Compute the average angular acceleration and the angular displacement during the 2 seconds a rotating object speeds up from 0.5 rad/s to 0.7 rad/s.

a = 0.1 rad/s\textsuperscript{2}~$\Delta\theta$~= 0.3 radians

a = 0.2 rad/s\textsuperscript{2~}$\Delta\theta$~= 0.5 radians

a = 0.1 rad/s\textsuperscript{2~}$\Delta\theta$~= 1.2 radians

a = 0.2 rad/s\textsuperscript{2~}$\Delta\theta$~= 1.2 radians

Overseas Competition->Knowledge Point->Number Theory Modules


A 35 kg child ziplines from rest on a platform 12 m high to the ground with negligible friction. In the last 8 m of the zipline, which is approximately horizontal, a braking mechanism applies a constant force opposing the motion to slow the child down so that she\textquotesingle s traveling at 2.5 m/s when she finally lands on the safety padding at the end. The padding compresses for1.5 s when the child lands on it and stops.  $\textasciitilde$  What is the magnitude of the force applied by the braking mechanism?


The $$7$$-digit number $$\overline{123P688}$$ is divisible by $$8$$. How many possible values are there for $$P$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders


What is the value of the digit $7$ in the number $32.679$?

seven hundred

\emph{seventy}

seven tenths

seven hundredths

seven thousandths

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits


George buys boxes of mangoes for $$$16$$ each and sells them for $$$23$$ per box. How many boxes of mangoes would he have to sell to make $$$56$$?


Find a whole number between $$0$$ and $$100$$ that has the following properties.  When the number is divided by $$5$$ the remainder is $$4$$.  When the number is divided by $$6$$ the remainder is $$0$$.  When the number is divided by $$7$$ the remainder is $$0$$.  What is the number?

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder ->Questions Involving Remainders


l am a four$$-$$digit number. The digit in the ones place is $$9$$. The digit in the thousands place has a value of $$1000$$. The digit in the tens place is twice the digit in the hundreds place. What number am I?

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers


Without calculating, determine if the following sums are odd or even.  $$25\times 3$$ is an~\uline{~~~~~~~~~~}~number，$$45\times 2$$ is an~\uline{~~~~~~~~~~}~number，$$33\times 5\times 7\times 9\times 8\times 11\times 13$$ is an~\uline{~~~~~~~~~~}~number． ~\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}

odd, odd, even

odd, even, odd

odd, even, even

even, odd, even

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers


Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Multiples and Least Common Multiples->Least Common Multiple of Two Numbers


Putting these lines~$\left\textbar{} \right\textbar$ round a number or calculation makes sure the answer is positive; for example both $\left\textbar{} 8\right\textbar$~and $\left\textbar{} -8\right\textbar$~ would give the answer $8$.What is the answer to:$10-\left\textbar{} 4-20\right\textbar$


Adil says "I have chosen a prime number less than $$20$$. It is one more than a multiple of $$4$$."  How many possible numbers could Adil have chosen?

Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers->Knowing Prime and Composite Numbers


With how many zeroes does the product of the first $$2006$$ consecutive prime numbers end?

Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization->The Number of Zeros at the end of a Product


The $$4$$-digit number $$6H74$$ is divisible by $$11$$. What is $$H$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules


Adam wrote out all the numbers from $$1$$ to $$60$$ inclusive. How many times did he use the digit $$5$$? ($$2008$$ Math Kangaroo Problem, Level $$1-2$$, Question \#$$15$$)

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value->Questions Involving Applying Place Value Principle


Yes

No


\textbf{Sums of squares}  Exactly one of these statements is correct. Which one?  Circle the correct answer:．

Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Questions involving Square Numbers


What is the size of a rectangle if the original $$15 cm$$ length is reduced by $40\textbackslash\%$~and the $$12 cm$$ width is reduced by $50\textbackslash\%$?

$$6cm\times 3cm$$

$$7cm\times 3cm$$

$$4cm\times 3cm$$

$$9cm\times 6cm$$

$$9cm\times 7cm$$


How many of the following statements are true?  ($$A$$) If a number $$A$$ is a multiple of $$4$$, then any multiple of $$A$$ is a multiple of $$4$$.  ($$B$$) If $$4$$ is a factor of $$A$$, then any multiple of $$4$$ is also a multiple of $$A$$  ($$C$$) If both number $$A$$ and number $$B$$ are multiple of $$4$$, Then $$A+B$$ is a multiple of $$4$$.  ($$D$$) If a number $$B$$ is a multiple of $$20$$, then $$B$$ is a multiple of $$4$$.

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples


A seven-digit number $$\overline{579A379}$$ is divisible by $$11$$. Which number does $$A$$ represent? ．


I multiply a whole number by $$3$$.  Which of the following could be my answer?


If $1a2a3a4a5a$ is divisible by $11$, what is the value of $a$?


There are~\uline{~~~~~~~~~~}~common multiples of $$3$$ and $$4$$ that are smaller than $$30$$.

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples


Find the difference in the values of digit $$4$$ in $$4100$$ and $$8340$$.


Which of the following prime factorizations below is correct?

Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization


What is the total value of all the odd numbers between $$34$$ and $$42$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers


In a restaurant, there are $$7$$ tables with $$2$$ chairs each; $$5$$ tables with $$4$$ chairs each; $$4$$ tables with $$6$$ chairs each and one table with 8 chairs. If each chair is used by $$5$$ customers who spend $$$20$$ per day, what is the total daily revenue of all the chairs?


How many perfect cubes lie between 2\textsuperscript{8}~+1 and 2\textsuperscript{18}+1, inclusive?

Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers


In $$47186$$, the digit $$7$$ stands for．

$$7$$ ten thousands

$$7$$ thousands

$$7$$ hundreds

$$7$$ tens


Is the answer of 1+2+3+4+5+6+\ldots+23 an odd number or even number?

Odd

Even


Which \textbf{ONE~}of the following numbers is \textbf{NOT} divisible by $$3$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules->Simple Questions of Division without Remainders


A large cuboid box measures~$$9 cm \times 15 cm \times 12 cm$$. How many cubes with an~edge length of $$3 cm$$ can fit in this large box?

Overseas Competition->Knowledge Point->Number Theory Modules


The five-digit number $24x8y$ is divisible by $$4$$, $$5$$, and $$9$$. The sum of the digits $$x$$ and $$y$$ is equal to ．


The diameter of an iron atom is $0.000000014$ inches, what is the diameter of an iron atom written in scientific notation?

$1.4\times 10^{8}$ inches

$1.4\times 10^{-8}$ inches

$0.14\times 10^{9}$ inches

$0.14\times 10^{-9}$ inches

Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->The Relationship between Exponents and the Number of Factors


Several different positive integers are written on the board. Exactly two of them are divisible by $$2$$ and exactly $$13$$ of them are divisible by $$13$$. Let $$M$$ be the greatest of these numbers. What is the smallest possible value of $$M$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules->Questions Involving Properties of Dividing without Remainders


Adam wrote out all the numbers from $$1$$ to $$60$$ inclusive. How many times did he use the digit $$5$$?


What is the sum of all the prime numbers are between $$10$$ and $$20$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers


How many digit 1 can you see below?  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases


Which of these numbers is exactly divisible by $$3$$ and $$9$$?

N/A.  Revise from (GL Assessment book$$1$$《Paper $$2$$》 $$6$$ years Question \#$$23$$)


Barry wrote 6 different numbers, one on each side of 3 cards, and laid the cards on a table, as shown. The sums of the two numbers on each of the three cards are equal. The three numbers on the hidden sides are prime numbers. What is the average of the hidden prime numbers?

Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers


There~are eighteen squares, when placed next to each other in two rows, that fit exactly into a rectangle. If the perimeter of a square is $$4 cm$$, what is the perimeter of the rectangle?


Overseas In-curriculum->Knowledge Point->Algebra->Numbers and Figures->Patterns in Number Sequences


A number is greater than $$15$$ but smaller than $$20$$. It is divisible by $$2$$ and $$3$$. What is this number?~\uline{~~~~~~~~~~}~

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders


A number when divided by $$5$$ gives a quotient of $$170$$ and a remainder of $$4$$.What is the number?

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder


What is the difference between the largest $$5$$-digit number and the smallest $$6$$-digit number?~\uline{~~~~~~~~~~}~

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value


Which one of the following is an odd number?


There~are 18 squares, when placed next to each other in 2 rows, that fit exactly into a rectangle. If the perimeter of a square is $$4 cm$$, what is the perimeter of the rectangle?


Adam wrote out all the numbers from $$1$$ to $$60$$ inclusive. How many times did he use the digit $$5$$? ($$2008$$ Math Kangaroo Problem, Level $$1-2$$, Question \#$$15$$)

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value->Questions Involving Applying Place Value Principle


One day Randy was bored and he wrotre all the whole numbers from 49 to 97 on his paper. How many times did he write the digit \textquotesingle\textquotesingle8\textquotesingle\textquotesingle{} on his paper?

None of the above

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits


Grandmother baked cookies for her grandchildren, some of whom were going to visit her that day. She wanted each of her grandchildren to have the same number of cookies, but she forgot if three, five, or six grandchildren were coming. So, she baked enough cookies so that there would be an equal number for every grandchild regardless of how many visited. Which of these could be the number of cookies Grandmother baked?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Word Problems Involving Factors and Multiples->Multiples Word Problems


Which of the following is a set of prime numbers?

$$1$$, $$5$$, $$37$$, $$41$$

$$2$$, $$77$$, $$86$$, $$13$$

$$3$$, $$11$$, $$29$$, $$41$$

$$9$$, $$13$$, $$56$$, $$79$$


Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders


If n is an even positive integer, the double factorial notation n!! represents the product of all the even integers from 2 to n. For example, $8!!=2\cdot4\cdot6\cdot8$. What is the units digit of the following sum?  $2!!+4!!+6!!+\cdot\cdot\cdot+2018!!+2020!!+2022!!$

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples


The smallest positive integer greater than $1$ that leaves a remainder of $1$ when divided by $4$, $5$, and $6$ lies between which of the following pairs of numbers?

$$2$$ and $$19$$

$$20$$ and $$39$$

$$40$$ and $$59$$

$$60$$ and $$79$$

$$80$$ and $$124$$


The muzzle velocity of a 0.003-kg paintball pellet is 90 m/s. If it takes 0.002 s for the pellet to be shot from the paintball gun, what is the average force of the recoilon the paintball gun?


a

B

c

D

Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization


In $$39$$, the value of the digit in the tens place is．

$$3$$ ones

$$30$$ ones

$$30$$ tens

$$30$$ hundreds

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers


Which of the following is not a multiple of $6$?

$$(49+35)\times 6$$

$$(49-35)\times 42$$

$$24\times 12-1$$

$$35\times 6+48$$


The value of the side of a square is a prime number and which of the following statements is true?

The value of its area is a prime number

The value of its area is a composite number

It can not be determined whether the value of its area is a prime number or not.


Which of the following numbers is not divisible by $$2$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules


How many zeroes does the number $$12^{2}\times15^{3}$$ end with?

Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization->The Number of Zeros at the end of a Product


Elmo is packing $$107$$ cookies. He wants to put $$5$$ cookies exactly in each plastic bag. How many cookies will not be packed into plastic bags?


Determine if the result of~$$1+2+3+4+5+6\cdots\cdots+99+100$$~is an odd or even~number.

Odd

Even

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers


There are $$17$$ children participating in a competition. The competition requires them to divide into $$4$$ teams on the average. How many more children are needed for this competition?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders->Guessing Dividends


George has $$120$$ stamps; Gina has $$220$$ stamps and John has $$320$$ stamps. If all the stamps were mixed together and redistributed to these three children, how many stamps would each person get?

Overseas Competition->Knowledge Point->Number Theory Modules


Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn\textquotesingle t know her house number. She tells him, "My house number has two digits, and exactly three of the following four statements about it are true."  (1) It is prime.  (2) It is even.  (3) It is divisible by $7$.  (4) One of its digits is $9$.  This information allows Malcolm to determine Isabella\textquotesingle s house number. What is its units digit?


In a cricket match, George scores double~the runs in each round compared to the one before. If George scored $$1$$ run in the first round, in which round did he score $$32$$ runs?


Which of the following statements is correct?

$$4$$ is a factor of $$38$$.

$$6$$ is a factor of $$72$$.

$$8$$ is a common factor of $$72$$ and $$84$$.

$$9$$ is a common factor of $$38$$ and $$72$$.

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples


Adrian has two ribbons of length $$12 \rm{cm}$$ and $$30 \rm{cm}$$. He cuts each ribbon into shorter pieces of equal length. Every shorter piece from both ribbons is of the same length. What is the greatest length of each shorter piece?

None of the above


Without calculating, determine if the sum of $$1+2+3+\cdots +1993$$ is an odd or even number.

Odd

Even


What is the remainder when dividing the sum: $$2001+2002+2003+2004+2005$$ by $$2004$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder ->The additive property of the remainder


A ball is thrown from the top of a building, and each time the ball bounces to half of its previous height. If the height of the building is $$1024m$$, what is the height it bounces to on the fifth bounce?


How many factors of 2020 have more than 3 factors? (As an example, 12 has 6 factors, namely 1,2,3,4,6 and 12)


After adding a two-digit number $$N$$ and a two-digit number that has the same digits as $$N$$ but written in reverse order, we got a square of a natural number as result. How many such numbers $$N$$ are there?

other answer

Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers


Divide $$74$$ by $$6$$. The remainder is ．

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders->Relationship between Dividend, Divisor, Quotient and Remainder in Division


The smallest positive integer greater than $1$ that leaves a remainder of $1$ when divided by $4$, $5$, and $6$ lies between which of the following pairs of numbers?

$2$ and $19$

$20$ and $39$

$40$ and $59$

$60$ and $79$

$80$ and $124$


on

off


Which \textbf{ONE~}of the following numbers is \textbf{NOT} divisible by $$25$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules->Simple Questions of Division without Remainders


A number is called flippy if its digits alternate between two distinct digits. For example, 2020 and 37373 are flippy, but 3883 and 123123 are not. How many five-digit flippy numbers are divisible by 15?


How many squares of 5cm side can fit in a square of $$20cm$$ side?


How many hundreds are there in eight million?

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value


Jack and Linda participated in the school activity, got a total of $90$ dollars of charity money. Linda got $10$ dollars more than Jack, how many dollars of charity money did Jack get?


How many multiples of $5$ are there from $1$ to $50$?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples


N/A.  (US $$2004$$ Math kangaroo Problems, Level $$7-8$$, Question \#$$3$$)$$


What is the next square number after $$49$$?  Choose the answer.


There are $15$ floors in a building, and every two floors have the same number of stairs. They tell us that person $A$ goes up the stairs twice as fast as person $B$, so they both start on floor $1$, and when person $B$ gets to floor $6$, which floor is Person $A$ on?

on the $11$th floor

on the $12$th floor

on the $8$th floor

on the $6$th floor

on the $7$th floor


When t = 4, which answer is the odd one out?

$t + 2$

$32 \div t$

$t + 4$

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers


All~\uline{~~~~~~~~~~}~numbers are divisible by $2$.

even

odd


$$10^{2}$$;~$$10^{1}$$;~$$10^{0}$$; $$111$$

$$5^{2}$$;~$$5^{1}$$;~$$5^{0}$$; $$117$$

$$5^{2}$$;~$$5^{1}$$;~$$5^{0}$$; $$31$$

$$10^{2}$$;~$$10^{1}$$;~$$10^{0}$$; $$432$$

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Properties and Applications of Number Bases


$$6$$ hundreds $$+ 48$$ thousands $$=\square $$  What is the missing number in the box?


A bicycle wheel with a diameter of 62.2 cm and a rotational inertia of 0.40 kg·m\textsuperscript{2} is rotating at a rate of 8 rad/s when the brakes are applied. The brakes apply a normal force of 85 N on the brake pad at the edge of the wheel.The coefficient of kinetic friction between the brake pad and the wheel is 0.32. How long does it take for the bicycle to stop?


Let $N$ be the greatest five-digit number whose digits have a product of $120$. What is the sum of the digits of $N$?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples


How many positive factors does $$23,232$$ have?

Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization


A number is opposite to $$-\frac{1}{3}$$ and the aboslute value of that number is~\uline{~~~~~~~~~~}~.


A ball is thrown from the top of a building and each time the ball bounces to half of its previous height. If the height of the building is $$512$$ meters, which time does it bounce when it bounces to a height of $$16$$ meters?


What is seventy thousand and fourty-one in figures?

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits


What is the probability of getting an letter grade that is lower than $B$ from "THINK ACADEMY"?


Find the difference between $56$ hundreds and $19$ tens and $5$ ones.

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases


In the apartment building where Linda lives, $13$ floors above the ground are residential buildings, and $2$ underground floors are parking lots. When Linda takes the elevator from the 2nd underground floor to the $26$th floor. How many floors does the elevator go up?


a

B

C

d


Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn\textquotesingle t know her house number. She tells him, "My house number has two digits, and exactly three of the following four statements about it are true."  (1) It is prime.  (2) It is even.  (3) It is divisible by 7.  (4) One of its digits is 9.  This information allows Malcolm to determine Isabella\textquotesingle s house number. What is its units digit?


Seven million, three hundred and eight thousand and twenty-eight in numerals is．

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers


I\textquotesingle m thinking of a number.  When I divide the number by $$5$$, its quotient is $$43$$ and its remainder is $$3$$.  What is the number?

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders

Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Division of Whole Numbers->Division with Remainder->Meaning of Division with Remainders


Which one of the following numbers has $$4$$ as a factor?


The numbers $1$, $2$, $3$, $7$, $8$, $10$, $14$ and $15$ are divided into groups of one or more numbers. The sum of the numbers in each group is the same. Which of the following can be the sum of the numbers in each group?

Overseas Competition->Knowledge Point->Number Theory Modules


How many hundreds are there in eight million?


How many factors of $2020$ have more than $3$ factors? (As an example, $12$ has $6$ factors, namely $1$,$2$,$3$,$4$,$6$ and $12$)


Bud is setting a problem for \textquotesingle Find the Number!\textquotesingle{}  She wants the number to be $$75$$.  Her first two clues are:  Clue $$1$$: The number is a factor of $$150$$.  Clue $$2$$: The number is a multiple of $$3$$.  What should her third clue be to completely identify the number?

The number is divisible by $15$.

The number is divisible by $25$.

The number is a two-digit number.

The number is an odd number.

The number is a prime number.


Adil says "I have chosen a prime number less than $$20$$. It is one more than a multiple of $$4$$."  How many possible numbers could Adil have chosen?

Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers->Knowing Prime and Composite Numbers


Divide $$74$$ by $$6$$. The remainder is ．


Two numbers have infinite amount of~\uline{~~~~~~~~~~}~.

multiples

least common multiples

factors

greatest common factors

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Multiples and Least Common Multiples


How many times does the number $$2$$ appear when counting from $$1$$ to $$43$$?


Change a digit of the number $12315$ to make the new five-digit number be divisible by $25$. What is the new five-digit number?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules


Which answer is \textbf{NOT} a square number?

Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers


Ravi divides a large number by a smaller number.  The remainder is $$5$$.  Which of these numbers could he have divided by?

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders->Feature of Remainder


Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->The Relationship between Exponents and the Number of Factors


An ice cream stand was selling ice cream in five different flavors. A group of children came to the stand and each child bought two scoops of ice cream with two different flavors. If none of the children chose the same combination of flavors and every such combination of favors was chosen, how many children were there?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Word Problems Involving Factors and Multiples->Multiples Word Problems


One class is on PE class. If each row is $12$ people, the last row is $8$ people. If each row is $15$ people, the last row is $11$ people. Two student of the class were sick and absent from the PE class. How many students are there in the class?


Odd

Even

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers


The characteristic of numbers that are divisible by $$9$$ is．

Last digit is divisible by $$9$$.

Last two digits are divisible by $$9$$.

The sum of digits is divisible by $$3$$.

The sum of digits is divisible by $$9$$.

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders


George buys boxes of mangoes for $$$18$$ each and sells them for $$$25$$ per box. How many boxes of mangoes would he have to sell to make $$$63$$?


The teacher writes a two-digit number on the whiteboard, then writes the smallest one-digit number to its right, and at last, adds $$11$$ to the number. The teacher gets a sum of $$111$$. ~Which two-digit number did the teacher write at first on the whiteboard?


What is thirty million, fourty-five thousand, five hundred and three in figures?

3 450 503

3 045 503

30 045 053

30 450 503

30 045 503


How many divisors does the number $$ 2\times 3\times5\times7\times11$$ have?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Theorem of the Number of Factors of a Number->Applying Theorem of the Number of Factors of a Number Directly->The Total Number of Factors


The children go outing together, the number of the first team is more than the second team, the number of first team is less than the third team. The number of fourth team is more than the second team. Which group has the most people?

team $3$

team $1$

team $2$

team $4$

None of them above


A number gives a remainder of $$1$$ when divided by $$5$$, a remainder of $$2$$ when divided by $$6$$, and a remainder of $$9$$ when divided by $$11$$. What is the smallest number?

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems


109 divided by a 2-digit number has a remainder of 4. How many such 2-digit numbe are there?


Which of the following is not a multiple of $$8$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples


The 5-digit number~\uline{2018U}~is divisible by 9. What is the remainder when this number is divided by 8?


a

B

c

d

Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization


What is the theoretical probability of getting an "$A$" from "THINK ACADEMY"?


A large clinical trial was designed to determine whether a certain vitamin improves the general health of adults.The investigators first identified 85 variables that measure various aspects of the general health of adults. Because each adult in the clinical trial was to serve as his or her own control, the 85 variables were measured for each adult, both before taking the vitamin and after taking the vitamin for three months. The investigators then performed 85 matched-pair t-tests, one for each variable. They found statistically significant results at the 0.05evel in 2 of the variables, both in the direction of improved general health. Which of the following should the investigators conclude?

There is evidence that the vitamin improves the health of adults because 2 of the 85 tests were statistically significant.

There is evidence that the vitamin improves the health of adults because in clinical trials investigators typically underestimate the proportion of the population that is helped by a vitamin.

There is insufficient evidence that the vitamin improves the health of adults because at the 0.05 significance level, one could easily get statistically significant results in 2 out of 85 tests just due to chance variability.

There is insufficient evidence that the vitamin improves the health of adults because the sample size of 85 is not large enough to draw a conclusion.

No conclusion can be drawn because an even number of variables is needed for a matched-pairs design.


Take a piece of string of length $8$, fold it in half $3$ times, cut it down the middle with scissors, and get some short string. So how many ropes are there of length $1$?


When a number is divided by $$8$$, the quotient and the remainder are the same. which of the following is the number?


A wall measures $$\rm 8m$$ by $$\rm 20m$$.  Pip wants to wallpaper this wall with square pictures.  What is the length of the largest picture he can use so that all of the wall will be covered?

$$\rm 2m$$

$$\rm 3m$$

$$\rm 4m$$

$$\rm 5m$$

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Factors and the Greatest Common Factors->The Greatest Common Factor of Two Numbers


Which one of these numbers has exactly two different prime factors?  $$42\textasciitilde\textasciitilde\textasciitilde11\textasciitilde\textasciitilde\textasciitilde26\textasciitilde\textasciitilde\textasciitilde49\textasciitilde\textasciitilde\textasciitilde30$$


There are $$100$$ cars and motorcycles parked in a parking lot. If there are $$360$$ wheels in total, how many motorcycles are parked there?


Which of the following is the correct expression of the base $7$ numeral system?

$\left (3423\right )\_5$

$\left (5143\right )\_6$

$\left (3256\right )\_7$

$\left (3634\right )\_5$

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Properties and Applications of Number Bases


989 pieces of candy are packed into packages, each of which contains 4 pieces of candy. In order to complete the last package, how many more pieces of candy are needed?

None of the above


What number between 37 and 47 is exactly divisble by both 2 and 3?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples


Which of the following is a prime number? ．

Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers


a

b

c

d


Which of the following statements is incorrect?

$$3$$ is a multiple of $$39$$

$$2$$ is a common factor of $$26$$ and $$54$$

$$52$$ is a multiple of $$13$$

$$6$$ is a common factor of $$18$$ and $$72$$


There is a three-digit number. The hundreds digit of the number is $$6$$ more than the smallest even number. The tens digit is the smallest odd number and this number is a multiple of both $$2 $$ and $$5$$ . What is this number? ．

Overseas Competition->Knowledge Point->Number Theory Modules


The first four numbers of a sequence are $$12$$, $$15$$, $$18$$, and $$21$$. What is the difference between the sixth and tenth numbers of this sequence?


Which of the numbers below is odd regardless of the value of the natural number $$n$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Mixed Calculations of Odd and Even Numbers


Which of these numbers is not a prime number?

Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Prime Factorization (Equations)


Today, the restaurant sold $$5$$ sandwiches, and $$3$$ less than hamburgers. How many sandwiches and hamburgers did the restaurant sell today?


The numbers $1$, $2$, $3$, $5$, $6$, $7$ and $8$ are divided into groups of one or more numbers. The sum of the numbers in each group is the same. Which of the following can be the sum of the numbers in each group?

$$8$$ or $$16$$


Which of the following numbers is not an integer? ($$2015$$ Math Kangaroo Problem, Level $$7-8$$, Question \#$$6$$)

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers


How many three-digit numbers are there such that the sum of their digits equals $$4$$? (2001 Math Kangaroo Problem, Level 3-4, Question \#20)

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits


Determine if the results of the following are odd or even numbers.

Odd

Even


Chris bought $$$89.90$$ worth of groceries and paid $$10$$\% GST (Goods and Services Tax) for them. How much did he pay in total?


Which of the following numbers is a multiple of $$25$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules


Alice and Sara made a total of $26$ cookies. Sara\textquotesingle s number of cookies is three times that of Alice, and there are two more. How many cookies did Sara make?


odd

even


Which number is divisible by both $$3$$ and $$4$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules->Simple Questions of Division without Remainders


George has $$46$$ stamps; Gina has $$28$$ stamps and John has $$22$$ stamps. If all the stamps were mixed together and redistributed to these three children, how many stamps would each person get?


When three identical rectangles are placed next to each other, they form a square. If the area of a rectangle is $$48$$ square centimetres, what is the length of the rectangle?


A person pushes a 60 kg grocery cart, initially at rest, across a parking lot. He exerts a pushing force directed 20$^{\circ}$~below the horizontal. If the person pushes the cart with a force of 300 N for 5 m across horizontal ground and then releases the cart, the cart has a speed of 3 m/s. What is the work done by friction during this motion?


If $n$ is an even positive integer, the double factorial notation $n!!$ represents the product of all the even integers from $2$ to $n$. For example, $8!!=2\cdot4\cdot6\cdot8$. What is the units digit of the following sum?  $2!!+4!!+6!!+\cdot\cdot\cdot+2018!!+2020!!+2022!!$

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples


Lily cut a disc~with a radius of $$10 cm$$ from the middle. What is the circumference of each half disc after cutting?($\pi=3$)

$$20 cm$$

$$30 cm$$

$$40 cm$$

$$50 cm$$

$$60 cm$$


When you divide a natural number $$n$$ by $$7$$, you get a remainder of $$4$$. When you divide the number $$n$$ by $$11$$ you also get a remainder of $$4$$. What is the smallest value of $$n$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder ->Questions Involving Remainders


There are $$19$$ girls and $$12$$ boys in the school yard. At least how many students need to join them so that six groups with the same number of students can be formed?


The $$5$$-digit number $$2022U$$ is divisible by $$11$$. What is the remainder when this number is divided by $$4$$?


There are $$13$$ coins in John\textquotesingle s pocket,and each of them is either a $$5$$ cent coin or a $$10$$ cent coin. Which of the numbers below cannot be the total value of John\textquotesingle s coins?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Word Problems Involving Factors and Multiples->Multiples Word Problems


Which of the following is a common factor of $$12$$ and $$16$$?


Which of the following shows a set of prime numbers?

$$1$$, $$5$$, $$37$$, $$41$$

$$2$$, $$77$$, $$86$$, $$13$$

$$3$$, $$11$$, $$29$$, $$41$$

$$9$$, $$13$$, $$56$$, $$79$$


Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders


A number is multiplied by itself.  The answer is $$64$$. What is the number?  Choose the answer.

Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers


$$8$$, $$9$$

$$9$$, $$21$$

$$11$$, $$21$$

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples


Jack knot the $5$ ropes together in sequence, into a long rope, how many knots on this long rope?

There is no right answer.


（$$2016$$ Maha Bodhi School, Topical Assessment $$1$$, Primary Two, Question \#$$6$$）  Use the digits below to form the geatest $$3-$$digit even number.  $$0$$~ ~ $$9$$~ ~ $$5$$~ ~ $$7$$  Which is the greatest $$3-$$digit even number?

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers


Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems


A given number is a multiple of $$6$$. It is between $$10$$ and $$20$$. It is also a factor of $$24$$. What is the number?


If a number is divisible by $$66$$ then it must also be divisible by.

$$5$$ and $$3$$

$$3$$ and $$11$$

$$9$$ and $$4$$

$$6$$ and $$6$$


The remainders of 5543 when divided by 4 and 9 respectively are ．

1, 8

3, 7

3, 8

1, 7


If I switch the digits in the two digit-number which expresses my father\textquotesingle s age, I will obtain a number that expresses my age. Which of the following numbers can express my father\textquotesingle s age when I was born?

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value->Questions Involving Applying Place Value Principle


An object is thrown upwards with an initial velocity of 20 m/s. What is the object\textquotesingle s velocity after 2 seconds? Assume no air resistance.

0 m/s

10 m/s upwards

20 m/s upwards

30 m/s upwards


The 5-digit number~\uline{2018U}~is divisible by 9. What is the remainder when this number is divided by 8?


What is the value of $81$ tenths, $\frac{28}{25}$ and $0.139$?

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases


a

b

c

d


Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization


Which of the following numbers is divisible by $$11$$?


If the length of each side of a rectangle increases by $20\textbackslash\%$, by what percentage does the area of the rectangle increase?

Overseas Competition->Knowledge Point->Number Theory Modules


Researchers investigated whether a new process for producing yarn could reduce the mean amount of volatile organic compounds (VOCs) emitted by carpet. From random samples of carpets, the researchers found the mean reduction of VOCs emitted by carpets made with yarn produced by the new process compared with thatof carpets made with yarn produced by the traditional process was 13 parts per million (ppm). All conditionsfor inference were met, and the p-value for the appropriate hypothesis test was 0.095. Which of the following statements is the best interpretation of the p-value?

The probability that the null hypothesis is true is 0.095

The probability that the alternative hypothesis is true is 0.095

The probability of observing a mean reduction of 13 ppm is 0.095

If the null hypothesis is true, the probability of observing a mean reduction of at least 13 ppm is 0.095

If the null hypothesis is true, the probability of observing a mean reduction of at most 13 ppm is 0.095


When 4 identical rectangles are placed next to each other, they form a square. If the area of a rectangle is $$16$$ square centimetres, what is the length of the rectangle?


The positive integer N is such that the product of its digits is $45$.  Which of the following could not be the product of the digits of $N+1$？


Which of these numbers are prime numbers?  $2\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} 6\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} 7\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} 9\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} 12\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} 15$

$2$ and $9$

$6$ and $7$

$9$ and $15$

$2$ and $7$

Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers->Judging Prime and Composite Numbers


On the number line, any number on the left side of the origin is ．

Positive number

Negative Number

Non-postive number

Opposite Number


a

b

c

d

Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers


l am a four$$-$$digit number. The digit in the ones place is $$9$$. The digit in the thousands place has a value of $$1000$$ The digit in the tens place is twice the digit in the hundreds place. What number am I?

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers


When a number is divided by $$8$$, the quotient and the remainder are the same. which of the following is the number?

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders


The main difference between a $\chi^{2}$ test for independence and a~$\chi^{2}$ test for homogeneity of proportions is which of the following?

They are based on a different number of degrees of freedom.

One of the tests is for a two-sided alternative and the other is for a one-sided alternative.

In one case, two variables are compared within a single population. In the other case, two populations are compared in terms of a single variable.

For a given value of $\chi^{2}$, they have different P-values.

There are no differences between the tests. They measure exactly the same thing.


How many of the numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, and $$9$$ can be written as a sum of two of the other numbers?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders


John, George and Oscar ran around the circular track in the same direction at the same time. John took 16 seconds, George took $$20$$ seconds, and Oscar took $$30$$ seconds. If they continue to chase each other, when will they meet again at the starting point?

$$6$$ hours

$$1$$ day

$$4$$ minutes

$$124$$ minutes

$$9$$ hours


Emma, Gina and Lisa ran a $$400$$-metre circular track in the same direction at the same time. Emma took $$54$$ seconds, Gina took $$45$$ seconds, and Lisa took $$48$$ seconds. If they continue to chase each other, when will they meet again at the starting point?

$$36$$ hours

$$25$$ days

$$36$$ minutes

$$216$$ minutes

$$39$$ hours


Which of these statements is always true?

If there are at least two twos in a number then it must be a multiple of two.

If a number ends in five then it must be a multiple of $25$.

If the last two digits in a number are a multiple of four then the number must be a multiple of four.

If a number is an even number then it must be a multiple of $4$.

If the sum of all the digits in a number is a multiple of five then the number must be a multiple of five.


The first four numbers of a sequence are $$1$$, $$4$$, $$7$$, and $$10$$. What is the difference between the sixth and tenth numbers of this sequence?


An apple, $2$ pears and a strawberry together weigh $$12$$ pounds. $3$ apples and a strawberry weigh $$10$$ pounds. A pear and a strawberry together weigh $$2$$ pounds more than an apple. How much does an apple weigh?

$$1$$ pounds

$$2$$ pounds

$$3$$ pounds

$$4$$ pounds

$$5$$ pounds


Which of the following numbers are not divisible by $5$?


A simple pendulum swings about the vertical equilibrium position with a maximum angular displacement of 5° and period T. If the same pendulum is given a maximum angular displacement of $$ 10^{\circ} $$, then which of the following best gives the period of the oscillations?

$$ \frac{T}{2} $$

$$ \frac{T}{\sqrt{2}} $$

T


$$989$$ pieces of candy are packed into packages, each of which contains $$4$$ pieces of candy. In order to complete the last package, how many more pieces of candy are needed?

None of the above

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules


Which of the following is not a prime number?


There are $$19$$ apples in $$4$$ baskets. John wants $$4$$ baskets to have the same weight. How many apples should he pick up at least?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders->Guessing Dividends


Which one of the following numbers is a factor of $$24$$?


If a four-digit number $$A4A8$$ can be divisible by $12$, the digit that $$A$$ represents is  .


Find the largest whole number between $$76$$ and $$91$$ that is divisible by $$4$$ and $$5$$.

None of the above


How many months of the year have exactly $$30$$ days?

None of the above


Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers


What is the remainder when $$17+18+19$$ is divided by $$4$$ ．

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder


a

B

c

d


a

b

c

d

e


Teacher Lele\textquotesingle s school bought $35$ more boxes of white chalk than colored chalks, and the number of boxes of white chalk was $5$ times more than that of colored chalks, $3$ more boxes. How many boxes of white chalk and colored chalks did the school buy?

8; 43

7; 43

6; 43

8; 42

7; 42


Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->The Relationship between Exponents and the Number of Factors


What is the quotient when $$525$$ is divided by $$5$$?


Helen\textquotesingle s age is a factor of 120 and is an odd number. Her mother gave her a polaroid camera as a birthday present for her 6th birthday. How old is she?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples


What is the smallest mumber bigger than $$2007$$, in which the sum of its digits is equal to the sum of the digits of $$2007$$?


How many three-digit numbers are there such that the sum of their digits equals $$4$$? (2001 Math Kangaroo Problem, Level 3-4, Question \#20)

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits


In the four-digit number $192N$, what value of $N$ will allow the four digit number to be divisible by $6$?


For a positive integer~~the factorial notation $n!$ represents the product of the integers from $n$ to $1$ (For example,~$6!=6\cdot5\cdot4\cdot3\cdot2\cdot1$) What value of $N$ satisfies the following equation? $5!\cdot9!=12\cdot N!$

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples


A

B

c

d


How many factors do $8, 12$ and $20$ have in common?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Factors and the Greatest Common Factors->The Greatest Common Factor of Multiple Numbers


When you divide a natural number $$n$$ by $$7$$, you get a remainder of $$4$$. When you divide the number $$n$$ by $$11$$ you also get a remainder of $$4$$. What is the remainder when $$n$$ is divided by $$77$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder ->Questions Involving Remainders


Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Factors and the Greatest Common Factors->The Greatest Common Factor of Two Numbers


What is the length of a pendulum whose period, at the equator, is 1 s?

Overseas Competition->Knowledge Point->Number Theory Modules


What is the sum of the first four odd numbers?

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers


There are~\uline{~~~~~~~~~~}~common multiples of $$6$$ and $$8$$ that are smaller than $$50$$.

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples


On the number line, any number on the right side of the origin is ．

positive number

negative Number

non-postive number

opposite Number


Adrian has two ribbons of length $$12 \rm{cm}$$ and $$30 \rm{cm}$$. He cuts each ribbon into shorter pieces of equal length. Every shorter piece from both ribbons is of the same length. What is the greatest length of each shorter piece?

None of the above

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders


Tintin is taller than Tiantian, Amy is shorter than Tiantian. Do you know which child is the tallest?

Amy

Tintin

Tiantian

They have the same height

None of them above


Use the graph to find the profit the monopoly makes with the socially efficient price regulation. Is it positive, negative, or zero?

Positive

Negative

Zero

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases


I have two equations: one multiplication and one division.  Is it possible for both these equations to contain the exact same numbers, but in different places, and have different final answers?

Yes

No


Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders


The sum of 2 SAME digits is ODD or EVEN?

Odd

Even


A two-digit number can be divided by both $$3$$ and $$5$$. It is also an even numebr. How many such numbers are there?

None of the above


Which of these numbers is exactly divisible by $$2$$ and $$3$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules->Simple Questions of Division without Remainders


What is the quotient when $$525$$ is divided by $$5$$?


Find the smallest prime number that is greater than $90$.

Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers


How many expressions following have two-digits quotients?  $$750\div 7$$~ ~ ~$$75\div 7$$~ ~ ~ $$750\div 8$$~ ~ ~$$705\div 7$$

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Short Division


After the first blow, the balloon becomes two times as~big as the original. And after the second blow, the size of the balloon becomes four times the original size. Each time the balloon is blown, the size of the balloon becomes twice as large as the last time. How many times does the balloon become the original after the sixth blowing?


What is the average power used to pitch a 0.142 kg baseball at 42 m/s, if it takes 0.3 s to accelerate it from rest?


A

B


After the first blow, the balloon becomes two times as~big as the original. And after the second blow, the size of the balloon becomes four times the original size. Each time the balloon is blown, the size of the balloon becomes twice as large as the last time. How many times the does balloon become the original after the sixth blowing?


Find the difference between the values of the digit $$5$$ in $$5034$$ and $$3054$$.

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers


On the number line, any number on the left side of the origin is ．

Positive number

Negative number

Non-positive number

Opposite number


How many numbers are there from $34$ to $82$? (including both $34$ and $82$)

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers


Use the octal system (base-$8$ numeral system) to calculate $\left (773\right )\_8 + \left (6\right )\_8$. The answer should be~\uline{~~~~~~~~~~}~.

$\left (1001\right )\_8$

$\left (779\right )\_8$

$\left (111\right )\_8$

$\left (781\right )\_8$

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Properties and Applications of Number Bases


The remainder of dividing $$3^{20}\times 5^{30}-2$$ by $$15$$ equals．


The North lighthouse flashes every $$20$$ seconds.  The South lighthouse flashes every $$25$$ seconds.  The two lighthouses have just flashed at the same time.  How many seconds will it be before they next flash at the same time?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Word Problems Involving Factors and Multiples->Multiples Word Problems


Which one of the following numbers is a factor of $$24$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples


At a restaurant, every $$2$$\textsuperscript{nd} customer is given a free drink, every $$5$$\textsuperscript{th}~customer is given a free sweet and every $$9$$\textsuperscript{th} customer is given a free chocolate bar. Lynn was given all three gifts on her first visit. Given that she was among the first $$100$$ customers, what was Lynn\textquotesingle s queue number?


A number when divided by $$5$$ gives a quotient of $$170$$ and a remainder of $$4$$.What is the number?

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder


Person $A$ has six times as many storybooks as $B$. If each of them buys two more, $A$ has four times as many books as $B$. How many storybooks does $A$?


Tom bought $$$100$$ worth of groceries and paid $$10$$\% GST (Goods and Services Tax) for them. How much did he pay in total?


The perimeter of a rectangle is $$18cm$$. Assuming that the side lengths are integers, how many different cases are there for the area of this rectangle?


In order to take the OC exam, John spent five weeks practising the OC exercises. In the first week, he practised one set of OC exercises. Since then, he had practised twice as many times each week as the previous before. How many sets of exercises did John practise in total while preparing for the OC exam?


A department store manager wants to know if a greater proportion of customers on the store\textquotesingle s mailing list would redeem a coupon for $\textbackslash$$5 off the price of an item than would redeem a coupon for 10 percent off the price of anitem. The manager mails a $\textbackslash$$5 off coupon to a random sample of 500 customers and mails a 10 percent off coupon to an independent random sample of 500 customers. The number of coupons of each type that were redeemed was recorded. Assuming that the conditions for inference are met, what test procedure should be usedto answer the manager\textquotesingle s question?

A one-sample t-test for a mean

A one-sample z-test for a proportion

A t-test for the slope of a regression line

A matched-pairs t-test for a mean difference

A two-sample z-test for a difference between two proportions


$\textasciitilde$  The digit $$3$$ in $$7.934$$ stands for $$3$$．

ones

tens

tenths

hundredths

Overseas In-curriculum->Knowledge Point->Knowing Numbers->Decimals->Meaning for Decimals ->Decimal Place Value


What is the quotient when $$525$$ is divided by $$5$$?


With how many zeroes does the product of the first $$2006$$ consecutive prime numbers end?

Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization->The Number of Zeros at the end of a Product


There is a three-digit number. The hundreds digit of the number is $$6$$ more than the smallest even number. The tens digit is the smallest odd number and this number is a multiple of both $$2 $$ and $$5$$ . What is this number?

Overseas Competition->Knowledge Point->Number Theory Modules


A

B

c

d

Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization


The answer of the following equation:  $$(203+204+\ldots \ldots +288)-(49+50+51+\ldots \ldots +131)$$ is an~\uline{~~~~~~~~~~}~number.

odd

even


A two-sample t-test of the hypotheses H\textsubscript{0} :~$\mu\_{1}-\mu\_{2}$~= 0 versus H\textsubscript{a}~:~$\mu\_{1}-\mu\_{2}$ \textgreater{} 0 produces a p-value of 0.03. Which of the following must be true?  $\textasciitilde$ I. A 90 percent confidence interval for the difference in means will contain the value 0.  $\textasciitilde$ Il. A 95 percent confidence interval for the difference in means will contain the value 0.  $\textasciitilde$ II. A 99 percent confidence interval for the difference in means will contain the value 0.

I only

III only

I and II only

Il and III only

I, Il, and I


When a number is divided by $$9$$, it gives a quotient of $$23$$ and a remainder of $$5$$. What is the number?


a

b

c

d

e

f

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules


Which of the following is the correct expression of the base $7$ numeral system?

$\left (3423\right )\_5$

$\left (5143\right )\_6$

$\left (3256\right )\_7$

$\left (3634\right )\_5$


Without calculating, determine if the answer is an odd or even number.  $$33 \times 7 \times 11$$ is an~\uline{~~~~~~~~~~}~number, $$28 \times 9 \times 4$$ is an~\uline{~~~~~~~~~~}~number.

odd, even

even, even

even, odd

odd, odd

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Multiplication Rules of Odd and Even Numbers


There are~\uline{~~~~~~~~~~}~common multiples of $$6$$ and $$8$$ that are smaller than $$50$$.

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples


The least whole number whose digits add up to $$82$$ hasdigits.


a

b

c

d


How many zeroes does the number $$2^{29}\times5^{10}$$ end with?


Which of these numbers is a factor of $12$?


In the $$3$$-digit number $$2M4$$ is divisible by $$6$$, what is the smallest value of the digit $$M$$?

None of the above

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders


When my number is divided by $$3$$, I have a quotient of $$15$$ and a remainder of $$2$$.  What number am I?

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders


Which of the following is the correct expression of the base-$7$ numeral system?

$\left (3423\right )\_5$

$\left (5143\right )\_6$

$\left (3256\right )\_7$

$\left (3639\right )\_7$


The correct prime factorization of number $84$ is ．

$$1\times 2\times 2\times 2\times 7$$

$$14\times 6$$

$$7\times 12$$

$$2\times 2\times 3\times 7$$


Which of the following is a factor of $21$?

Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers


A number when divided by $$5$$ has a quotient of $$62$$ and a remainder of $$3$$.  What is the number?


What is the square root of the number whose square is $$16$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers


Which of the following numbers is divisible by $$4$$?


Which \textbf{ONE~}of the following numbers is \textbf{NOT} divisible by $$3$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules->Simple Questions of Division without Remainders


The smallest positive integer greater than 1 that leaves a remainder of 1 when divided by 4, 5, and 6 lies between which of the following pairs of numbers?

2 and 19

20 and 39

40 and 59

60 and 79

80 and 124


Elmo is packing 107 cookies. He wants to put 5 cookies in each plastic bag. How many cookies will not be packed into plastic bags?


Which of the following is a factor of 36?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples


In the number $$67 543$$, the digit~\uline{~~~~~~~~~~}~is in the ten thousands place.

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers


a

b


a

b

c

d

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases


In the number $2.369$ what does the $6$ mean?

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits


Simplify the following fraction using GCF:  $\dfrac{16}{54}=$

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Factors and the Greatest Common Factors


In a car race, George was $$50$$ metres behind Chris and $$40$$ metres ahead of John. Emma was $$60$$ metres behind George. What is the distance between the first car and the last car?


There are~\uline{~~~~~~~~~~}~common multiples of $$6$$ and $$8$$ that are smaller than $$50$$.


If~no adjacent digits that are identical are written down, then how many digits are required to write down the numbers from $$5$$ to $$85$$?


How many perfect cubes lie between $2^{8}+1$ and $2^{18}+1$, inclusive?

Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers


If the length of a simple pendulum is doubled, its period will

decrease by 2

increase by 2

decrease by~$\sqrt{2}$

increase by~$\sqrt{2}$


The sum of the following equation:  （203 + 202 + \ldots\ldots{} + 288）-（49 + 50 + 51 + \ldots\ldots{} + 131） is an~\uline{~~~~~~~~~~}~number.

odd

even

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers


If a four-digit number $$7A2A$$ can be divisible by $15$, the digit that $$A$$ represents is  .


If the length of each side of a rectangle increases by $10\textbackslash\%$, by what percentage does the area of the rectangle increase?

Overseas Competition->Knowledge Point->Number Theory Modules


Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Division of Whole Numbers->Dividing Multi-digit Numbers by 1-digit Numbers->Mental Calculation Involving Dividing Multi-digit Numbers by 1-digit Numbers


If~no adjacent digits that are identical are written down, then how many digits are required to write down the numbers from $$1$$ to $$99$$?


Several different positive integers are written on the board. Exactly two of them are divisible by $$2$$ and exactly thirteen of them are divisible by $$13$$. Let $$M$$ be the greatest of these numbers. What is the smallest possible value of $$M$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules->Questions Involving Properties of Dividing without Remainders


Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn\textquotesingle t know her house number. She tells him, "My house number has two digits, and exactly three of the following four statements about it are true."  (1) It is prime.  (2) It is even.  (3) It is divisible by $7$.  (4) One of its digits is $9$.  This information allows Malcolm to determine Isabella\textquotesingle s house number. What is its units digit?


The sum of two numbers is 300. One number is 5 times of the other number.  What is the difference between the two numbers?

None of the above


Which of the following numbers is divisible by $$9$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules


$$9 132 500 = 9 000 000+132 000+$$$\square$  What is the missing number in the box?

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value


When two pieces of cloth of the same length are sold, the first piece is $10$ meters. When the second piece is sold $7$ meters, the second piece is four times as long as the first one. How many meters are the second cloth originally?


Which of the following numbers is both an even number and a cube number?

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Multiplication Rules of Odd and Even Numbers


Two apples cost $10$ cents, and two peaches cost $4$ cents. How much do one apple and one peach cost in total? (Adapted from 2019 Math Kangaroo Problem, Level 1-2, Question \#8)

$5$ cents

$6$ cents

$7$ cents

$8$ cents

$9$ cents


What number between $37$ and $47$ is exactly divisble by both $2$ and $3$?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples


Teacher Angel wrote the numbers $1$ to $20$ on a blackboard. How many times is the digit \textquotesingle$1$\textquotesingle{} written on the board?


What is three million, ninety thousand and four in numeral?

Overseas In-curriculum->Knowledge Point->Knowing Numbers->Whole Numbers->Knowing Numbers Beyond 10000->Reading and Writing Large Numbers


Lan is $$2\textasciitilde cm$$ taller than George and George is $$3\textasciitilde cm$$ shorter than Kelly. If the Kelly is $$147\textasciitilde cm$$, what is Lan\textquotesingle s height?


Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Multiples and Least Common Multiples->Least Common Multiple of Two Numbers


Tom drove the car for $$150$$ km and consumed a quarter of the fuel tank. The average fuel consumption of this car is $$10$$ km/litre. If the fuel cost is $$$1.20$$ per litre, how much would he have to pay to fill an entire empty tank?


John buys a farm with $$25$$ rabbits and chickens. If there are $$80$$ legs in total, find the number of chickens on the farm.


Eight days after the day before yesterday is Friday. Which day of the week is tomorrow?

Friday

Saturday

Sunday

Thursday

None of the above

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems


Using the octal system (base $6$ numeral system) to calculate $\left (243\right )\_6 + \left (15\right )\_6$, the answer should be．

$\left (302\right )\_6$

$\left (258\right )\_6$

$\left (331\right )\_6$

$\left (262\right )\_6$

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Properties and Applications of Number Bases


Is $$123$$ divisible by $$11$$? If not, what is the remainder? ．

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Congruence


In the relay race, Tom ran $$100$$ metres in $$11$$ seconds and George ran $$10$$ metres more than Tom in the same time. What is the total distance covered by Tom and George?


$$7$$ and $$9$$

$$8$$ and $$9$$

$$9$$ and $$21$$

$$11$$ and $$21$$

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples


I am thinking of a number. The number is smaller than $$40$$.  It can be found in both the multiplication tables of $$6$$ and $$8$$.  What number am I thinking of?


For a positive integer~~the factorial notation n! represents the product of the integers from n to 1 (For example,~$6!=6\cdot5\cdot4\cdot3\cdot2\cdot1$) What value of N satisfies the following equation? $5!\cdot9!=12\cdot N!$

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples


How many positive three-digit integers have a remainder of 2 when divided by 6, a remainder of 5 when divided by 9, and a remainder of 7 when divided by 11?


Which of the following statements is incorrect?

$$108$$ is a multiple of $$3$$ and $$9$$

$$105$$ is a multiple of $$5$$, but it is not a multiple of $$10$$

$$164$$ is a multiple of $$4$$

$$134$$ is a multiple of $$6$$


A 90 percent confidence interval for the slope of a regression line is determined to be (-0.181, 1.529). Which of the following statements must be true?

The correlation coefficient of the data is positive.

The sum of the residuals for the data based on the regression line is positive.

A scatterplot of the data would show a linear pattern.

The slope of the sample regression line is 1.348.

The slope of the sample regression line is 0.


In the number $$67 543$$, the digit~\uline{~~~~~~~~~~}~is in the ten thousands place.

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers


A cube~box with a size of~$$15 cm \times 15 cm \times 15 cm$$ is used to hold small cubes. The size of small cubes is $$3 cm \times 3 cm \times 3 cm$$. How many small cubes can this large cube box hold?


Write $$32$$ hundreds and $$4$$ ones in numerals.


Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers


A survey of a random sample of 210 male teens and 228 female teens, ages 13 years to 17 years, found that 122 of the male teens and 160 of the female teens brush their teeth at least twice a day. If there is no difference between the proportions in the population of all male and female teens ages 13 years to 17 years who brush their teeth at least twice a day, approximately how many males and females in the sample would be expected to brush their teeth at least twice a day?

105 males and 114 females

122 males and 160 females

135 males and 147 females

141 males and 141 females

219 males and 219 females


Gary, Ivan and Martin are doing arithmetic problems. The number of problems Gary does is three times that of Martin, and the number of problems Ivan does is two times that of Gary. Ivan does 15 to more problems than Martin. How many questions did they do altogether?


What is the sum of the digits in the number $$2009$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits


I am thinking of a number. The number is smaller than $$40$$. It can be found in both the multiplication tables of $$6$$ and $$8$$. What number am I thinking of?


The teacher writes a one-digit number first on the whiteboard, then writes the largest single digit to its right, and at last, adds $$38$$ to the number. The teacher gets a sum of $$117$$. Which one-digit number did the teacher write at first on the whiteboard?

Overseas Competition->Knowledge Point->Number Theory Modules


A number when divided by $$5$$ has a quotient of $$62$$ and a remainder of $$3$$.  What is the number?

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders


For any positive integer M, the notation M! denotes the product of the integers 1 through M. What is the largest integer n for which 5n is a factor of the sum 98! + 99! + 100! ?


Cut four identical squares with a perimeter of $$4 cm$$ each at~the corner out~of a $$15 cm \times 6 cm$$ rectangle. What is the perimeter of the rest~of~the shape?


A 40-kg box slides down an incline that is angled 30$^{\circ}$ above the horizontal. The box starts from rest at a height of 8 m, and the coefficient of kinetic friction is 0.2. What is the total work done on the box as it slides to the bottom of the incline?


During Easter, tickets are $$$6$$ for a single person and $$$18$$ for a family ($$2$$ adults and $$2$$ children). What is the difference in price between $$4$$ single tickets and a family ticket?


Find the difference between the values of the digit $$5$$ in $$5034$$ and $$3054$$.


If I fold a square into two equal parts, the two parts can\textquotesingle t be

rectangle

parallelogram

square

trapezoid

triangle


The houses on the street where Teacher Miu lives are numbered from 1 to 35.  How many times does the digit 3 appear in the numbering of those houses?~\uline{~~~~~~~~~~}~


Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders


A large cuboid box measures~$$28 cm \times 16 cm \times 8 cm$$. How many cubes with an~edge length of $$4 cm$$ can fit in this large box?


A

B

C

D


hundreds

thousands

ten thousands

hundred thousands


There are four different natural numbers, the sum of any two of them is a multiple of $$2$$, and the product of any three numbers is a multiple of $$3$$. In order to make the sum of these four numbers as small as possible, these four numbers are ．


Which one of the following statements is true?

If you add two odd numbers you always get an odd number.

If you multiply two odd numbers you always get an even number.

If you add an odd and an even number you always get an even number.

If you multiply an odd and an even number you always get an even number.

If you multiply two even numbers you always get an odd number.

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers


Ming, Liang and Gang went fishing. They counted the number of fish they caught and found that Ming caught $4$ times as many fish as Liang caught, Liang caught $5$ fewer fish than Xiao Gang caught, Gang caught $7$ fewer fish than Ming caught. How many fish did Ming catch？


There is a $$4$$-digit number.  The first digit and the last digit of the number are even.  The difference between the first digit and the last digit of the number is $$2$$.  The digit in the hundreds place is the sum of the digit in the thousands place and tens place.  What is the number?

Overseas In-curriculum->Knowledge Point->Fun Problems in Math->Reasoning


In the number $$67 543$$, the digit~\uline{~~~~~~~~~~}~is in the ten thousands place.


The radius of a circle is $$\frac{1}{2}$$~the length of the side of the square. How many times the perimeter of a square is the diameter of a circle?


The store sold $25$ red balloons and blue balloons. The number of red balloons sold is four times that of blue balloons. How many red balloons and blue balloons are sold respectively?

$$5$$ and $$20$$

$$18$$ and $$7$$

$$15$$ and $$10$$

$$20$$ and $$5$$

$$21$$ and $$4$$


In the number $$3602$$, the digit \textquotesingle$$6$$\textquotesingle{} is in the．

tens place.

hundreds place.

thousands place.

ones place.

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases


How many prime numbers are between $$10$$ and $$20$$.

Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers


I am thinking of a number. The number is smaller than $$40$$. It can be found in both the multiplication tables of $$6$$ and $$8$$. What number am I thinking of?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples


George buys boxes of mangoes for $$$16$$ each and sells them for $$$23$$ per box. How many boxes of mangoes would he have to sell to make $$$56$$?


Which of the following statements is correct?

$$4$$ is a factor of $$38$$.

$$6$$ is a factor of $$72$$.

$$8$$ is a common factor of $$72$$ and $$84$$.

$$9$$ is a common factor of $$38$$ and $$72$$.


$14532$ can be written as $10000 + 4000 + 500 + 30 + 2$  What is the value of the 6 in the number $3796423$?

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value->Expression of Place Value Principle


John, George and Oscar ran around the circular track in the same direction at the same time. John took $$6$$ seconds, George took $$20$$ seconds, and Oscar took $$30$$ seconds. If they continue to chase each other, when will they meet again at the starting point?

$$6$$ hours

$$1$$ day

$$4$$ minutes

$$124$$ minutes

$$9$$ hours


Which one of these numbers has exactly two different prime factors?  $$78\textasciitilde\textasciitilde\textasciitilde105\textasciitilde\textasciitilde\textasciitilde121\textasciitilde\textasciitilde\textasciitilde97\textasciitilde\textasciitilde\textasciitilde183$$

Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers->Knowing Prime and Composite Numbers


Let N be the greatest five-digit number whose digits have a product of 120. What is the sum of the digits of N?


Ellie travels 65km each month starting from March. Ryan travels 80km each month starting in June.  In which month will Ellie and Ryan have an equal total distance travelled?

July

August

September

October

November


Cut four identical squares~at~the corner out~of a $$15 cm \times 6 cm$$ rectangle. The perimeter of the 4 squares is 4 cm each. What is the perimeter of the rest~of~the shape?


Choose the number that can be divided exactly by both $$2$$ and $$5$$.

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Word Problems Involving Factors and Multiples->Multiples Word Problems


Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Factors and the Greatest Common Factors->The Greatest Common Factor of Two Numbers


With how many zeros does the product of the first $$10$$ consecutive prime numbers end?

Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization->The Number of Zeros at the end of a Product


Let $N$ be the greatest five-digit number whose digits have a product of $120$. What is the sum of the digits of $N$?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples


I am a $2$ digit number.  When $2$ is subtracted from me and the answer is doubled,  I am the same $2$ digit number with my digits reversed.  What number am I?

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value->Questions Involving Applying Place Value Principle


Which one of the following numbers has the digit `$$3$$' in the ten thousands place?

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers


A pie is $3$ dollars more expensive than $2$ donuts and a biscuit. A donut, a biscuit and a pie are $22$ dollars in total. A pie is $10$ dollars more expensive than a donut. How much are $2$ donuts, a biscuit and a pie in total?

$$15$$ dollars

$$20$$ dollars

$$22$$ dollars

$$25$$ dollars

$$27$$ dollars


Find the smallest prime number that is greater than $$70$$.


The month of December of a certain calendar year has exactly $$5$$ Saturdays and $$4$$ Sundays. On which day of the week does the first day of December fall?

Monday

Tuesday

Wednesday

Thursday

None of the above

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems


Which one of the following is not a common factor of $$24$$ and $$32$$?


How many factors of $2020$ have more than $3$ factors? (As an example, $12$ has $6$ factors, namely $1$,$2$,$3$,$4$,$6$ and $12$)


Which of the following statement is correct?

$$7$$ is a factor of $$28$$

$$12$$ is a multiple of $$8$$

$$3$$ is a common factor of $$18$$ and $$32$$

$$24$$ is a common multiple of $$6$$ and $$14$$


There is a row of chairs with $27$ seats, in order to make the person to go to sit at any position are adjacent to the original person. How many people should sit first at least?

Overseas Competition->Knowledge Point->Number Theory Modules


Last year, Gina saved $$$4$$ in January, $$$8$$ in February, $$$12$$ in March, $$$16$$ in April, and so on. She saved $$$48$$ in December. How much money did Gina save in total over the last year?


How many squares of 4cm side can fit in a square of $$16cm$$ side?


Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders


The sum of the digits of the $$10$$-digit number is $$9$$. What is the product of the digits of this number?

$$9\times 8\times 7\times \cdots \times 2\times 1$$


I am thinking of a number. The number is smaller than $$40$$. It can be found in both the multiplication tables of $$6$$ and $$8$$. What number am I thinking of?


$$40509$$  What is this number in words?

Four thousand five hundred and nine

Four thousand and fifty-nine

Fourty thousand fifty hundred and nine

Fourty thousand and fifty-nine

Fourty thousand five hundred and nine

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits


Odd

Even

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers


For a positive integer~~the factorial notation $n!$ represents the product of the integers from $n$ to $1$ (For example,~$6!=6\cdot5\cdot4\cdot3\cdot2\cdot1$) What value of $N$ satisfies the following equation? $5!\cdot9!=12\cdot N!$


There are three whole number $A$, $B$, $C$. $A\times B=91$, $B\times C=112$, $$B\neq1$$. $A+B+C=$~\uline{~~~~~~~~~~}~.

Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization


There are only apple trees and pear trees in the orchard. The number of apple trees is three times that of pear trees. Pear trees are 12 less than apple trees. How many fruit trees are there in the orchard？


After adding a two-digit number $$N$$ and a two-digit number that has the same digits as $$N$$ but written in reverse order, we got a square of a natural number as result. How many such numbers $$N$$ are there?

other answer

Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers


What is the remainder when dividing the sum: $$2001+2002+2003+2004+2005$$ by $$2004$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder ->The additive property of the remainder


Which of the following prime factorization is correct?

$$85=5\times 17$$

$$64=8\times 8$$

$$52=1\times 2\times 2\times 13$$


There is a balance and four weights $$1$$g, $$2$$g, $$5$$g and $$10$$g. If Sara wants to weigh an object weighing $$8$$g, how many weights should she use at least?


There are boys and girls swimming in the swimming pool. The number of boys is four times that of girls. There are $6$ girls less than boys. How many children are swimming in the swimming pool in total?


Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders


Which of the following numbers are divisible by $3$?


In $$7108$$, the digit $$1$$ is in the  place.

ones

tens

hundreds

thousands


a

b

c

d

e


A number when divided by $$5$$ has a quotient of $$62$$ and a remainder of $$3$$.  What is the number?


Which one of the following numbers has $$4$$ as a factor?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples


Elmo is packing $$107$$ cookies. He wants to put $$5$$ cookies exactly in each plastic bag. How many cookies will not be packed into plastic bags?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules


Ali surveyed 200 students at a school and recorded the eye color and the gender of each student. Of the 80 male students who were surveyed, 60 had brown eyes. If eye color and gender are independent, how many female students surveyed would be expected to have brown eyes?


Five-digit number $$63\square 25$$ can be divisible by $$45$$. What digit should be filled in the $$\square $$?


Suppose N is a whole number.  If N satisfies that $\dfrac{N}{10}+\dfrac{N}{15}$~is also an integer, how many such N\textquotesingle s are there within 100?


Which answer is \textbf{NOT} a square number?

N/A.  Revise from (GL Assessment book$$2$$《Paper $$4$$》 $$6$$ years Question \#$$9$$)


If two different natural numbers have the same digits but in reverse order, each number is called the palimage of the other.  For example, 12 and 21 are palimages of~each other.  What is the maximum difference between two-digit palimages？


The five-digit number $$25M48$$ is a multiple of $$9$$. What digit does $$M$$ represent?

None of the above


If I switch the digits in the two digit-number which expresses my father\textquotesingle s age, I will obtain a number that expresses my age. Which of the following numbers can express my father\textquotesingle s age when I was born?


All natural numbers from $$1$$ to $$1000$$ were written down. How many times was the digit $$4$$ used?


A rocket of mass m is launched with kinetic energy K\textsubscript{0~}from the surface of the Earth. How much less kinetic energy does the rocket have at an altitude of two Earth radii in terms of the gravitational constant, G; the mass of the Earth, m\textsubscript{E}; the radius of the Earth, R\textsubscript{E}; and the mass of the rocket?


Which of the following statements is correct?

$$4$$ is a factor of $$38$$.

$$6$$ is a factor of $$72$$.

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples


With how many zeros does the product of the first $$10$$ consecutive prime numbers end?


During Easter, tickets are $$$4$$ for a single person and $$$12$$ for a family ($$2$$ adults and $$2$$ children). What is the difference in price between $$4$$ single tickets and a family ticket?


There are $$34$$ children at a game carnival. They are being grouped to form a complete team of $$7$$ players. How many children will not be able to form a complete team?


Which of the following numbers is an odd number? ．

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers


Using the octal system (base-$8$ numeral system) to calculate $\left (773\right )\_8 + \left (6\right )\_8$, the answer should be．

$\left (111\right )\_8$

$\left (779\right )\_8$

$\left (781\right )\_8$

$\left (801\right )\_8$

$\left (1001\right )\_8$

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Properties and Applications of Number Bases


$$2$$ tens

$$28$$ tens

$$2$$ tens $$8$$ ones

$$20$$ tens $$8$$ ones


Without calculating, can you quickly determine whether the result of each expression is even or odd? Choose the right answer.  (1) $$18-9-14+8+3$$．  (2) $$18+28+19-7+29$$．

(1) Even; (2) Odd

(1) Even; (2) Even

(1) Odd; (2) Even

(1) Odd; (2) Odd

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Addition and Subtraction Rules of Odd and Even Numbers


The three ropes are $126$ meters long. The first root is twice as large as the second root, and the second root is twice as large as the third root. How long are the each three ropes?

$72$, $36$, $18$

$72$, $24$, $30$

$72$, $44$, $10$

$72$, $20$, $34$

$72$, $46$, $8$


Only one of the following three numbers is a square number. Which one is it?


The four-digit number $$17X8$$ is divisible by $$3$$. If $$X$$ is an odd digit, find the value of $$X$$.

None of the above


Overseas In-curriculum->Knowledge Point->Algebra->Numbers and Figures->Patterns in Number Sequences


The five digit number $$154xy$$ is divisible by $$72$$. What is the value of $$x+y$$?


Which one of the following numbers has $$4$$ as a factor?


How many multiples of $$3$$ are there between $$13$$ and $$101$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples


What is the highest common factor of $$12$$ and $$18$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Factors and the Greatest Common Factors->The Greatest Common Factor of Two Numbers


a

B

c


Which of the following numbers is divisible by $$3$$?


Which of the following numbers cannot be written as the sum of $$4$$ consecutive whole numbers?

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder


How many times does the number $$9$$ appear when counting from $$10$$ to $$120$$ ?

Overseas Competition->Knowledge Point->Number Theory Modules


A

B

C

D


If~no adjacent digits that are identical are written down, then how many digits are required to write down the numbers from $$2$$ to $$99$$?


Which one of the following is an odd number?


What is one million, nine hundred and two thousand and twenty-eight in numerals?

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers


Which of the following numbers has the digit $$6$$ in the hundreds place?


The value of the digit $$3$$ in $$93412$$ is．


The radius of a circle is $$\frac{1}{3}$$~the length of the side of the square. How many times the perimeter of a square is the diameter of a circle?


a

b

c

d

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases


John and Ali start counting on from $$0$$.  They each count on in steps of a different size.  The first number that John and Ali both reach is $$120$$.  What size steps could they have been counting in?

$$10$$ and $$12$$

$$11$$ and $$13$$

$$9$$ and $$14$$

$$8$$ and $$15$$

$$6$$ and $$20$$

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Word Problems Involving Factors and Multiples->Multiples Word Problems


Divide $$74$$ by $$6$$. The remainder is ．

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders->Relationship between Dividend, Divisor, Quotient and Remainder in Division


What number between $37$ and $47$ is exactly divisble by both $2$ and $3$?


Grandpa Gao is in the habit of taking a walk after dinner. One day, he walked along the road at an even speed. It took him $12$ minutes to walk from the first tree to the $13$th tree. Grandpa Gao walked a few more trees and then went back. When he reached back to the fifth tree, it took him $50$ minutes. So which tree grandpa Gao reached when he decided to walk back?

There is no right answer.


Which of the following numbers are not divisible by $2$?


Without calculating, determine if the following sums are odd or even.  $$25+33-14+525$$ gives an~\uline{~~~~~~~~~~}~number, while $$675-312-13+256$$ gives an~\uline{~~~~~~~~~~}~number．

odd, even

even, odd

odd, odd

even, even

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers


The four-digit number $$\overline{764Z}$$ is divisible by $$9$$. What is the value for $$Z$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders


How many positive three-digit integers have a remainder of $2$ when divided by $6$, a remainder of $5$ when divided by $9$, and a remainder of $7$ when divided by $11$?

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems


Which one of these numbers has exactly three different prime factors?

Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers->Knowing Prime and Composite Numbers


The digit $$3$$ in $$7.934$$ stands for $$3$$．

ones

tens

tenths

hundredths

Overseas In-curriculum->Knowledge Point->Knowing Numbers->Decimals->Meaning for Decimals ->Decimal Place Value


What is the sum of all the prime numbers between $$10$$ and $$20$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers


Lan is $$2\textasciitilde cm$$ taller than George and George is $$3\textasciitilde cm$$ shorter than Kelly. If Kelly is $$147\textasciitilde cm$$, what is Lan\textquotesingle s height?


What is the difference between the third multiple and the seventh multiple of $$7$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples


If the digit $$4$$ is replaced by the digit $$3$$ in each of the numbers below, which number is reduced by the largest amount?

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value->Applying Place Value Principle in Calculation


Which one of the following numbers is not divisible by $$11$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules->Simple Questions of Division without Remainders


Which one of the following numbers is a multiple of 8?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples


The houses on the street where John lives are numbered from $$1$$ to $$24$$. How many times does the digit $$2$$ appear in the numbering of those houses?

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value->Questions Involving Applying Place Value Principle


Which of the following is not a prime number?

Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers


The radius of a circle is $$\frac{1}{2}$$~the length of the side of the square. How many times the perimeter of a square is the diameter of a circle?

Overseas Competition->Knowledge Point->Number Theory Modules


A $$4$$-digit number $$\overline{56\square3}$$ is divisible by $$9$$, find the number in the $$\square$$.

None of the above


The perimeter of a rectangle is $$14 cm$$. Assuming that the side lengths are integers, how many different cases are there for the area of this rectangle?


Lily has a total of 1$8$ pink skirts and blue skirts. The number of pink skirts is twice that of blue skirts. How many pink skirts are more than blue skirts?


The first common multiple of $$6$$ and $$8$$ is．

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples


Divide $$438$$ by $$8$$.~ What is the remainder?

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders


Is $$1234$$ divisible by $$11$$? If not, what is the remainder? ．

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Congruence


If~no adjacent digits that are identical are written down, then how many digits are required to write down the numbers from $$7$$ to $$86$$?


o(╥﹏╥)o Teacher Jihan is sick today and he can\textquotesingle t make it to the office hour. His body temperature is the LCM of $2$ and $19$ ℃. What is his body temperature now?

Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Factors and the Greatest Common Factors


In order to take the OC exam, John spent five weeks practising the OC exercises. In the first week, he practised one set of OC exercises. Since then, he had practised twice as many times each week as the previous week. How many sets of exercises did John practise in total while preparing for the OC exam?


The rabbit pulled out $10$ radishes. If it pulled out $2$ more radishes, the rabbit pulled out twice as many radishes as the gray rabbit. How many radishes did the little grey rabbit pull?


Which value does the $$2$$ in $$352107$$ represent?

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value->Expression of Place Value Principle

N/A.  revise from (GL Assessment book$$1$$《Paper $$2$$》 $$6$$ years Question \#$$1$$)


The teacher writes a two-digit number on the whiteboard, then writes the smallest one-digit number to its right, and at last, adds $$11$$ to the number. The teacher gets a sum of $$117$$. ~Which two-digit number did the teacher write at first on the whiteboard?


Which of the following number is a multiple of $2$?


Which of the numbers below is odd regardless of the value of the natural number $$n$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Mixed Calculations of Odd and Even Numbers


Jack is $8$ years old and her mother is $34$ years old. How old is Jack when her mother is $3$ times as old as Xiao Dong?


If the four-digit number $$147B$$ is divisible by $$3$$, how many possible values are there for the digit $$B$$?

None of the above

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders


Riley had $$4$$ dollar in her piggy bank on $$1^{st}$$ December $$2022$$, which is a Thursday. She will put $$1$$ into the piggy bank every Monday, Wednesday, Friday and Sunday. On which day would she reach $$$16$$ in her piggy bank?

Friday

Sunday

Monday

Wednesday

Tuesday

Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems


Jim and Adam participated in the shooting competition. Jim\textquotesingle s score was three times that of Adam. Adam was $18$ points less than Jim. How many points did Jim and Adam get together?


Amy wants to set a $4-$digit password, and she uses the following rules:  The first digit is the least composite number, and the second digit is both an even number and a prime number. The third digit is the least odd number and the last digit is both an odd number and a composite number.  What is her password?

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers


Which one of the following numbers is not divisible by $$99$$?


In a certain mumber, the first digit is greater than the second digit by $$2$$, and the second digit is greater than the third digit by $$3$$. It is one of the numbers listed below. What number is this? ($$2007$$ Math Kangaroo Problem, Level $$1-2$$, Question \#$$19$$)


There are $$45$$ students in Year $$3$$. One out of nine participated in the debate. How many students did~not participate in the debate?


Lane cut a disc~with a radius of $$12 cm$$ from the middle. What is the circumference of each half disc after cutting?($\pi=3$)

$$54 cm$$

$$60 cm$$

$$64 cm$$

$$86 cm$$

$$99 cm$$