 28, 47$$ Find the sum of the 8th and 7th terms.
    A. 189
    B. 210
    C. 280
    D. 241
    E. 166
13. How many unique necklaces can be made such that they contain 7 equally spaced beads of 7 different colours?
    A. 5040
    B. 720
    C. 2520
    D. 360
    E. 840
14. Find the value of: $$\sum_{j=2}^{\infty}\left( \sum_{j=1}^{\infty}\frac{1}{9i} \right)^{\frac{j}{3}}$$
    A. 1
    B. $\sqrt{\frac{1}{7}}$
    C. $\frac{1}{2}\times\sqrt{\frac{1}{7}}$
    D. $\frac{1}{2}$
    E. $\frac{1}{7}$
15. Given 𝑓: 𝑅 → 𝑅 is a quadratic polynomial $$𝑓(1) = 1, 𝑓(2) =\frac{1}{2},f(3)=\frac{1}{3}$$ Find $f(4)$.
    A. $\frac{1}{4}$
    B. 4
    C. $\frac{7}{24}$
    D. $\frac{1}{2}$
    E. Insufficient information
16. For positive real numbers 𝑥, 𝑦 and 𝑧, it is given that $$\frac{x}{3y+2z}+\frac{3y}{x+2z}+\frac{2z}{x+3y}=\frac{3}{2}$$ Find the value of $$\frac{(7x+12y)^2}{z^2}$$
17. How many times the digit ‘0’ appears in the list of numbers from 1000 to 2021 including both numbers?
18. If $𝑓(𝑥) = 2^𝑥 + 86$ and $𝑔(𝑥) = 3𝑥^2 + 𝑥 − 4$ then find: $$𝑔$$
19. What is the shortest distance an ant needs to travel from its current position (7,10) to the anthill (19,25) if the ant must touch the x-axis where sugar is spread all along with it?
20. A number in base 3 has all its digits as 1, but its last digit is 0 in base 2. Which is the largest 4-digit number, in base 10, that has this property?
21. If the following is given: $$𝑥^4 + 𝑥^3 + 𝑥^2 + 𝑥 + 1 = 0$$ Then find the value of $𝑥^{2021 − x}$.
22. Find the sum of three positive integers 𝑝, 𝑞, 𝑟, if the following is given:
    
23. Find the ordered set of 4-tuples, of positive integers, such that: $$𝑤 + 𝑥 + 𝑦 + 𝑧 = 21$$
24. Find the value of a positive integer 𝑥. $$x=\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+...}}}}$$
25. Seven unique awards need to be handed to 7 exceptional students. If the probability that the chief guest hands all awards to the incorrect recipient is $\frac{a}{b}$ in simplest form, then find the value of 𝑎 + 𝑏. (It is given that the probability to do so with 5 and 6 awards is $\frac{11}{30}$ and $\frac{53}{144}$, respectively.)

1. How many numbers of the series have a terminating decimal expansion? $$\frac{1}{1},\frac{1}{2},\frac{1}{3}\cdots\frac{1}{98},\frac{1}{99},\frac{1}{100}$$
   A. 15
   B. 16
   C. 14
   D. 13
   E. 18
2. Solve: $$\sqrt{4^3}-\sqrt{2^6}$$
   A. 2
   B. 4
   C. 8
   D. 12
   E. 1
3. Solve the following $$(\sqrt{7}-1)\times(\sqrt{49}+\sqrt{7}+1)$$
   A. 48
   B. 50
   C. 6
   D. 8
   E. 7
4. How many positive integers 𝑁 satisfy the following equation. $$441 − 42𝑁 + 𝑁^2 = 64$$
   A. 2
   B. 1
   C. 0
   D. 4
   E. 3
5. Find the sum of all the unique prime factors of 656656.
   A. 74
   B. 1044
   C. 553
   D. 473
   E. 687
6. In the adjoining figure, 𝐴𝐵 is the diameter of the circle and 𝐶, 𝐷 lie on the same side of the diameter. If ∠𝐴𝐵𝐶 = 75° and ∠𝐷𝐴𝐶 = 33°, then find the measurement of ∠𝐷𝐶𝐴, in degrees.
   
   A. 33
   B. 24
   C. 72
   D. 42
   E. 27
7. A metal cylinder is re-casted into a cone with twice the radius. If the height of the cylinder was 12 m, then what is the height of the new cone?
   A. 24 m
   B. 16 m
   C. 6 m
   D. 9 m
   E. 36 m
8. In the diagram, 𝐴𝐵𝐶 is a right-angled triangle, 𝐴𝐷 = 4 and 𝐶𝐷 = 6. Find the length of 𝐷𝐵 if 𝐶𝐷 is perpendicular to 𝐴B.
   
   A. 8
   B. 9
   C. 10
   D. 4
   E. 12
9. A rhombus of the length 17 and the length of one of its diagonals is 16. Find the length of the other diagonal.
   A. 15
   B. 30
   C. 32
   D. 34
   E. $\sqrt{545}$
10. Tom travels first 25 km with a speed of 60 km/h. Then due to the conditions of the remaining road, he had to slow down and travel the rest of the distance with a speed of 𝑥 km/h. If the average speed over 50 km was found to be 40 km/h. Find the value of 𝑥.
    A. 36
    B. 20
    C. 30
    D. 15
    E. None of these
11. Count the number of square numbers between (6^4 + 1) and (4^6 − 1).
    A. 28
    B. 17
    C. 29
    D. 16
    E. 27
12. Find the 1000th root of $10^{(10^{10})}$
    A. $10^{(10^{7})}$
    B. $10^{(7^{10})}$
    C. $\sqrt{10}^{(\sqrt{10}^{\sqrt{10}})}$
    D. $7^{(10^{10})}$
    E. $10^{\frac{1}{10}}$
13. A cuboid has faces of area 24, 15, 10 square units. If the lengths of the sides of the cuboid are 𝑎, 𝑏, 𝑐 then find 𝑎𝑏𝑐 + 2(𝑎 + 𝑏 + 𝑐).
    A. 72.5
    B. 49
    C. 90
    D. 85
    E. Insufficient information
14. What is the greatest number of regions can 7 lines divide a circle into?
    A. 14
    B. 28
    C. 29
    D. 15
    E. 35
15. How many unique necklaces can be made such that they contain 7 equally spaced beads of 7 different colours?
    A. 5040
    B. 720
    C. 2520
    D. 360
    E. 840
16. In the figure, the difference between any two neighbouring horizontal and vertical dots is 1. Find the area of the triangle.
    
17. If 𝑛! = 𝑛 × (𝑛 − 1)! × … × 2 × 1, find the simplest value of the following. $$\frac{20!+21!}{2\times 19!+4\times 19!+16\times 19!}$$
18. What is the number of unique 4 letter words that can be formed with the word MATHS?
19. In a 3-digit number XYZ, X, Y and Z are non-zero digits in an arithmetic progression. If XYZ - ZXY = M, find the largest value of M a 3-digit number (X, Z≠0).
20. In a class of 50 students if 15 like maths, 27 like English and 13 like none then how many like both Maths and English.
21. The numbers 411, 666 and 870 give the remainder when divided by a positive integer 𝑁. Find the greatest possible value of 𝑁.
22. In a sequence of numbers, each subsequent term is the sum of cubes of digits of the previous term. If one such sequence starts with the number 244, find the 2021st term in it.
23. In how many ways can you reach any circle on the 10th row from the circle on the top if you can only move down left or right but cannot pass through the black circle?
    
24. Find the maximum value of the following expression. $$\sqrt{781-X}+\sqrt{X-59}$$
25. The factorisation of a semi-prime number is $𝑝_1 × 𝑝_2$ where $𝑝_1$ and $𝑝_2$ are prime numbers. Let the probability that the sum of faces of 3 standard dice is a semi-prime number be $\frac{𝑎}{𝑏}$ in simplest form. Find the value of 𝑎 + 𝑏.

1. Find the possible value(s) of $\sqrt{(\sqrt{0.0081}+\sqrt{0.0001}+\sqrt{0.81})}.$
   A. 1
   B. -1
   C. Both 1 and -1
   D. Decimal numbers do not have square roots
   E. √0.019
2. If 5 is added to the numerator and denominator of the fraction $\frac{6}{11}$, how will the value of the fraction change?
   A. No change
   B. Increase
   C. Decrease
   D. It increases by $\frac{11}{16}$
   E. The fraction evaluates to 1
3. If a mother makes 𝑥 cakes in 2 hours and 𝑦 pizzas in 3 hours, how many cakes and pizzas altogether does she make in 6 hours? Assume she is making both together and that she works just as fast as if she made them separately.
   A. $6(\frac{x}{2}+\frac{y}{3})$
   B. $6(\frac{y}{2}+\frac{x}{3})$
   C. $6(2x+3y)$
   D. $6(3x+2y)$
   E. 30
4. Sasha wants to fit an image into a box on her computer screen. Her original image was $1\frac{1}{2}$ inches wide and $2\frac{1}{4}$ inches tall. Her computer screen box is 4 inches wide. She needs to adjust the box on her computer screen. How tall does the computer screen box need to be for her to fit the image exactly and snugly into the box, without squishing or stretching the image? The choices shown are in inches.
   A. $\frac{9}{32}$
   B. $\frac{27}{32}$
   C. 6
   D. $4\frac{3}{4}$
   E. $2\frac{1}{2}$
5. I have a set of four numbers 𝑃,𝑄, 𝑅, 𝑆 in ascending order. The average of 𝑃, 𝑄, and 𝑅 is 22, and the average of 𝑄, 𝑅, and 𝑆 is 24. The largest number is 27. Then, the smallest number in this set:
   A. is prime
   B. is a multiple of 9
   C. is a multiple of 11
   D. is a multiple of 7
   E. cannot be determined with this information
6. The difference in the place values of the numeral 7 in the largest and the smallest numbers formed using 3, 4, 5, 6, 7 (each digit is used once and exactly once) is
   A. 69,993
   B. 41,976
   C. 76,536
   D. 9,999
   E. 70
7. Assume that all sections within each of the given shapes are the same size. Consider only the area represented by the flower, the circle, etc. without including any surrounding area around it. Which fraction below represents the fraction of the shaded part of any shape in the simplest form?
   
   A. $\frac{6}{13}$
   B. $\frac{4}{10}$
   C. $\frac{1}{4}$
   D. $\frac{2}{3}$
   E. $\frac{1}{2}$
8. A tessellation is a set of figures that can cover a plane without overlapping or leaving any gaps. Tessellations with triangles would look like the following:
   
   You can continue in the horizontal and vertical directions infinitely to place more such triangles to form larger such tightly fitted spaces with no gaps or overlaps. Consider three identical regular pentagons. In how many ways can 3 such pentagons be arranged so that they form a tessellation?
   A. Zero
   B. One
   C. Two
   D. Four
   E. Infinite
9. Look at the following graph. Which of the following sections of the graph have the highest rate of change?
   
   A. 𝐴 to 𝐵
   B. 𝐵 to 𝐶
   C. 𝐴 to 𝐶
   D. 𝐷 to 𝐸
   E. 𝐸 to F
10. A paper is folded as shown below and punched in its folded state. When the paper is opened out again, what will be the pattern of holes formed?
    
    
11. Which of the following Venn diagrams represents soccer players, high school Math enthusiasts, and students?
    
12. 40 people are in a movie theatre which offers two snack options – popcorns and chips. 26 people like popcorns but they do not like chips. 32 students like popcorns. Everyone in the theatre likes at least one of the two snack options. Find the number of people who like both.
    A. 6
    B. 8
    C. 32
    D. 40
    E. Indeterminate
13. The surface areas of the two spheres are in the ratio 4: 9. Find the ratio of their volumes.
    A. 2: 3
    B. 16: 31
    C. 3: 2
    D. 4: 9
    E. 8: 27
14. How many three-digit natural numbers are divisible by 7?
    A. 141
    B. 142
    C. 143
    D. 128
    E. 129
15. A lattice point is a point in a Cartesian coordinate system such that both its $x$- and $y$-coordinates are integers. How many lattice points are there in a line with (2,4), (3,6)?
    A. 12
    B. 6
    C. 1
    D. 2
    E. Infinitely many
16. Suppose you have a number with 2021 digits. Let 𝑃 be its sum of digits. Let 𝑄 be the sum of the digits of 𝑃. Let 𝑅 be the sum of the digits of 𝑄. (Assume simple addition but not digital sum or recursive sum.) Find the largest value of 𝑄.
17. Given
    
    where 𝐴, 𝐵, 𝑋, 𝑌, 𝑍 are unique positive single-digit numbers, what is the number of possible combinations for 𝑋 and 𝑍 to satisfy this equation?
18. A steel cuboid is reshaped into a cube. Initially, its length, breadth, and depth were 270 cm, 100 cm, and 64 cm respectively. Find the sum of digits of the surface area of the cube.
19. If (3𝑥 − 4) ∶ (𝑦 + 15) is a fixed ratio and if 𝑥 = $\frac{7}{3}$, then 𝑦 = 12. Find the value of 𝑥 + 𝑦 when 𝑥 = 2.
20. What is the sum of prime numbers between 2000 and 2021?
21. A lattice point is a point in a Cartesian coordinate system such that both its $x$- and $y$-coordinates are integers. A point lattice is constructed by plotting all of the points $(a,b)$ such that $a$ and $b$ are positive integers. How many points in the point lattice lie on the line 𝑦 = −4𝑥 + 8?
22. Several people were surveyed for their preference from 4 drinks 𝐴, 𝐵, 𝐶, 𝐷. All the people surveyed are represented in the graph below. If the fraction of people who preferred 𝐴 is $\frac{𝑚}{𝑛}$, find 𝑚 + 𝑛.
    
23. How many three-digit natural numbers ‘𝑛’ can there be such that all the three conditions given below are satisfied:
    Condition 1: 𝑛 − 14 is divisible by 7,
    Condition 2: 𝑛 − 24 is divisible by 8, and
    Condition 3: 𝑛 − 36 is divisible by 9.
24. Simplify and round off to the nearest whole number: $$\frac{16}{\sqrt{14}+\sqrt{10}}-\frac{58}{3\sqrt{5}-4}+\sqrt{180}+\sqrt{160}$$
25. Use all 9 digits exactly once - 1, 2, 3, 4, 5, 6, 7, 8, 9, as numerator and denominator, create a fraction equalling $\frac{1}{3}$ (one third). The digits in the numerator and denominator should together have all the 9 digits shown here. What is the numerator?

1. Evaluate: (5 × 7 × 2 × 17) ÷ (14 × 34 × 35)
   A. 14
   B. 0.71
   C. 0.071
   D. 17
   E. $\frac{1}{17}$
2. What is the value of $0^1$?
   A. 0
   B. 1
   C. ∞
   D. 10
   E. None of these
3. A triangle has sides 35 cm, 37 cm, and 12 cm. Identify the type of triangle it is.
   A. Acute angle triangle
   B. Obtuse triangle
   C. Right-angled triangle
   D. It cannot be determined from knowing just the side lengths
   E. Open triangle
4. A child gets $\$$10 pocket money every day. He saves $\$$1 on the first day, $\$$2 on the second day, $\$$3 on the third day, $\$$4 on the fourth day, and so on. On which day will he have saved enough to buy his sister a $\$$50 school bag?
   A. Day 50
   B. Day 25
   C. Day 9
   D. Day 10
   E. Day 5
5. A photographer expands a photo diagonally in a software, to make it fit into a digital album. The bigger photo is neither squished nor stretched and looks proper. The original dimensions of the photo were 6 inches by 4 inches. Now the stretched photo is of the dimensions 12 inches by 𝑝 inches. Find the value of 𝑝.
   A. 8 inches
   B. 12 inches
   C. 10 inches
   D. 2 inches
   E. None of the above
6. How many lines of symmetry does a parallelogram have?
   A. 1
   B. 2
   C. 3
   D. 4
   E. 0
7. Evaluate: 32.345 + 32.435 − 23.435
   A. 88.215
   B. -23.435
   C. 41.345
   D. -23.525
   E. 23.345
8. Assume that all sections within each of the given shapes are the same size. Consider only the area represented by the flower, the circle, etc. without including any surrounding area around it. Which figure has the smallest fraction of itself shaded?
   
   A. Shape a
   B. Shape b
   C. Shape c
   D. Shape d
   E. Shape e
9. The number of shortest paths along a 3 × 3 grid from one corner to the diagonally opposite corner is:
   A. 1
   B. 2
   C. 3
   D. 6
   E. 12
10. Look at the following table: Which two cars are going at the same speed?
    
    A. A & B
    B. B & C
    C. A & C
    D. A & D
    E. All are going at different speeds
11. A paper is folded as shown below and punched in its folded state. When the paper is opened out again, what will be the pattern of holes formed?
    
    
12. A sports club offers three sports – soccer, basketball and baseball. All their members play at least one sport. Which of the following Venn diagrams represents the members of the sports club? Assume that there are no limits to the number of sports one can play and that some people may be physically strong enough and able enough to play any or all sports.
    
13. A rectangular park is to be fenced with a stone wall. There is a gate along the perimeter that is 2 m long, which is made of steel. Find the cost of fencing the park, if its dimensions are 100 m by 50 m. The entire perimeter may be taken to be the same height of 3 m. Take the cost of stone fencing as $\$$23 per $\text{m}^2$ and steel fencing as $\$$17 per $\text{m}^2$.
    A. $\$$10,384
    B. $\$$6,900
    C. $\$$20,700
    D. $\$$456
    E. $\$$20,664
14. How many three-digit natural numbers are divisible by 5? Natural numbers are positive integers starting from 1.
    A. 200
    B. 201
    C. 180
    D. 198
    E. 199
15. The interest on $\$$1200 is more than the interest on $\$$1000 by $\$$30 in 3 years. Find the rate of interest for each year.
    A. 5%
    B. 6%
    C. 5.5%
    D. 4%
    E. Cannot be found
16. Evaluate: (45 × 37 × 27) ÷ 185
17. Several people were surveyed for their preference from 4 drinks A, B, C, D. All the people surveyed are represented in the graph below. If the fraction of people who preferred A to those who preferred D is $\frac{𝑚}{𝑛}$, what is 𝑚 + 𝑛?
    
18. Find the smallest integer, which when divided by 7 gives a remainder of 0, but when divided by 10 gives a remainder of 1.
19. A steel cuboid is reshaped into a cube. Initially, its length, breadth, and depth were 270 cm, 100 cm, and 64 cm respectively. Find the sum of digits of the surface area of the cube.
20. Two identical rectangular cards partially overlap. The area of overlap is a square with an area 4 $\text{cm}^2$, and the total area of the regions of the faces of the two cards that do not overlap is 12 $\text{cm}^2$. What is the area of one card?
21. Find the sum of digits of the next number in the series: $$11, 143, 2431, 46189, ......$$
22. The mean of four consecutive odd numbers is 24. Find the sum of the middle two numbers in this set.
23. Find the largest four-digit number which when divided by 4, 7, and 13 leaves a remainder of 3 in each case.
24. $2^{400}$ can be equivalently written as a repeated product of the number 16. For example, 16 × 16 × 16 × … (𝑛 times). What is the value of 𝑛?
25. Theo’s football coaching starts at 6:30 am, and his mother wants him to wake up at 6 am to be on time for coaching. But currently, Theo wakes up late. Theo promises to wake up 5 minutes earlier than he did the day before. If Theo woke up at 6:50 am on a Sunday, and keeps his promise every day, on what day will he wake up on time for football coaching? Leave your answer as 0001 for Monday, 0002 for Tuesday, …, and 0007 for Sunday.

1. 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
2. 2021 is the sum of at least how many positive two-digit numbers?
   A. 20
   B. 21
   C. 202
   D. 203
   E. 1011
3. 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
4. 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
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
6. 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
7. 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
8. 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 $\text{cm}^3$
9. 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
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
11. 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
12. What is the 2021st number in the sequence below? $$7, 9, 11, 13, …$$
    A. 2028
    B. 4041
    C. 4047
    D. 4050
    E. 4042
13. Which of the following numbers has an odd number of even prime factors?
    A. 182
    B. 442
    C. 128
    D. 100
    E. 400
14. 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
15. 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
16. 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.
17. 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?
18. 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?
    
19. 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?
    
20. 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.
21. 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 $\text{cm}^2$.
    
22. 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.
23. 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.
    
24. A 4-digit number in the form 𝑎𝑎𝑏𝑏 is a perfect square. What is the square root of 𝑎𝑎𝑏𝑏?
25. 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?

1. Four kids can paint four balls in four minutes. If everyone works at the same speed, how many kids can paint 12 balls in 12 minutes?
   A. 4
   B. 6
   C. 8
   D. 10
   E. 12
2. Find the value of $$25 × 48 + 32 × 25 + 25 × 20$$
   A. 1250
   B. 25000
   C. 2500
   D. 2525
   E. 2505
3. How many natural numbers from 1 to 100 are not divisible by 5 or 7?
   A. 68
   B. 66
   C. 76
   D. 78
   E. 80
4. The following 3 × 3 grid is filled with numbers from 1 to 9. The numbers in all sides add up to 15 horizontally and vertically. Find the value of *.
   
   A. 4
   B. 5
   C. 6
   D. 7
   E. 8
5. Find the sum of 𝐴 + 𝐵 + 𝐶 if different letters stand for different digits.
   
   A. 15
   B. 12
   C. 10
   D. 8
   E. 7
6. What is the largest 3-digit number which is divisible by 24?
   A. 999
   B. 996
   C. 992
   D. 984
   E. 968
7. The following picture shows a 4 × 4 square. How many squares of any sizes are there comprised of the one marked with X?
   
   A. 1
   B. 4
   C. 5
   D. 10
   E. 16
8. Find the value of 𝐴5𝐵 + 𝐶9.
   
   A. 400
   B. 417
   C. 444
   D. 527
   E. 544
9. Sarah and Rose have few pencils. Two-fifths of Sarah’s pencils and eight-ninths of Rose’s pencils are both 40 each. Who has more pencils and by how much?
   A. Sarah, 40
   B. Rose, 40
   C. Sarah, 50
   D. Rose, 50
   E. Sarah, 55
10. There are 5 green, 9 orange, 6 red, and 4 blue candies in the bag. At least how many candies must Sam take to ensure he gets the first red candy?
    A. 19
    B. 4
    C. 10
    D. 3
    E. 15
11. The following 4 × 4 × 4 cube is painted red on all its faces. Find the number of smaller cubes with at most two faces painted.
    
    A. 8
    B. 16
    C. 24
    D. 36
    E. 56
12. The combined age of Ram and Shyam five years from now will be 37. Ram was twice as old as Shyam 3 years ago. How old is Ram now?
    A. 7
    B. 10
    C. 14
    D. 17
    E. 20
13. Two regular 6-sided dice were thrown on the ground. All the numbers visible on the dice were added. The sum of numbers on all the visible faces was 31. What is the difference between the numbers facing the ground?
    A. 0
    B. 1
    C. 2
    D. 3
    E. 4
14. Ron and Vanda each thought of a two-digit number. The product of their digits was 24 and 35 respectively. The difference between their numbers was 37. What is the sum of their numbers?
    A. 95
    B. 100
    C. 113
    D. 121
    E. 139
15. Ann read a book with 1000 pages. How many digits were used to print the page numbers on the book?
    A. 3000
    B. 2550
    C. 2987
    D. 3193
    E. 2893
16. Sam filled up some boxes with sweets. If he put 5 sweets in each box, he was left with 4 extra sweets. If he put 6 sweets in each box, the last box would have only 2 sweets. Find the number of sweets Sam had.
17. When the product of 9 and a number is divided by 4 and then multiplied by 25, the result is 19800. Find the number.
18. What is the largest possible value of ‘𝑚’ in 653𝑚2 such that it is divisible by 3?
19. 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.
20. Find the sum of the numbers in the 12th group of the following sequence: $$(1, 4, 6), (2, 6, 10), (3, 8, 14), …$$
21. 16 trees are planted on one side of the road. Two cars are parked between every two trees. How many cars are there?
22. Ten small ropes of the same length were knotted together to form a big rope of 81 cm. If the knotted area was 1 cm for every rope, how long was each rope?
23. Find the value of the digit at the ones place of the following expression: $$99 × 101 × 103 × 105 × 107 − 100 × 102 × 104 × 106 × 108$$
24. Among Jack, Jade and James, one of them is a painter, the other is a lawyer and the third is a firefighter. Jack is older than the firefighter while the lawyer is younger than James. Also, Jade and lawyer are not the same age. Find who the firefighter is. (Put Jack=1, Jade=2 and James=3 in your answer)
25. Patrick scored 82 and 85 marks respectively in English and Science. If the total marks of these papers are 100, how many marks should he score in Mathematics so that his average marks in these three subjects becomes 87?

1. Solve: $$100 + 90 − 80 − 70 + 60 + 50 − 40 − 30 + 20 + 10$$
   A. 90
   B. 110
   C. 100
   D. 130
   E. 120
2. Rohit can go home on Diwali which falls on Thursday, 12th November this year. Diwali is 45 days later. What day is today?
   A. Sunday
   B. Friday
   C. Wednesday
   D. Monday
   E. Tuesday
3. What will be the digit in hundreds place of the sum of the following expression? $$40444 + 44044 + 44404 + 44440$$
   A. 0
   B. 4
   C. 8
   D. 2
   E. 3
4. Find the sum of 𝐴 + 𝐵 + 𝐶 if different letters stand for different digits.
   
   A. 15
   B. 12
   C. 10
   D. 8
   E. 7
5. Chloe’s current age is a multiple of 6. Next year, her age will be a multiple of 5. She is more than 30 years old and less than 70 years old. Find her age 4 years from now.
   A. 62
   B. 59
   C. 60
   D. 61
   E. 58
6. $$▼ +2■ = 26$$ $$■ + 2● = 20$$ $$● + 2 ▼= 17$$ Find the product of ▼, ● and ■.
   A. 210
   B. 21
   C. 300
   D. 30
   E. 60
7. The following picture shows a 4 × 4 square. How many squares of any sizes are there comprised of the one marked with X?
   
   A. 1
   B. 4
   C. 5
   D. 10
   E. 16
8. A 5-digit number is a palindrome. A palindrome is a number that reads the same forward or backward. The number satisfies the following conditions:
   - The sum of the first three digits is 14,
   - 3rd digit is half of the 2nd digit,
   - The sum of the second, third and fourth digit is 15.
   Find the number.
   A. 58158
   B. 66366
   C. 56356
   D. 64246
   E. 56365
9. The lamp is more costly than the watch and the candle stand. The candle stand is less expensive than the watch but more expensive than the basket. Which is the second most expensive item?
   A. Lamp
   B. Candle Stand
   C. Basket
   D. Sofa
   E. Watch
10. Harry brought few marbles to school. He distributed one-third of the marbles among his friends on the bus. He gave 20 marbles to his classmates. Now he is left with only one-fourth of his marbles. How many marbles did he have at first?
    A. 24
    B. 36
    C. 48
    D. 40
    E. 42
11. In the following picture, every adjacent four cells have a sum of 20. Find the value of 𝑋 + 𝑌.
    
    A. 12
    B. 14
    C. 8
    D. 10
    E. 6
12. Piyush’s clock is not working properly. For every hour it lags 5 minutes behind. He set the clock correctly at 12.00 pm. What time will it be on his clock if the time now is 2.00 am?
    A. 1.00 pm
    B. 1.10 am
    C. 12.30 am
    D. 1.50 am
    E. 12.50 am
13. Jack and his father’s weight add up to 100 kg. If Jack loses 4 kg, he will be exactly half of his father’s weight. What is the difference between their weights, in kg?
    A. 28
    B. 30
    C. 32
    D. 34
    E. 36
14. Identify the pattern and find the missing value.
    
    A. 31
    B. 20
    C. 12
    D. 22
    E. 44
15. It takes 10 women to stitch 50 soft toys in 2 hours. How many soft toys will be done by 6 women in 4 hours, assuming all women work at the same pace?
    A. 50
    B. 60
    C. 40
    D. 100
    E. 80
16. Kevin cycles 10 km in 1 hour and 15 minutes. How many km will he complete in 5 hours?
17. A basket contains an equal number of balls and pebbles. They are either white or black in color. The number of white balls is 30 and the total number of black items is If the difference between the number of black and white balls is 20, find the number of white pebbles.
18. A book has 250 pages. How many digits are used to print the page numbers of the book?
19. Study the pattern and find the sum of the 9th and 10th term. $$50, 53, 56, 61, 66, 73, 80 …$$
20. 60 potatoes weigh 4 kg. If the cost of 1 kg of potato is $30. What is the price of 2 dozen potatoes?
21. The numbers 20, 21, 22, …, 63, 64 are written as a 90-digit number $$2021222324 … 626364$$ All the odd digits are then removed. How many digits remain?
22. Ten small ropes of the same length were knotted together to form a big rope of 81 cm. If the knotted area was 1 cm for every rope, how long was each rope?
23. Find the value of the digit at the ones place of the following expression: $$99 × 101 × 103 × 105 × 107 − 100 × 102 × 104 × 106 × 108$$
24. If a number pyramid was built as shown in the picture, what will be the 10th number in the 12th row?
    
25. A number has a remainder of 1 when divided by 2, 3, or 6 and has a reminder of 4 when divided by 5. If this number is divisible by 7, find the smallest such number.

1. Find the sum: $$4 + 16 + 24 + 36 + 44 + 56$$
   A. 160
   B. 170
   C. 180
   D. 190
   E. 200
2. The sum obtained after we add double of 25 to one-third of 21 is subtracted from 100. What is the final number in the end?
   A. 60
   B. 29
   C. 43
   D. 57
   E. 71
3. Suzy has five kids. Amy is older than Beth but younger than Carla. David is older than Erwin but younger than Beth. Who is the eldest child?
   A. Amy
   B. Beth
   C. Carla
   D. David
   E. Erwin
4. Sarah’s birthday falls on 6th September each year. Today is 27th July and is a Sunday. What day will be Sarah’s birthday this year?
   A. Thursday
   B. Saturday
   C. Sunday
   D. Monday
   E. Friday
5. On the number table of 1-100, we finally reached 50 after we added 72 and subtracted 36 from the original number. What is the original number?
   A. 86
   B. 14
   C. 48
   D. 50
   E. 84
6. How many natural numbers are there which are less than 300 and their digits add up to 5?
   A. 18
   B. 10
   C. 12
   D. 15
   E. 14
7. Roy walks 10 m to his school and then continues the remaining three-fourths of the whole journey by bus. How far is Roy’s school from his house?
   A. 134 m
   B. 100 m
   C. 30 m
   D. 40 m
   E. 400 m
8. 𝐴𝐵𝐶𝐷 is a square with an area of 72 $\text{m}^2$. It is further divided into 9 smaller squares with equal areas. Find the area of 5 such smaller squares, in $\text{m}^2$.
   A. -36
   B. 40
   C. 45
   D. 50
   E. 52
9. A 1-liter bottle was filled up using a 150-ml and a 50-ml jug. Both jugs were poured thrice into the empty 1-liter bottle. How much more liquid can be poured into the bottle to fill it to the brim?
   A. 600 ml
   B. 650 ml
   C. 450 ml
   D. 400 ml
   E. 500 ml
10. If all alphabets are represented by a number starting with 𝐴 = 1, 𝐵 = 2, 𝐶 = 3, and so on, find the sum of the digits represented by the word 𝑆𝑀𝐴𝑅𝑇.
    (Note: 𝐷𝑂𝐺 is written as 4157)
    A. 20
    B. 24
    C. 26
    D. 28
    E. 30
11. How many times do the hour and minute hand cross an even number on the clock from 1 a.m. to 1 p.m.?
    
    A. -70
    B. 72
    C. 78
    D. 76
    E. 80
12. Count the number of blocks in the following picture.
    
    A. -15
    B. 18
    C. 20
    D. 21
    E. 24
13. A fan has three blades. How many blades will there be in 150 such fans?
    A. 450
    B. 150
    C. 500
    D. 50
    E. 45
14. Count the number of triangles in the picture.
    
    A. 5
    B. 6
    C. 4
    D. 3
    E. 9
15. What number has 2 hundreds, 5 more tens than 20 and 1 less than 7?
    A. 251
    B. 272
    C. 276
    D. 271
    E. 254
16. Harry scored 3 more marks than Alwin. Sophia scored the same as Harry. The sum of their scores was 51. How many marks did Alwin score?
17. Alice picked two cards from deck such that the sum of the numbers on the two cards was 15. Find how many combinations she may have. (In the deck of cards, 𝐴 = 1, 𝐽 = 11, 𝑄 = 12, 𝐾 = 13 while the remaining cards are numbers 2 to 10)
18. Five students entered a contest where they had to guess the number of candies in a box. Alan guessed 25 candies while Beth guessed 30. Charles guessed 27 and David guessed 35. Roma was declared as the winner. One of the students guessed 4 more than Roma’s number while another student guessed 4 less than hers. What was the number guessed by Roma?
19. 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?
20. 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 numbers that she sees is less than 8. How many different sets of numbers are there?
    
21. If the digits of a two-digit number are reversed to form a new number, the difference between the two numbers is 45. How many different such pairs are there?
22. Harry wrote 1, 2, 3, 11, 22, 33, 111, 222, 333, … until he got 17 numbers. What is the sum of the digits of the last number he wrote?
23. A jar of 30 chocolates is shared among Ann, Alice, and Alisha. Alice takes more than anyone else. What is the least number of chocolates she could have taken?
24. Few kids were playing cricket. Each of them carried 4 balls. While playing, 17 balls were hit outside the ground and lost. In the end, they were left with a total of 55 balls. How many kids were playing together?
25. Patrick started jumping every day. He jumped 10 times on Day 1. He jumped 8 more times than Day 1 on Day 2. He jumped 8 more times than Day 2 on Day 3. He continued to jump 8 more times than the previous day every day. Which day will be the first day when he would have jumped at least 100 times in one day?

American Math Olympiad (AMO) adalah kompetisi matematika internasional untuk siswa sekolah dasar, menengah, dan atas yang diselenggarakan bersama oleh SIMCC dan Southern Illinois University (SIU). Kompetisi ini mempromosikan pentingnya dan pemahaman yang lebih mendalam tentang matematika. AMO terbuka untuk semua siswa kelas 2 hingga 12 dan kerangka kerjanya didasarkan pada Standar Common Core AS. Sekelompok pendidik terbaik dari Southern Illinois University dengan pengetahuan dan pengalaman komprehensif dalam kurikulum Matematika Common Core merancang soal-soal unik untuk menantang siswa dan sekaligus meningkatkan minat mereka dalam matematika. Beberapa manfaat utama (atau manfaat kunci) dari AMO adalah beasiswa universitas, Program Cendekiawan Global, keanggotaan International Junior Honor Society (IJHS), hibah biaya kuliah, dan magang.

• Target Peserta: Siswa Grade 2 - Grade 12 (SD, SMP, SMA).
• Format Soal: 25 soal matematika berbahasa Inggris (15 soal pilihan ganda, 10 soal isian singkat).
• Durasi: Umumnya 1,5 hingga 2 jam (tergantung tingkat kelas).
• Larangan: Tidak diperbolehkan menggunakan kalkulator.
• Tujuan: Menguji kemampuan berpikir kritis, strategi pemecahan masalah, dan mental kompetitif.

• Medali & Sertifikat: Peraih medali Emas, Perak, dan Perunggu diberikan oleh SIMCC.
• Jalur Kompetisi Internasional: Pemenang (perunggu ke atas) berhak mengikuti Singapore International Math Olympiad Challenge (SIMOC) dan International Junior Math Olympiad (IJMO).
• Beasiswa & Program: Kesempatan beasiswa 4 tahun di SIU (untuk pemenang medali emas kelas 11/12) dan undangan ke Program Kehormatan Universitas (UHP) SIU.

• Waktu: Biasanya diadakan setiap tahun di bulan Oktober atau November.
• Biaya: Sekitar Rp315.000 - Rp350.000 per siswa.
• Pendaftaran: Melalui pusat pelatihan atau secara daring di situs resmi https://smo-testing.com.