SIMOC - KOMUNITAS JELAJAH NALAR

SIMOC 2019 - Grade 10, 11, 12

Admin dot — Thu, 18 Jun 2026 07:07:07 +0000

Find the value of $$(\frac{1}{\sqrt{0}+\sqrt{1}}+\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{2017}+\sqrt{2018}})^2$$
A. 2016
B. 2017
C. 2018
D. 2029
E. None of the above
A triangle, circle and square are drawn on a rectangular (with different dimensions) piece of paper. What is the greatest number of regions that can be formed?
A. 4
B. 19
C. 23
D. 27
E. None of the above
A positive integer is said to be a “double square” if it can be written as a sum of two perfect squares. Given that all the following options below are prime, which of them is a “double square”?
A. 15139
B. 23357
C. 35803
D. 41183
E. None of the above
The value of 30! is computed and all the ending digits “0” are removed from the result. What is the last digit of the remaining value?
A. 2
B. 4
C. 6
D. 8
E. None of the above
A small circle with radius 𝑟, rolls along the inner circumference of the larger circle with radius of 3𝑟. How many rotations has the smaller circle done around its centre when it reaches the original starting position?

A. 1
B. 1.5
C. 2
D. 4
E. None of the above
The letters “C”, “I”, “M”, “O” and “S” are rearranged to form all five-letter words. The list of words is then arranged in dictionary order. For example, the first word is CIMOS and the last word is SOMIC. What is the order of ‘SIMOC’ in the list?
A. 101
B. 106
C. 109
D. 120
E. None of the above
If $ab+bc+ca=0$, what is the value of $\frac{1}{a^2-bc}+\frac{1}{b^2-ca}+\frac{1}{c^2-ab}$?
A. 2
B. 3
C. 4
D. 5
E. None of the above
In the figure below, arc AOB is a semicircle centered at M, with O being the middle point. Another arc centered at O passing through A and B is drawn. Given that MA = 5, the area enclosed by the figure can be written as $a+b\pi$, where $a$ and $b$ are positive rational numbers. What is the value of $a+b$?

A. 25
B. 50
C. 75
D. 100
E. None of the above
Some white and black cubes are combined to build a 3 × 3 × 3 bigger cube. Five faces of the big cube are shown below:

Given that the middle square of the 6th remaining face is white, how many black squares are there on the 6th remaining face?
A. 1
B. 3
C. 5
D. 7
E. None of the above
There are 3 different types of special power pill found in the lab: 33 Strength, 37 Agility and 49 Intelligence pills. A pharmacist is tasked to reduce the quantity of special power pills in the lab until only one Intelligence pill is left.
- She can combine 1 Strength and 1 Agility pill to get 1 Intelligence pill
- She can combine 1 Strength and 1 Intelligence pill to get 1 Agility pill
- She can combine 1 Agility pill and 1 Intelligence pill to get 1 Strength pill.
Before she starts the combination process, she must add one more pill. Once the pill combination process has started, no additional pills can be added. Which pill must the pharmacist add to achieve her task?
A. Strength
B. Agility
C. Intelligence
D. Adding any type of pill will give you the intelligence pill
E. None of the above
Let $a$ be a positive number such that $a^2+\frac{1}{a^2}=7$. What is the value of $a^3+\frac{1}{a^3}$?
A. $\pm$12
B. $\pm$15
C. $\pm$18
D. $\pm$27
E. None of the above
You are given an empty 3 litres and 8 litres jug. You can perform any of the following steps:
- Fill a jug completely with water.
- Completely empty a jug.
- Pour water from one jug to another until either of the jugs is either empty or full.
What is the minimum number of steps required to obtain exactly 1 litre of water in one of the jugs?
A. 6
B. 7
C. 8
D. 9
E. None of the above
A group of knights, knaves and traders joined a conference hosted by the King. Knights always tell the truth; knaves always lie while traders alternate between telling the truth or lying. The King asked each person the 4 questions below in the following order:
1. Are you a knight?
2. Are you a trader?
3. Are you a knave?
4. Are you a knight?
Thirty-eight people replied “Yes” to the first 2 questions, 15 people replied “Yes” to both the second and third questions, no one replied “Yes” to both questions 3 and 4 and 28 people replied “Yes” in both the first and last questions. How many knights are there?
A. 3
B. 4
C. 5
D. 6
E. None of the above
How many 3-digit numbers are divisible by 6, 7 or 12?
A. 30
B. 196
C. 216
D. 257
E. None of the above
What is the sum of the coefficients of $x^n$, where 𝑛 is even, in the expansion of: $$(2x^2-3x+2)^2(x^2-2x+2)^4$$
A. 202
B. 3884
C. 15313
D. 17212
E. None of the above
If 𝑃(𝑥) is a non-zero polynomial with all integer coefficients and has the root: $$x=\sqrt{2019}+\sqrt{2020}$$ What is the minimum degree of 𝑃(𝑥)?
Find the number of real solution(s) of the following equation. $$\sqrt{-x^2+8x-17}+\sqrt{3x^2-24x+48}=\sqrt{2x^2-16x+65}$$
We have three coins, one is fair (head on one side and tail on the other), one has Head on both sides, and one has Tail on both sides. We pick a coin at random and toss it. If it shows Head facing up, the probability that the other side of the coin is also a Head is $\frac{a}{b}$. If $\frac{a}{b}$ is a fraction in simplest form, find the value of 𝑎 + 𝑏.
Let $f$ and $g$ be two functions on $\mathbb{R}$ such that: $$f(x)=\frac{10}{\log_x e^{10}},\text{ }\text{ }\text{ }g(x)=e^{\frac{10}{x(x+1)(x+2)}}$$ Let $S$ be the sum of composite functions such that: $$S=f(g(1))+f(g(2))+...+f(g(10))$$ If $S=\frac{a}{b}$, where $\frac{a}{b}$ is a fraction in simplest form. Find the value of $a+b$.
The function 𝑆(𝑥) is the sum of the digits of the positive integer 𝑥. If the sum of the positive integer 𝑥 and 𝑆(𝑥) is equal to 2019. What is the smallest possible value of 𝑥?
Let $a_n$ and $b_n$ be 2 distinct roots of the equation $x^3-12x+16=0$ for all $n=1,2,...,100$. Find the value of: $$|\frac{3}{(a_1-1)(b_1-1)}+\frac{3}{(a_2-1)(b_2-1)}+...+\frac{3}{(a_{100}-1)(b_{100}-1)}|$$
What is the smallest positive integer 𝑛 such that the first 4-digit of the number 𝑛 × 2019 is 2018?
How many positive integers 𝑛 satisfy all the criteria below?
$n^2-3n+2$ is divisible by 24
$n^2+5n+6$ is divisible by 7
$n\le 200$
A triangle ABC is inscribed in a circle with radius of 6 cm. Point M is the intersection point of the heights of the triangle ABC. If ∠BAC = 60°, find the length (in cm) of the segment AM.
Given that $$a+b=3$$ $$a^+b^2=1$$ Find the sum of digits of $a^{10}+b^{10}$.

SIMOC 2019 - Grade 9

Admin dot — Thu, 18 Jun 2026 06:17:19 +0000

Which of the following numbers has the largest value? $$2^{13},5^{14},6^{10},10^{11},18^7$$
A. $2^{13}$
B. $5^{14}$
C. $6^{10}$
D. $10^{11}$
E. $18^7$
What is the smallest value of $\frac{a}{|a|}+\frac{|b|}{|b|}+\frac{|c|}{c}$?
A. 0
B. 1
C. 2
D. 3
E. None of the above
A triangle and a circle are drawn on a rectangular (with different dimensions) piece of paper. What is the greatest number of regions can be formed?
A. 8
B. 11
C. 13
D. 16
E. None of the above
How many prime numbers from 1 to 100 can be written as a sum of two perfect squares?
A. 10
B. 11
C. 12
D. 13
E. None of the above
A number is written on the board. It starts with one digit “1”, four digits “2”, nine digits “3”, …, 81 digits “9”, 100 digits “0”, 112 digits “1”, 122 digits “2” and so on. In other words, the number is as follow: $$12222\underset{9\text{ digits}}{\underbrace{333333333}}...\underset{81\text{ digits}}{\underbrace{999...999}}\text{ }\underset{100\text{ digits}}{\underbrace{000...000}}\text{ }\underset{11^2\text{ digits}}{\underbrace{111...111}}\text{ }\underset{12^2\text{ digits}}{\underbrace{222...222}}...$$ What is the 2019th digit of the number?
A. 5
B. 6
C. 7
D. 8
E. None of the above
The following calculations lead to 2 = −2:
(1) We rewrite 2, which is $\sqrt{4}$, as $\sqrt{(-1)(-1)\times 4}$.
(2) We rewrite the single root as product of multiple roots: $\sqrt{-1}\times\sqrt{-1}\times\sqrt{4}$
(3) Since $\sqrt{-1}\times\sqrt{-1}=-1$, the expression is simplified to $-\sqrt{4}$.
(4) Hence, $2=-2$.

How many steps are wrong?
A. Only 1 step
B. Only 2 steps
C. Only 3 steps
D. All 4 steps
E. The proof is correct; 2 is equal to -2.
Extra air is pumped into a spherical balloon so that the volume of the balloon becomes 8 times larger. What is the percentage change of the surface area of the balloon?
A. 100%
B. 200%
C. 300%
D. 400%
E. None of the above
The letters “H”, “I”, “K”, “O” and “S” are rearranged to form all possible five-letter words. The list of words is then arranged in dictionary order. For example, the first word is HIKOS and the last word is SOKIH. What is the order of ‘SHIOK’ in the list?
A. 90
B. 98
C. 101
D. 120
E. None of the above
A number is said to be square-free if the largest power of a prime in its prime factorization is one. It is given that $$\sqrt{2+\sqrt{3}}=\frac{\sqrt{a}+\sqrt{b}}{2},$$ where 𝑎, 𝑏 are square-free positive integers, what is the value of $𝑎^2 + 𝑏^2$?
A. 5
B. 13
C. 40
D. 45
E. None of the above
The operator $\bullet$ acts on two numbers to give the following outcomes:

What is the value of 20 $\bullet$ 1?
A. 0
B. 19
C. 20
D. 32
E. None of the above
Chloe and Linda have been arrested for retail theft. If they both cooperate and confess to their crime, they will be sentenced to 3 months in jail. If only one of them confesses, the person who confesses will be sentenced to 2 months in jail and the other person will be sentenced to 10 months in jail. If neither of them confesses, they both will not be sentence to jail. Assuming they will not know the decision made by the other person, what should Chloe and Linda do to obtain the best possible outcome for themselves?
A. Chloe should confess and Linda should not confess.
B. Chloe should not confess, and Linda should confess.
C. Chloe should not confess, and Linda should not confess.
D. Chloe should confess and Linda should confess.
E. No matter what they do, the outcome will still be the same.
A standard dice is rolled five times. What is the probability that three rolls have a same face value and the other two rolls have a different same face value?
A. $\frac{1}{2}$
B. $\frac{25}{648}$
C. $\frac{5}{1296}$
D. $\frac{60}{7776}$
E. $\frac{18}{46656}$
A group of knights, servants and traders joined a conference hosted by the King. Knights always tell the truth; servants always lie while traders alternate between telling the truth or lying. The King asked each person the 4 questions below in the following order:
1. Are you a knight?
2. Are you a trader?
3. Are you a servant?
4. Are you a knight?
Thirty-two people replied “Yes” to the first 2 questions, 18 people replied “Yes” to both the second and third questions, no one replied “Yes” to both questions 3 and 4 and 19 people replied “Yes” in both the first and last questions. How many knights are there?
A. 3
B. 4
C. 5
D. 6
E. None of the above
For any positive real number 𝑥 and positive integer 𝑛, which of the following options below is true?
A. $n^2<2^n$
B. $(1+x)^n\ge 1+nx$
C. $(1+2+...+n)^2>1^3+2^3+...+n^3$
D. $\frac{1+2+...+n}{n}<\sqrt{1+2+...+n}$
E. None of the above
Five close friends each brought one gift to a Christmas party. They put all the five gifts on a table and distributed to each other such that no one receives his/her own gift. In how many ways can the gifts be distributed?
A. 12
B. 44
C. 120
D. 480
E. None of the above
Starting from the cell at row 0 and column 0, positive integers are written in a spiral way in an infinite table, as follow:

What is the number written on the cell of row 19 and column 19?
In the expansion of: $$(2x^2-3x+2)^3(x^2-2x+2)^3$$ Find the sum of digits in the sum of the coefficient of $x^{2n}$, where 𝑛𝑛 is a positive integer.
What is the smallest positive integer 𝑛 such that the first 4 digits of the number 𝑛 × 2018 is 2017?
Different letters represent different digits. Find the four-digit number “HOLE”.
It is given that $$\text{sin}^2 0° + \text{sin}^2 5° + \text{sin}^2 10° + ⋯ + \text{sin}^2 85° + \text{sin}^2 90° = \frac{a}{b},$$ where $\frac{a}{b}$ is a fraction in simplest form. Find the value of 𝑎 + 𝑏.
If 𝑃(𝑥) is a non-zero polynomial with all integer coefficients and has the root: $$𝑥 = 2019 + \sqrt{2} + \sqrt{3}$$ What is the minimum degree of 𝑃(𝑥)?
Teacher Victor thinks of a four-digit “key” with different digits. He then asks his students to guess the “key”. In each turn, Victor’s students suggest a four-digit number with distinct digits. He then gives certain responses, as follow:

: One of the digits is in the “key” and in the correct position.
$\bullet$: One or more the digits are in the “key” but not in the correct position.
: One of the digits is not in the “key”.
For example, if the “key” is 1234 and the students guess the number 1345, the response will be . If the students guess 7234, the response will be . Find the “key” teacher Victor is thinking of.
There are 20 diagonals in a regular octagon. When the diagonals intersect each other, how many distinct intersection points are there inside the octagon are there?
Find the minimum value of $\sqrt{x^2-8x+25}+\sqrt{x^2-8x+97}$ where 𝑥 is a positive real number.
A triangle ABC is inscribed in a circle with radius of 5 cm. Point D is the intersection point of the heights of the triangle ABC. If ∠BAC = 60°, find the length (in cm) of the segment AD.

SIMOC 2019 - Grade 8

Admin dot — Thu, 18 Jun 2026 04:52:35 +0000

Find the value of $$\frac{1}{\sqrt{1^3}}+\frac{1}{\sqrt{1^3+2^3}}+\frac{1}{\sqrt{1^3+2^3+3^3}}+\frac{1}{\sqrt{1^3+2^3+3^3+4^3}}$$
A. $\frac{1}{15}$
B. $\frac{2}{15}$
C. $\frac{8}{5}$
D. $\frac{17}{3}$
E. None of the above
A triangle is drawn on a rectangular piece of paper. What is the greatest number of regions that can be formed?
A. 2
B. 3
C. 4
D. 5
E. None of the above
What is the value of $(\sqrt{5+2\sqrt{6}}+\sqrt{5-2\sqrt{6}})^2$?
A. 2
B. 3
C. 8
D. 9
E. None of the above
Fermat proved that an odd prime number can be written as a sum of two perfect squares if the odd number gives a remainder of 1, 5 or 9 when divided by 12. Given that all the following choices are prime numbers, which of them can be written as a sum of two perfect squares?
A. 54324223
B. 66843247
C. 73831151
D. 92138363
E. None of the above
Four empty bottles of fruit juice can be exchanged for 1 new bottle of milk. Five empty bottles of soda can be exchanged for 1 new bottle of fruit juice. If Sheryl initially buys 5 dozen of soda bottles, what is the greatest number of bottles of any beverage that she can drink?
A. 6
B. 36
C. 56
D. 75
E. None of the above
What is the largest amount of money that cannot be obtained using only $\$$3 and $\$$8 denominations?
A. $\$$13
B. $\$$23
C. $\$$67
D. $\$$97
E. $\$$100
One hundred and fifty students are selected to participate in a survey. The report states that 120 students have played League of Legends, 75 students have played Piano Tiles and 50 students have played Battleground. What is the largest possible number of students who have played both Piano Tiles and Battleground but have never tried League of Legends?
A. 15
B. 20
C. 25
D. 30
E. None of the above
The letters “S”, “T”, “A”, “L” and “L” are rearranged to form all five-letter words. The list of words is then arranged in dictionary order. For example, the first word is ALLST and the last word is TSLLA. What is the order of ‘STALL’ in the list?
A. 45
B. 46
C. 92
D. 600
E. None of the above
Some married couples participate in the Indoor Dancing Competition. Before the competition starts, every person shakes hands with each other except for his/her spouse. The organiser and his wife then enter the competition venue. They select some couples, and for each selected couple, the organiser shakes hand with the lady while his wife shakes hand with the gentleman. Given that there have been 2018 handshakes so far, how many couples are selected to shake hands with the organiser and his wife?
A. 15
B. 16
C. 17
D. 18
E. None of the above
A number is written on the board. It starts with one digit “1”, three digits “2”, five digits “3”, …, 17 digits “9”, 19 digits “0”, 21 digits “1”, 23 digits “2” and so on. In other words, the number is as follows: $$122233333 …\underset{17\text{ digits}}{\underbrace{999...999}}\text{ }\underset{19\text{ digits}}{\underbrace{000...000}}\text{ }\underset{21\text{ digits}}{\underbrace{111...111}}\text{ }\underset{23\text{ digits}}{\underbrace{222...222}}...$$ What is the 2019th digit of the number?
A. 2
B. 3
C. 4
D. 5
E. 6
In the Star Event, the Lucky Award is awarded to a couple of opposite gender with the same zodiac signs. It also awards a group of at least 5 people with the same gender and zodiac signs. For instance, 2 couples where each pair has the opposite gender and same zodiac signs will get 1 Prize each. Given that there are 12 zodiac signs, at least how many people should the event organiser invite to ensure at least one Lucky Award will be given out?
A. 4
B. 13
C. 49
D. 50
E. None of the above
In the diagram below, the lines CF and AE meet at point D and the line AD bisects ∠BAC. If ∠ADC = 90°, which of the following options below is true?

A. ∠ABC > ∠ACD
B. ∠ACD > ∠ABC
C. ∠BCF > ∠AFC
D. ∠ACF > ∠AFC
E. None of the above
Six performances are to be included in the Singapore International Discrete Mathematics Challenge Prize Ceremony. All the performances have different durations. The third performance must be longer than the first, while the fourth performance must be longer than the second and so on. How many ways can the organiser arrange the performances?
A. 6
B. 18
C. 20
D. 120
E. None of the above
In the diagram below, ABDC is a rectangle with dimensions 6 cm by 4 cm and EFGH is a parallelogram. It is given that CG = EB = 2 cm, CF = BH = 3 cm and CFXG = 5 $\text{cm}^2$. Find the area of the quadrilateral BEXH.

A. 5
B. 8
C. 11
D. 14
E. None of the above
Information about four students: Elizabeth, Miyuki, Stephanie and Tracy are as stated below.
1) Each of the student has a different nationality and come from Thailand, India, Singapore and Uzbekistan.
2) Their ages are 21, 24, 26 and 30; each of them do not share the same age.
3) Each of them plays a different musical instrument which could be a cello, drums, saxophone and horn.
4) Stephanie is not 21 years old.
5) Elizabeth is from Thailand.
6) The student playing the saxophone is not 30 years old.
7) Stephanie does not play the horn.
8) The student playing the cello is not Singaporean.
9) Miyuki is younger than Elizabeth.
10) Stephanie is older than the student playing the saxophone
11) The student playing the cello is not 26 years old.
12) The 30-year-old student is not Indian.
13) Tracy is older than Stephanie.
14) Elizabeth does not play the cello or drums.
15) The student playing the saxophone is not Singaporean.
16) Stephanie does not play the drums.

Who plays the drums?
A. Elizabeth
B. Miyuki
C. Stephanie
D. Tracy
E. Not enough information
The operator $\bullet$ acts on two numbers to give the following outcomes:

The operator only returns “0” or “1”. What is the value of 20 $\bullet$ 00?
Find the positive integer value of 𝑥 such that $\sqrt{x^2-36}+\sqrt{x^2+23x-174}$ is minimum.
Given that $𝑥^2 − 3𝑥 + 1 = 0$, what is the value of $𝑥^3 +\frac{1}{x^3}$?
There are 2019 consecutive positive integers such that $a_1
Only one button of a calculator is working. If $x$ is the number displayed, it returns the value $x(2 + x)$. Initially, the number 1 is displayed. The number that is shown on the calculator when it is pressed 25 times is of the form $a^{b^c}+d$. Find the value of 𝑎 + 𝑏 + 𝑐 + 𝑑.
How many triangles are there in the figure below?
If 𝑃(𝑥) is a non-zero polynomial with all integer coefficients and has the root: $$𝑥 = 2019 + \sqrt{2} + \sqrt{3}$$ What is the minimum degree of 𝑃(𝑥)?
You are given an empty 3 litres and 7 litres jug. You can perform any of the following steps:
-Fill a jug completely with water.
-Completely empty a jug.
-Pour water from one jug to another until either of the jugs is empty or full.
What is the minimum number of steps required to obtain exactly 1 litre of water in one of the jugs?
How many positive integers 𝑛 satisfy all the criteria below?
$𝑛^2 − 3𝑛 + 2$ is divisible by 24
$𝑛^2 + 5𝑛 + 6$ is divisible by 7
$𝑛 ≤ 200$
Republic of SIMOC territory consists of 2019 islands. The government wants to build some bridges between the islands. A bridge is a two-way connection between two and exactly two islands. Due to lack of financial assistance, the government decides to build as few bridges as possible while still ensuring the connectivity between any two islands. Assume the bridge construction is optimal, what is the minimum number of bridges that must be crossed between any 2 islands?

SIMOC 2019 - Grade 7

Admin dot — Thu, 18 Jun 2026 04:25:44 +0000

Find the value of $$\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\frac{1}{1+2+3+4+5}$$
A. $\frac{1}{15}$
B. $\frac{3}{15}$
C. $\frac{3}{5}$
D. $\frac{5}{3}$
E. None of the Above
The operator $\bullet$ acts on two numbers to give the following outcomes: $$4 \bullet 8 = 48$$ $$8 \bullet 9 = 172$$ $$6 \bullet 9 = 318$$ $$15 \bullet 20 = 560$$ What is the value of $19 \bullet 19$?
A. 190
B. 1919
C. 2019
D. 3600
E. None of the Above
A circle is drawn on a rectangular (with different dimensions) piece of paper. What is the largest possible number of regions can be formed?
A. 2
B. 3
C. 4
D. 5
E. None of the above
A number is written on the board. It starts with one digit “1”, two digits “2”, three digits “3”, …, nine digits “9”, ten digits “0”, eleven digits “1”, twelve digits “2”, etc. In other words, the number is as follow: $$122333444455555 …\underset{9\text{ digits}}{\underbrace{999999999}}\text{ }\underset{10\text{ digits}}{\underbrace{0000000000}}\text{ }\underset{11\text{ digits}}{\underbrace{111...111}}\text{ }\underset{12\text{ digits}}{\underbrace{222...222}}...$$ What is the 2019th digit of this number?
A. 2
B. 4
C. 6
D. 8
E. None of the above
The letters “A”, “C”, “L” and “O” are rearranged to form all four-letter words. The list of words is then arranged in dictionary order. For example, the first word is ACLO and the last word is OLCA. What is the order of ‘COLA’ in the list?
A. 10
B. 11
C. 12
D. 13
E. None of the above
A group of teachers attended a conference hosted by the Wonderland’s Ministry of Education. Before the conference starts, every teacher shook hands with each other. After all the teachers shook hands with one another, the Minister and his secretary entered the conference room. They shook hands with some of the teachers, so that no teacher shook hands with both of them. Given that there were 2019 handshakes made, how many teachers attended the conference?
A. 62
B. 63
C. 64
D. 65
E. None of the above
The following calculations lead to 2019 = −2019:
(1) We write 2019 as $\sqrt{2019^2}$
(2) Since $2019^2=(-2019)^2$, we further rewrite 2019 as $\sqrt{(-2019)^2}$.
(3) The expression is simplified to $\sqrt{(-2019)^2}=-2019$.
(4) Hence, $2019=-2019$.
Which step is the first one that contains errors?
A. (1)
B. (2)
C. (3)
D. (4)
E. The proof is correct; 2019 is equal to -2019.
In the following diagram, each number in a box is the least common multiple of the two numbers in the boxes that it touches above it. Given the configuration shown below, what is the smallest possible number that could be in the top rightmost box?

A. 2
B. 4
C. 16
D. 32
E. None of the above
In the SIMOC Kingdom, only coins of value 19 dollars and 20 dollars are circulated. Which of the following amount of money cannot be paid exactly in this Kingdom?
A. 40
B. 140
C. 727
D. 2019
E. None of the above
Five empty bottles of lemonade can be exchanged for 1 new bottle of coke. Four empty bottles of coke can be exchanged for 1 new bottle of milk. If Sarah initially buys 5 dozen of lemonade bottles, what is the greatest number of bottles of any beverages can she drink? (1 dozen is 12 pieces)
A. 25
B. 50
C. 75
D. 100
E. None of the above
Which option below is an odd term in the following sequence? $$11, 13, 24, 37, 61,98, 159, …$$
A. 51th
B. 57th
C. 75th
D. 100th
E. 102th
Abel and Amenadial start on opposite ends of a pool and start swimming towards each other. Abel’s speed is 3 m/s and Amenadial’s speed is 1.8 m/s. Each time they reach the opposite end of the pool, they turn around and continue swimming. Swimming 1 lap means swimming from one end of the pool to the opposite end. What is the smallest number of laps that Abel needs to swim before they meet each other at the middle of the pool?
A. 2
B. 3
C. 4
D. 5
E. None of the above
Refer to the figure below. The bigger semicircle is centered at D and has a radius of 9cm. The smaller semicircle is centered at E and has a radius of 6 cm. Also, FD and HE are perpendicular to DB and EB respectively. Find the area of the shaded region.

A. $16\pi+2\text{ cm}^2$
B. $\frac{9}{4}\pi+\frac{9}{2}\text{ cm}^2$
C. $\frac{7}{2}\pi+\frac{1}{4}\text{ cm}^2$
D. $\frac{11}{2}\pi+\frac{16}{3}\text{ cm}^2$
E. None of the above
Which of the following options below is divisible by 3?
A. $1^{11}$
B. $2^{13}-1$
C. $3^{428}-1$
D. $4^{999}-1$
E. None of the above
Information about four students: Amy, Hannah, Rebecca and Yuki are as stated below.
1) Each of the student has a different nationality and come from among Bulgaria, China, Japan or Philippines.
2) Their ages are 17, 18, 19 or 20; each of them do not share the same age.
3) Each of them plays a different musical instrument which could be a clarinet, guitar, piano or violin.
4) Hannah is younger than Amy.
5) The student playing the piano is not a Japanese, and is younger than Rebecca.
6) The 20-year-old student is not a Chinese, and does not play the piano.
7) Yuki is older than Rebecca.
8) The student playing the clarinet is not a Japanese, and is not 19 years old.
9) Rebecca is not 17 years old, and does not play the guitar or violin.
10) Amy is from Bulgaria, and she does not play the clarinet or guitar.
Who plays the violin?
A. Amy
B. Hannah
C. Rebecca
D. Yuki
E. Not enough information
Positive integers are written in the infinite table as follow.

What number is written on the cell of row 2019 and column 2019?
William writes on the board all integers from 1 to 100. He then erases all the numbers with digit(s) “3” or divisible by 3. How many numbers are left on the board?
In the following cryptarithm, all the different letters stand for different digits. What is the sum of the digits in the 6-digit number DURIAN?
What is the largest positive integer 𝑛𝑛 such that $𝑛^2 + 50$ is divisible by $𝑛 + 2$?
In the Star Event, the Lucky Award is awarded to a couple of opposite gender with the same zodiac signs. It also awards a group of at least 5 people with the same gender and zodiac signs. For instance, 2 couples where each couple has opposite gender and same zodiac signs will get 1 Prize each. Given that there are 12 zodiac signs, at least how many people should the event organiser invite to ensure at least one Lucky Award will be given?
The lines BF and GC bisect ∠GFD and ∠DCB respectively, and the meet at point E. Given that ∠GEB = 100° and ∠FDC = 140°, find ∠FAC.
Yvonne and Zavier can complete painting a house in 12 days. Whereas, Xander and Yvonne can complete painting the same house in 6 days. When Xander and Zavier work together, they will take 10 days to complete it. If all 3 of them work together but Zavier only comes for 1 day to help out, it will take them $\frac{x}{y}$ days to complete painting the house. Suppose $\frac{x}{y}$ is in simplest form, what is value of 𝑥 + 𝑦?
You are given an empty 5 litre jug and 7 litre jug. You can perform any of the following steps:
1) Fill a jug completely with water.
2) Completely empty a jug.
3) Pour water from one jug another until of the jugs is either empty or full.
What is the minimum number of steps required to obtain exactly 1 litre of water in one of the jugs?
Given that $a_1+a_2+a_3+...+a_{n-1}+a_n=n^2$ for any positive integer $n$. Find the value of $x+y$, where $$\frac{1}{a_1+1}+\frac{1}{a_2+1}+\frac{1}{a_3+1}+\frac{1}{a_4+1}+\frac{1}{a_5+1}=\frac{x}{y}$$
Nineteen Figure 1s are drawn side-by-side to form Figure 2. How many triangles are there in Figure 2?

SIMOC 2019 - Grade 6

Admin dot — Thu, 18 Jun 2026 03:50:26 +0000

What is the value of $$\frac{1\times 2\times 3+3\times 6\times 9+7\times 14\times 21}{1\times 4\times 5+3\times 12\times 15+7\times 28\times 35}$$
A. 2/5
B. 3/7
C. 2/3
D. 3/10
E. None of the above
What is the last digit of the sum $76^{2019} + 25^{2019}$?
A. 1
B. 5
C. 6
D. 11
E. None of the Above
It takes 8 persons 3 days to finish baking 144 cookies. At the same rate, how many cookies can 12 persons bake in 6 days?
A. 12
B. 324
C. 432
D. 500
E. None of the Above
Allan, Bob and Charles were comparing the number of marbles they had. Allan had 2/3 of the combined number of marbles that Bob and Charles have. Bob had 2/5 of the combined number of marbles that Allan and Charles have. What fraction of the combined number of Allan’s and Bob’s marbles did Charles have?
A. $\frac{7}{12}$
B. $\frac{11}{24}$
C. $\frac{1}{2}$
D. $\frac{4}{15}$
E. None of the Above
We define the least common multiple (LCM) of two fractions, $\frac{a}{b}$ and $\frac{c}{b}$, to be the last fraction $\frac{x}{y}$ such that $\frac{x}{y}\div \frac{a}{b}$ are both integers. For example, LCM$(\frac{1}{2},\frac{2}{3})=\frac{2}{1}$, since $\frac{2}{1}\div \frac{1}{2}=4$ and $\frac{2}{1}\div \frac{2}{3}=3$, and $\frac{2}{1}$ is the least fraction with this property. Find the LCM$(\frac{15}{49},\frac{5}{21},\frac{25}{14})$.
A. $\frac{75}{7}$
B. $\frac{75}{14}$
C. $\frac{30}{7}$
D. $\frac{150}{7}$
E. None of the Above
Find the smallest whole number that we must add to $2 + 2^2 + 2^3 + ⋯ + 2^{10}$ for it to be divisible by 10.
A. 2
B. 4
C. 6
D. 8
E. None of the above
How many numbers between 1 and 202 are multiples of 3 or 4 but not 12?
A. 67
B. 117
C. 101
D. 133
E. None of the above
The ratios of the volume of a rectangular box to its length, width and height are 5 : 1, 1 : 3 and 5 : 3, respectively. Find the surface area of the box.
A. 7
B. 8.6
C. 14
D. 17.2
E. None of the Above
JustRunLah! had a race with 6 runners, among them Alice and Bob. If Alice finished ahead of Bob, how many possible outcomes are there for the final rankings of the runners?
A. 24
B. 120
C. 240
D. 360
E. None of the Above
Jerry walked into a computer store having $\$2000$. He bought a laptop with a 20% discount. To recover his expense, he sold the laptop for 50% more than the price he purchased it. If he had $\$2720$ at the end, how much was the cost of the laptop without the discount?
A. $\$1500$
B. $\$1600$
C. $\$1700$
D. $\$1800$
E. None of the Above
When is the first time after 4:00 AM that the minute hand is exactly 2 minutes past the hour hand?
A. 4:20 AM
B. 4:24 AM
C. 4:30 AM
D. 4:36 AM
E. None of the above
Peter brought some apples, oranges and kiwis to the local market to sell. After he sold 4 apples, he was left with 3 oranges for each remaining apple. He then sold 7 oranges and was left with 3 kiwis for each remaining orange. Finally, he sold 27 kiwis and was left with 3 kiwis for each remaining apple. How many kiwis did Peter bring to the local market?
A. 24
B. 51
C. 66
D. 68
E. None of the Above
The long road along Orchard Street is being repaired. When 10% of the road was successfully repaired, the road management team decided to buy new equipment to speed up the road repair. As a result, the rate at which the road was being repaired increased by 20% and the time to complete the road repair decreased by 15% (compared to the original). In total, it took 144.5 days to repair the road. How long, in days, was the original plan to finish the road repair?
A. 170
B. 180
C. 190
D. 200
E. None of the Above
The fractions $\frac{a}{3}$ and $\frac{b}{7}$ are proper fractions. If the value of $\frac{a}{3}+\frac{b}{7}$ is between 1.38 and 1.39, find $ab$.
A. 6
B. 8
C. 10
D. 12
E. None of the Above
Find the value of $$\frac{2019^2}{2019}-\frac{2018^2}{2019}+\frac{2017^2}{2019}-\frac{2016^2}{2019}+\cdots -\frac{4^2}{2019}+\frac{3^2}{2019}-\frac{2^2}{2019}+\frac{1^2}{2019}$$
A. 1010
B. 2019
C. 2020
D. $2019^2$
E. None of the Above
Let the operations ∆ and ∎ be defined for all numbers 𝑎 and 𝑏 as follows: $$𝑎∆𝑏 = 𝑎 + 3 × 𝑏$$ $$𝑎∎𝑏 = 𝑎 + 4 × 𝑏$$ For example, $$4∆7 = 4 + 3 × 7 = 25$$ $$9∎2 = 9 + 4 × 2 = 17$$ If $4∆(5 × 𝑦) = (5 × 𝑦)∎4$, what is the value of $15 × 𝑦$?
A terminating fraction is a fraction that has a terminating decimal representation. For example, $\frac{31}{40}$ is a terminating fraction since $\frac{31}{40}$ = 0.775 while $\frac{1}{3}$ is NOT since $\frac{1}{3}$ = 0.3333 ... The fraction $\frac{1}{2020}$ is not terminating. Find the least positive integer to be multiplied to $\frac{1}{2020}$ to make it a terminating fraction.
Two cars, A and B, on opposite sides of a long road, are traveling towards each other. Car A is traveling at a rate of 56 km/h while Car B is traveling at a rate of 48 km/h. Cars A and B meet for the first time when Car A has traveled 32 kilometers past midway. How long is the road in kilometres?
Simon and Peter are brothers. Working alone, Simon can paint a room 2 times as fast as his brother Peter. But when they work together, they horseplay and as a result, each of their working rates decreases by half. Last weekend, the two boys painted the room together for 20 minutes. After which, Peter left, leaving Simon alone to finish painting the room. Simon took another 25 additional minutes to finish the job. How long, in minutes, did it take Simon to paint the room alone?
Larry tells Mary and Jerry that he is thinking of two consecutive integers from 1 to 10. He tells Mary one of the numbers, and he tells Jerry the other number. Then the following conversation occurs between Mary and Jerry:
Mary: I don't know your number.
Jerry: I don't know your number, either.
Mary: Ah, now I know your number.
Assuming both Mary and Jerry used correct logic, what is the sum of the possible numbers Mary could have?
Refer to the figure below. The bigger semicircle is centered at D and has a radius of 9 cm. The smaller semicircle is centered at E and has a radius of 6 cm. Also, FD and HE are perpendicular to DB and EB, respectively. Find the area of the shaded region (Rounded off your answer to the nearest whole number and use 𝜋 = 3.14.)
At the most how many numbers can you choose from 1000 to 1550 so that the sum of any three numbers is divisible by 3?
Define 𝑛! = 𝑛 × (𝑛 − 1) × (𝑛 − 2) × … × 2 × 1 and 0! = 1. Find the number 𝑘 where 𝑘 = $𝑚^𝑛$ such that $\frac{2000!}{1000!}$ = 𝑘 × (1 × 3 × 5 × 7 × ⋯ × 1997 × 1999). Find the value of 𝑚 + 𝑛.
In triangle ABC, points D and E are on sides BC and AC such that AD and BE are perpendicular to BC and AC, respectively. Points F and G are on sides BC and AC such that AF and BG divide angles BAC and ABC into two equal parts, respectively. If ∠DAF = 7° and ∠EBG = 20°. Find the measure of ∠𝐶.
A large square and two congruent smaller squares share a vertex. The large square touches the other two squares as shown. The areas of the three squares are 320, 20 and 20 $\text{cm}^2$, and points D, E, and H are three of the vertices of the three squares as shown. Find the area of triangle EDH.

SIMOC 2019 - Grade 5

Admin dot — Thu, 18 Jun 2026 03:24:29 +0000

Calculate (2018 − 2016) + (2016 − 2014) + (2014 − 2012) + ⋯ + (6 − 4) + (4 − 2)
A. 2
B. 1008
C. 1009
D. 2016
E. None of the Above
It is given that 𝑛! = 𝑛 × (𝑛 − 1) × (𝑛 − 2) × … × 2 × 1. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. What is the remainder when 1! + 2! + 3! + 4! + ⋯ + 19! + 20! is divided by 20?
A. 12
B. 13
C. 14
D. 15
E. None of the Above
What is the remainder when the number $\underset{102s}{\underbrace{2222222222}}$ is divided by 7?
A. 3
B. 4
C. 5
D. 6
E. None of the Above
In how many ways can three students in a class receive grades A, B, C or D so that no two students receive the same grade.
A. 6
B. 24
C. 27
D. 64
E. None of the Above
The total number of apples and pears in a container is 220. Ben later gave away 38 pears and 5/9 of the apples. The remaining apples and the remaining pears in the container were now equal in number. How many pears were there in the container at first?
A. 38
B. 56
C. 94
D. 182
E. None of the Above
The clock in my bedroom shows the time which is four minutes ahead the real time. When the real time is 7:00 AM, it shows 7:04 AM. The clock in my kitchen is also faulty. When the one in the bedroom shows 8:55 AM, the one in the kitchen shows 8:53 AM. I can’t trust the clock in Dad’s car, either. When I got in the car yesterday, the clock in the kitchen showed 8:30 PM and the clock in the car said 8:24 PM. When I arrived to school, the clock outside the building showed 9:01 AM and the clock in the car said 8:56 AM. What did the clock outside school show when I got up at 6:30 AM, according to my bedroom clock?
A. 6:22 AM
B. 6:24 AM
C. 6:26 AM
D. 6:27 AM
E. None of the Above
In the figure below, $AB = AC = BC = BD$. What is the measure of $∠D$ in degrees?

A. 15
B. 30
C. 60
D. 120
E. None of the Above
John’s speed of climbing up a mountain is 2 km/h. His speed of descent is 6 km/h. What is his average speed (in km/h) for the whole journey?
A. 3
B. 4
C. 5
D. 6
E. 8
In a class of 42 students, 18 students are in the Math club, 5 students are in both the Math Club and Science Club, and 14 students are not in any clubs. How many students are in the Science Club?
A. 10
B. 15
C. 24
D. 28
E. None of the Above
Given that a number 3A4A6A9A2 is divisible by 11, what is the value of A?
A. 5
B. 6
C. 7
D. 8
E. None of the Above
John was computing for the average of the fractions $\frac{3}{4},\frac{4}{5},\frac{7}{9},\frac{9}{11}$ when he mistakenly interchanged the numerator and the denominator of one of the given fractions. What is the greatest possible difference between the new average and the supposed average of the original set of fractions?
A. 17/140
B. 9/80
C. 7/48
D. 10/99
E. None of the Above
How many triangles are there in the figure below?

A. 21
B. 63
C. 42
D. 84
E. None of the Above
The operation ⊗ is defined as $a$ ⊗ $b$ = $\frac{a}{b} + \frac{1}{a+b+ab-M}$. If it is known that 1 ⊗ 2 = $\frac{3}{4}$, find the value of 5 ⊗ 6.
A. $\frac{97}{120}$
B. $\frac{103}{120}$
C. $\frac{6}{7}$
D. $\frac{7}{6}$
E. None of the Above
The ratio of the perimeter of a rectangle to the length of one of its sides is 14 : 3. If the area of the rectangle is 27 $\text{cm}^2$, how long is the longer side?
A. 3 cm
B. 6 cm
C. 18 cm
D. 24 cm
E. None of the Above
Amy, working alone, can finish painting a house in 36 hours while Brad, working alone, can finish painting the same house in 48 hours. Each of them works exactly 8 hours everyday. However, Amy rests every Tuesday and Thursday while Brad rests every Wednesday. If they start painting the house together on a Monday, on what day of the week will they finish painting the house in the least possible amount of time.
A. Wednesday
B. Thursday
C. Friday
D. Saturday
E. Sunday
The perimeter of parallelogram ABCD is 68. Parallelogram ABCD has been divided into 9 smaller parallelograms by 4 parallel lines. The perimeters of four of the smaller parallelograms are 34, 38, 20 and 24 as shown. Find the perimeter of the shaded region.
In the multiplication sentence, $ABC\times DE=FG\times HI$ = 5568, the 9 letters represent the digits from 1 to 9 and they are used only once. What is the value of the 3-digit number $ABC$?
Elvis took several mathematics tests. He scored 76 in one of the tests and his average score for all the tests was 85. If he obtained 92 instead of 76, his average score would be 89. How many tests did Elvis take?
A special key in a calculator when pressed, displays the number 1 − $\frac{1}{x}$, when 𝑥 was displayed before. For example, when 2 is displayed and the special key is pressed, the calculator will display $\frac{1}{2}$ since 1 − $\frac{1}{2}$ = $\frac{1}{2}$. Initially, the number 2019 is displayed in the calculator. Find the number that will be displayed after pressing the special key 2019 times.
Larry tells Mary and Jerry that he is thinking of two consecutive integers from 1 to 10. He tells Mary one of the numbers, and he tells Jerry the other number. Then the following conversation occurs between Mary and Jerry:
Mary: I don't know your number.
Jerry: I don't know your number, either.
Mary: Ah, now I know your number.
Assuming both Mary and Jerry used correct logic, what is the sum of the possible numbers Mary could have?
Andrew, Bob, Carl and David together decided to buy a new air conditioning unit. The amount given by the eldest, Andrew, is one-half the total amount given by his 3 other siblings. The amount given by the second eldest, Bob, is one-third the total amount given by his 3 other siblings. The amount given by the third eldest, Carl, is one-fourth the total amount given by his 3 other siblings. If the amount given by the youngest, David, is $40 less than the amount given by Bob, what is the cost of the air conditioner?
John and James are brothers. The ratio of the monthly income of John to James is 4:3 while the ratio of their monthly expenses is 11:7. Last year, each of them saved $\$$9,000 for the whole year. How much is James’ monthly income?
Find the value of the following. $$\frac{2019\times 2020}{505+505^2}+\frac{2019\times 2020}{506+506^2}+\frac{2019\times 2020}{507+507^2}+\cdots+\frac{2019\times 2020}{672+672^2}$$
Calvin’s house is located at the point C as shown in the figure shown. Ed, whose house is located at point E, wants to visit Calvin. The segments on the grid are the only roads that Ed can use to move to other points in the grid. Ed also wants to visit Sam, whose house is located at point S. If Ed starts from his house and he can only move up or to the right. In how many ways can Ed go to Calvin’s house if he wants to visit Sam first?
A large square and two congruent smaller squares share a vertex. The large square touches the other two squares as shown. The areas of the three squares are 160, 10 and 10 $\text{cm}^2$, and points D, E, and H are three of the vertices of the three squares as shown. Find the area of triangle EDH.

SIMOC 2019 - Grade 4

Admin dot — Thu, 18 Jun 2026 02:57:59 +0000

Find the value of 87 × 27 + 72 × 87 + 87.
A. 2700
B. 7200
C. 8700
D. 9700
E. None of the Above
I am thinking of a number. First, I multiply it by 2, then add 14 to the result. Then divide the sum by 7 and subtract 3 from the result. I will get 9 as my final answer. What number am I thinking of?
A. 35
B. 14
C. 21
D. 42
E. None of the Above
Study the pattern below.

What is the value of A?
A. 28
B. 82
C. 68
D. 64
E. None of the above
Figure 1 is called a “stack map.” The numbers tell how many cubes are stacked in each position. Figure 2 shows these cubes, and Figure 3 shows the view of the stacked cubes as seen from the front.

Which of the following is the front view for the stack map in Figure 4?
A “funny number” is a number formed by writing two digits followed by their product. For example, 6 × 7 = 42, so 6742 and 7642 are “funny numbers”. The first digit of a “funny number” cannot be a 0. What is the difference between the largest and smallest “funny number?”
A. 9837
B. 9541
C. 9581
D. 9081
E. 9881
In a certain month, the number of Thursdays is more than the number of Wednesdays. Also, the number of Sundays is less than the number of Saturdays. On what day of the week will the 27th of that month fall?
A. Monday
B. Tuesday
C. Wednesday
D. Friday
E. Sunday
What is the remainder when the number $\underset{101s}{\underbrace{1111111111}}$ is divided by 7?
A. 3
B. 4
C. 5
D. 6
E. None of the Above
A boy always tells the truth on Mondays and Tuesdays, always tells lies on Saturday, and tells either truth or lies on the rest of the days of the week. For six days in a row, he was asked what his name was and he gave the following answers: Tom, Brad, Tom, John, Brad, John. What is the boy’s name?
A. Tom
B. Brad
C. John
D. Brad or John
E. Impossible to determine
Study the pattern below.

What is the value of 10 ⨂ 4 ?
A. 10
B. 14
C. 40
D. 50
E. None of the above
If a digit 𝑎 is added to the left of the one-digit number 8 and a digit 𝑏 is added to the right of it, a 3-digit number 𝑎8𝑏 is formed. If this number 𝑎8𝑏 is a multiple of 3, what is the largest possible product 𝑎 × 𝑏?
A. 8
B. 56
C. 84
D. 96
E. None of the Above
Ann, Betty and Clare, each bought beads from a market. Ann bought 400 beads more than Betty. The total number of beads of Ann and Betty bought were 900 more than Clare’s. If the three of them bought 4500 beads in total, how many beads did Clare buy?
A. 1150
B. 1550
C. 1800
D. 2700
E. None of the Above
The temperature relationship between degrees Celsius (C) and degrees Fahrenheit (F) is given by $\frac{9}{5}$ × 𝐶 + 32 = 𝐹. For example, 20° Celsius is equal $\frac{9}{5}$ × 20 + 32 = 68° Fahrenheit. At what degree Celsius will the value of the temperature in degrees Fahrenheit be exactly 5 times the value of the temperature in degrees Celsius?
A. 10
B. 20
C. 30
D. 40
E. 50
$\frac{3}{5}$ of the marbles in Box B are equal in number to $\frac{6}{7}$ of the marbles in Box U. There is a total of 85 marbles in the 2 boxes. How many marbles are there in Box U?
A. 35
B. 50
C. 60
D. 70
E. None of the Above
It takes 2 goats and 3 cows 6 days to eat 2 acres of grass. It takes 6 goats and 5 cows 10 days to eat 8 acres of grass. How many days will it take 8 goats and 8 cows to eat 17 acres of grass?
A. 5
B. 12
C. 15
D. 17
E. None of the Above
At a snack bar, the cost of 7 sandwiches, 5 drinks and 1 dessert is $\$32$, while the cost of 10 sandwiches, 7 drinks, and 1 dessert is $\$45$. Find the cost of 1 sandwich, 1 drink, and 1 dessert.
A. $\$6$
B. $\$7$
C. $\$7.50$
D. $\$19$
E. None of the Above
Study the pattern.

What is the value of $x$?
ABCD is a square of side length 12 cm. Point L is any point on side AB. Points H and I divide side AD into three equal parts. Points J and K also divide side BC into three equal parts. Finally, points G, F and E divide side DC into four equal parts. Find the total area (in $\text{cm}^2$) of the shaded region.
The numbers 11, 12, 13, 14, 15, 16, 17, 18 and 19 are placed in the 9 boxes shown below. The numbers 15, 16, and 19 have been placed accordingly. If the sum of the numbers placed horizontally is equal to the sum of the numbers placed vertically, what is the sum of all possible values of 𝑎?
Calculate the following $$192\times(\frac{1}{4\times 7}+\frac{1}{7\times 10}+\frac{1}{10\times 13}+\frac{1}{13\times 16})$$
Tom made number 869 using 19 matchsticks as shown below. He wants to construct the greatest possible four-digit number by moving exactly three matches. Find this greatest possible value.

(The figures of all the digits from 0 to 9 are shown below.)
Several commuters were on a bus when it started its journey from a bus interchange. At the first bus stop, 2 more than 1/3 of the commuters alighted. At the second bus stop, 4 more than 1/3 of the remaining commuters alighted. At the third bus stop, 8 more than 1/3 of the remaining commuters alighted. Then the bus was left with 16 commuters. How many commuters boarded the bus at the bus interchange?
If a three-digit number $\overline{a1b}$ is 9 times the 2-digit number $\overline{ab}$, find the number $\overline{ab}$.
The number of my house is a 4-digit number. One day, on my way home, I accidentally turned the number of my house upside down. I noticed that the new number formed by turning it upside down is bigger than the original number by 4872. What is the number of my house?
Find the value of $$2 + 4 + 8 + ⋯ + 512 + 1024$$
All the sides of the figure below meet at right angles. Use the numbers 1, 2, 3, 4, 5, 6, 7 and 8 to represent the sides $a, b, c, d, e, f, g$ and $h$ in some order. Find the largest possible area of the figure.

SIMOC 2019 - Grade 3

Admin dot — Wed, 17 Jun 2026 07:30:35 +0000

Calculate (20+21+22+...+49+50) - (10+11+12+...+39+40).
A. 290
B. 300
C. 310
D. 320
E. None of the Above
If Δ + Δ + Δ = 36, × Δ = 180, ∎ ÷ = 7, what is the value of ∎?
A. 105
B. 100
C. 120
D. 130
E. None of the Above
Study the pattern below.

What is the value of A?
A. 53
B. 54
C. 55
D. 56
E. None of the Above
Peter decorated his garden by hanging a lantern at each fixed interval of 8 metres, between 2 lampposts. He used 39 lanterns altogether. The distance between the first lamppost and the first lantern is 8 metres, and the distance between the second lamppost and the 39th lantern is also 8 metres. He did not hang any lanterns on the 2 lampposts. What was the distance between the 2 lampposts, in metres?
A. 312
B. 320
C. 328
D. 336
E. None of the Above
Father’s age is 5 times as his son’s age now. If the age of father 16 years ago is equal to the age of his son 12 years from now, how old is father now?
A. 35
B. 40
C. 45
D. 50
E. None of the Above
All of the following figures can be folded to form a cube except for one. Which one is it?
A boy always tells the truth on Mondays and Tuesdays, always tells lies on Saturday, and tells either truth or lies on the rest of the days of the week. For six days in a row, he was asked what his name was and he gave the following answers: Mark, James, Mark, John, James, John. What is the boy’s name?
A. Mark
B. James
C. John
D. James or John
E. Impossible to determine
In the Orchard Garden, there are 500 apple and orange trees. If the number of apple trees is 16 less than twice the number of orange trees, how many apple trees are there?
A. 170
B. 172
C. 328
D. 330
E. None of the Above
Figure 1 is called a “stack map.” The numbers tell how many cubes are stacked in each position. Figure 2 shows these cubes, and Figure 3 shows the view of the stacked cubes as seen from the front.

Which of the following is the front view for the stack map in Figure 4?
Allan, Bob and Charles bought a total of 12 pieces of bread for their breakfast. They agreed to divide the bread equally among the three of them.
At the cashier, Charles forgot to bring his money. As such, Allan paid for the 7 pieces of bread, while Bob paid for the 5 pieces of bread.
They all went home and had their breakfast. After eating all the bread, Charles brought out $\$4$ from his drawer and gave some money to Allan and Bob.
How much money did Allan get from Charles?
A. $\$1$
B. $\$2$
C. $\$3$
D. $\$4$
E. None of the Above
A dictionary uses 1215 digits for its page numbers. How many pages does the dictionary have?
A. 440
B. 441
C. 442
D. 443
E. None of the Above
John, an airline passenger, was bound for London. Upon reaching 1/3 of the total distance, he fell asleep. When he finally woke up, the remaining distance to London was 1/8 of the distance traveled when he was asleep. What fraction of the entire trip was John asleep?
A. 7/12
B. 7/24
C. 2/27
D. 16/27
E. None of the Above
In the following, all the different letters stand for different digits. Find the value of the A + B.

A. 6
B. 7
C. 8
D. 9
E. None of the Above
How many whole numbers smaller than 500 that are divisible by 3 can be formed by arranging the following digits 2, 4, 6 and 9. For each number, each digit can only be used once.

A. 11
B. 12
C. 13
D. 14
E. None of the Above
ABCD is a square. It consists of 2 rectangles, with areas 44$\text{cm}^2$ and 28$\text{cm}^2$, respectively and a smaller square. Find the sum of the areas of the two squares.

A. 65
B. 157
C. 170
D. 185
E. None of the Above
Observe the pattern: $$(2 × 2) − (1 × 1) = 3$$ $$(3 × 3) − (2 × 2) = 5$$ $$(4 × 4) − (3 × 3) = 7$$ $$⋮$$ $$(19 × 19) − (18 × 18) = 𝑨$$ What is the value of 𝐴?
Lisa has 415 cards more than Vincent. John has 926 cards fewer than what Lisa and Vincent have in total. If three of them have 4520 cards altogether, how many cards does Lisa have?
Kendra has a collection of math books, but she can’t remember the exact the number in her collection.
She knew that 3 of her friends Nicole, Mary and Paris borrowed some of the books.
First, Nicole borrowed half of the books plus 1 book. Then Mary borrowed half of the remaining books plus 2 books. Lastly, Paris then borrowed half of the remaining books plus 3 books. Afterwards, there are 2 books left in Kendra’s collection.
How many books are there in Kendra’s collection?
30 students numbered from 1 to 30 were asked to line up in a straight line. The first student in the line was asked to leave, the second student remained. The third student was asked to leave the line, the fourth student remained and so forth. This process was then repeated until there was only one student left in the line. What was the number of the only student left in the line?
5 cows and 6 horses can consume 139 kg of grass each day, while 6 cows and 5 horses can consume 125 kg of grass each day. How much in kilograms, can 1 horse and 1 cow consume each day?
Andrew and Barbara went to the bookstore to buy the same comic book.
Andrew did not bring enough money; in fact, to be able to buy that 1 comic book, he needs an additional $\$28$.
Meanwhile, Barbara, did not bring enough money either; in fact, to be able to buy that 1 comic book, she needs an additional $\$26$.
If Andrew and Barbara combine their money; they will have enough to buy that comic book, and will still have $\$26$ left.
How much does the comic book cost?
How many squares are there in the figure below?
A group of 99 people rented 27 boats, which are of two types. The first type has a capacity of 5 people and costs $\$40$ per boat. The second has a capacity of 3 people and costs $\$30$ per boat. The 99 people perfectly filled all 27 boats. What is the total cost of renting the 27 boats?
In the following, each box represents a single digit. What is the value of A + B + C?
Tom made number 869 using 19 matchsticks as shown below. He wants to construct the greatest possible four-digit number by moving exactly three matches. Find this greatest possible value.

(The figures of all the digits from 0 to 9 are shown below.)

SIMOC 2019 - Grade 2

Admin dot — Wed, 17 Jun 2026 06:36:05 +0000

Calculate (1+11+21+31+41)+(9+19+29+39+49).
A. 70
B. 80
C. 90
D. 100
E. None of the above
If 12+12+12+12+12 = 6×∆ , what is the value of ∆−3?
A. 7
B. 9
C. 11
D. 13
E. None of the above
If (Ο−∆) × (Ο−∆) = 121 and ∆ = 5 , what is value of Ο?
A. 6
B. 11
C. 16
D. 21
E. None of the above
The figure below is made up of several 1×1×1 cubes. How many 1×1×1 cubes make up the entire figure?

A. 24
B. 27
C. 30
D. 33
E. 36
In August 2018, there were 4 Saturdays and 5 Fridays. On what day of the week does August 9, 2018 fall?
A. Monday
B. Tuesday
C. Wednesday
D. Thursday
E. Friday
Study the pattern below:

What number does “?” represent?
A. 12
B. 14
C. 15
D. 16
E. None of the above
Jane, Joan, and Jean are all accountants. They are going to marry the three men named below.
Peter is a lawyer.
Joan will not marry the engineer.
The doctor’s wife is not Joan.
Mike will marry Jane.
Arthur is the engineer.
Who is the doctor?
A. Mike
B. Arthur
C. Peter
D. Cannot be determined
E. None of the above
Which of the following solids can be formed by the net below?
Mary is reading a book. On the first day, she read 8 pages. On each succeeding day, she reads 3 more pages than the previous day. She finishes reading the book by reading 32 pages on the last day. How long does it take Mary to finish reading the entire book?
A. 6
B. 7
C. 8
D. 9
E. None of the above
Find the sum of the next 2 numbers in the sequence 2, 5, 10, 13, 26, 29, ( ), ( ).
A. 119
B. 129
C. 139
D. 149
E. None of the above
Study the picture.

How many squares are needed to balance 1 triangle?
A. 2
B. 3
C. 4
D. 5
E. None of the above
In a game, there were 32 rows of participants. In each row, there were three times as many boys as girls. If there were 24 girls in each row, how many participants took part in the game?
A. 24
B. 72
C. 96
D. 2304
E. 3072
What is “x” in the figure below?
A figure made up of unit cubes appears from the different views. What is the minimum number of cubes which could be used to build this figure?

A. 6
B. 7
C. 8
D. 9
E. 10
Below are four labeled boxes. Each box is painted a different colour. There is a red box, which is next to a blue box. There is a green box, which is next to the red box and a yellow box. Which box could be painted red?

A. 1 only
B. 2 only
C. 3 only
D. 2 or 3
E. 1 or 4
Study the diagram below carefully. What is the missing number?

Question {Trick and additions}{Blue Book}
There are several heroes in 7 Universes: Universe T to Z. Universe T has 51 heroes;
Universe U has 1 more hero than Universe T; Universe V has 1 more hero than Universe
U; so on and so forth. How many heroes are there in total?
A father is 27 years older than his son, Moses. A mother is 24 years older than her son, Moses. The sum of the ages of the father and mother is 93. How old is Moses?
How many whole numbers smaller than 500 that are divisible by 3 can be formed by arranging the following digits 2, 4, 6, and 9? For each number, each digit can only be used once.
The bird feeder has two sections of the same size. The sections are connected internally so that the seeds from the upper section can move to the lower section. When the bird feeder is full, it can feed 6 birds at a time, 3 in the upper section, and 3 in the lower section. When the feeder is filled to its capacity, it takes the 6 birds 9 hours to empty the feeder. The 6 birds eat at the same rate, and they eat until their respective sections are empty. Also, the birds in the upper sections cannot go down the lower section to eat. How long will the 3 birds in the upper section of the feeder feed themselves?
Red had a certain number of bottle caps. He later gave 1/4 of them to Blue and 5/6 of the remainder to Green. If Blue received 40 bottle caps from Red, how many bottle caps did Red have at first?
The students from a primary school are going for a camping trip. If each bus takes 46 students, there will be 12 vacant seats. If each bus takes 37 students, 15 students will not get any seat. How many students are going for the camping trip?
Mr. Lee had some eggs on a tray. If the eggs were divided into groups of 4, 1 egg would be left on the tray. If the eggs were divided into groups of 6, 3 eggs would be left. If the eggs were divided into groups of 7, 5 eggs would be left. What was the least number of eggs Mr. Lee had on the tray?
The yellow, red, blue and green lights are able to make many types of signals. These signals can be made from one light, two lights, three lights or four lights at the same time. How many different signals can these lights make?
In the following, each letter represents a different digit from 0 to 9. What is the value of the sum A+B+C+D?
Tom made number 869 using 19 matchsticks as shown below. He wants to construct the greatest possible number by moving exactly two matches. Find this greatest possible value.

(The figures of all the digits from 0 to 9 are shown below.)

Informasi Lomba

Admin dot — Thu, 16 Apr 2026 01:13:14 +0000

SIMOC

(Singapore International Math Olympiad Challenge)

Singapore International Math Olympiad Challenge (SIMOC) adalah kompetisi matematika internasional bergengsi tahunan di Singapura untuk siswa kelas 1 SD hingga 12 SMA/A-Level. SIMOC memiliki konsep unik kompetisi matematika yang tidak hanya menguji kemampuan Anda dalam menyelesaikan soal matematika di atas kertas, tetapi juga menguji kemampuan Anda untuk bekerja sama dalam tim untuk memainkan permainan matematika interaktif dan memecahkan teka-teki. SIMOC memberi Anda kesempatan untuk bersaing dengan talenta matematika terbaik dari seluruh dunia dan belajar dari satu sama lain sebagai sebuah tim. Penghargaan pengakuan individu dan tim tersedia untuk diperebutkan.

Detail Utama Lomba SIMOC:

Kompetisi Individual: Tes tertulis matematika (25 pertanyaan, 90 menit) untuk SD-SMA.
Kompetisi Tim:
- Maths Warriors: Game strategi berhitung mental.
- Maths Master Mind: Permainan berbasis tim.
Struktur Tim: Siswa bekerja sama dengan rekan dari berbagai negara dalam tim beranggotakan 3 orang.
Penyelenggaraan: Biasanya diadakan pada bulan Juli di Singapura.
Kualifikasi: Peserta umumnya lolos seleksi melalui lomba seperti SASMO (Silver/Gold) atau SMGF.
Fokus: Menekankan pada penalaran logis, permainan matematika interaktif, dan kolaborasi.
Pendaftaran: Dapat dilakukan melalui situs resmi simoc.simcc.org dengan membuat akun terlebih dahulu.

SIMOC bertujuan membina bakat matematika muda dan mempromosikan interaksi internasional dalam suasana kompetisi yang suportif. Peserta juga berkesempatan mengikuti berbagai aktivitas tur di Singapura.