Carmel draws a plan of her school using a scale of $$1\text{cm}$$ to $$5\text{m}$$.  On the plan, the playground is $$6\text{cm}$$ long.  What is the real length of the playground?

$$11 \text{m}$$

$$7 \text{m}$$

Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Proportions->Scale


Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Multiplication and Division of Whole Numbers->Multiplication out of the Multiplication Table


（$$2016$$ Singapore Chinese Girls\textquotesingle{} School (Primary), Topical Test $$2$$, Primary Two, Question \#$$1$$）  $$660+237=$$~\uline{~~~~~~~~~~}~.

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction


The sum of two fractions is $$4\frac{2}{3}$$. If the smaller fraction is $$1\frac{1}{4}$$, what is the difference of the two fractions? Leave your answer as a mixed number.

Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions


Which of the following is equivalent to the given expression $\frac{(\frac{x^{2}}{y})}{y}$?

Overseas Competition->Knowledge Point->Calculation Modules


Which of these numbers is less than its reciprocal?

Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering->Comparing and Ordering Fraction by Comparing Its Reciprocal


Convert $\frac{4}{9}$ to a repeating decimal:~\uline{~~~~~~~~~~}~.

$0.\overline 4$

Overseas Competition->Knowledge Point->Calculation Modules->Decimals


The probability that a new microwave oven will stop working in less than 2 vears is 0.05. The probability that a new microwave oven is damaged during delivery and stops working in less than 2 vears is 0.04. The probability that a new microwave oven is damaged during delivery is 0. 10. Given that a new microwave oven is damaged during delivery, what is the probability that it stops working in less than 2 years?

Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables


Which fraction is equivalent to $$\frac{42}{54}$$?

Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions->Using Common Factors to Simplify Fractions


Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences


base number, exponent

exponent, base number

I don\textquotesingle t know

I am gonna need a calculator

Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Exponentiation of Powers


Consider a cross between pea plants. One parent has yellow seeds and the other parent has green seeds.~ If of the 20 offspring, 11 have yellow seeds and 9 have green seeds, what is the most likely genotypes of the parents?

YY x yy

Yy x Yy

Yy x yy

yy x yy

YY x Yy


None of the above


The first element of an arithmetic sequence is $$\frac{1}{3}$$ and the third element is $$\frac{1}{5}$$. What is the second element of this sequence?

Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences->The Number of Terms in an Arithmetic Sequence


The last five digits of Zoe\textquotesingle s phone number are $2$, $3$, $4$, $6$, and $8$. If four of these five numbers are filled in the square~$$\huge\square+\square =\square +\square $$, which number is not used?~(Adapted from 2017 Math Kangaroo Problem, Level 1-2, Question \#8)

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Horizontal Form


What is the next number in the sequence below?  $$7, 8, 6, 9, 5, 10, \cdots$$

None of the above

Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences


Which of the following fractions is equivalent to $$\frac{2}{3}$$.

Overseas Competition->Knowledge Point->Calculation Modules->Fractions


Peter has $9$ dollars and $20$ cents. One can of soft drink costs $1.20$ dollarss, and one chocolate bar is $60$ cents cheaper than one can of soft drink. After buying $3$ cans of soft drink and two chocolate bars, how much does he have left?

$4.8.$ dollars

$4.2.$ dollars

$3.6.$ dollars

$5.4.$ dollars

$6.4.$ dollars


Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals->Converting Decimals into Fractions


Calculate.　  $$61\times 13+12\times 11=$$．

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations


Which of the following is not an algebraic expression?

Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions


Cathy went to Miami the day before yesterday. It is Monday tomorrow. What day was the day when Cathy left for Miami?

Wednesday

Friday

Saturday

Sunday

Monday


A researcher is conducting a study of charitable donations by surveying a simple random sample of householdsin a certain city. The researcher wants to determine whether there is convincing statistical evidence that more than 50 percent of households in the city gave a charitable donation in the past year. Let p represent the proportion of all households in the city that gave a charitable donation in the past year. Which of the followingare appropriate hypotheses for the researcher?

H\textsubscript{0} : p = 0.5 and H\textsubscript{a}~: p \textgreater{} 0.5

H\textsubscript{0} : p = 0.5 and H\textsubscript{a}~: p * 0.5

H\textsubscript{0} : p = 0.5 and H\textsubscript{a} : p \textless{} 0.5

H\textsubscript{0}~: p \textgreater{} 0.5 and H\textsubscript{a} : p $\ne$0.5

H\textsubscript{0} : p \textgreater{} 0.5 and H\textsubscript{a} : p = 0.5


$40\times\square=12000$  What number needs to go in the box to make the statement correct?


Which number doesn\textquotesingle t round to 20?

Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Rounding Numbers


What fraction is exactly halfway between $\frac14$ and $\frac15$?


Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math


7.Daniel and Patrick had an equal number of stickers at first. Daniel then gave away 20 of his stickers to his friend Melvin, and Patrick bought another 12 stickers. In the end, Patrick had thrice as many stickers as Daniel. Find the number of stickers Daniel had at first?


Lily left home at 4:15pm to go to the cinema and arrived at the cinema at 4:35pm. An hour and a half later, she finished watching the movie and went home. She spent the same time on her way home as she went to the cinema. When did Lily get home?

Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation


We place the signs $$+$$, $$-$$ and $$=$$ between the digits: $$4$$ $$8$$ $$3$$ $$3$$ $$6$$ $$9$$ in such a way that an equality is made. The sequence of the signs is: ．

$$+$$, $$=$$, $\times$, $$-$$, $$+$$

Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)->Adjacent Numbers can be formed into Multi-Digit


In the equation below each letter represents a digit. What digit is represented by the letter $$M$$?  $$4\times KLMNP4=4KLMNP$$

Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (horizontal forms)


From $1$ to $40$, how many integers can be chosen at most to ensure that no two of chosen numbers sum to $35$?

Overseas Competition->Knowledge Point->Combinatorics->Constructing and Proving


bigger

smaller

bigger and smaller

Overseas Competition->Knowledge Point->Combinatorics->Patterns of Figures


Convert~$\dfrac{50}{4}$ to a mixed number in its simplest form.


Suppose $a$, $b$, and $c$ are non-zero real numbers, and $a+b+c=0$. What are the possible value(s) for~$\dfrac{a}{\left\textbar{} a\right\textbar}+\dfrac{b}{\left\textbar{} b\right\textbar}+\dfrac{c}{\left\textbar{} c\right\textbar}+\dfrac{abc}{\left\textbar{} abc\right\textbar}$?

1 and -1

2 and -2

0, 2 and -2

0, 1 and -1

Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value


Yohan had 10 white socks, 10 red socks and 10 black socks in his drawer. How  many socks at most, must Yohan take from his drawer without looking, till he gets a pair of white socks?

Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle


Pip and Bud are arranging three symbols in a certain pattern. What is the 20th symbol in the sequence?  △○★△○★△○★\ldots\ldots{}

Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Sports Competition->Single Cycle Race


Sara, Mary, Linda and Karina are comparing their heights.  (1) Linda says: "I\textquotesingle m taller than Karina."  (2) Sara says: "I\textquotesingle m taller than Linda."  (3) Linda is shorter than Mary.  Who is the shortest?

Sara

Mary

Linda

Karina

This cannot be determined

Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning


What is the smallest possible number of children in a family where each child has at least one brother and at least one sister?

Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions->Complex Reasoning


There are three songs on a certain CD. The first song is $$6$$ minutes and $$25$$ seconds long, the second song is $$12$$ minutes and $$25$$ seconds long, and the third song is $$10$$ minutes and $$13$$ seconds long. How long does it take to play the whole CD?

$$28$$ minutes $$30$$ seconds

$$29$$ minutes $$3$$ seconds

$$38$$ minutes $$10$$ seconds

$$31$$ minutes $$13$$ seconds

$$31$$ minutes $$23$$ seconds


Andrea needs an hour to get to the shopping center. If she leaves at $$4$$ PM, she gets there half an hour after the store closes. If she leaves at $$8$$ AM, she gets there half an hour before the store opens. What hours is the shopping center open? ($$2007$$ Math Kangaroo Problem, Level $$1-2$$, Question \#$$24$$)

$$7^{30}$$ to $$4^{30}$$

$$8^{30}$$ to $$5^{30}$$

$$7^{30}$$ to $$5^{30}$$

$$8^{30}$$ to $$4^{30}$$

$$9^{30}$$ to $$4^{30}$$


Given five different points on a line, labeled in order as $$A\_{1}$$, $$A\_{2}$$, $$A\_{3}$$, $$A\_{4}$$, $$A\_{5}$$. Point $$P$$ is placed on the line in such a way that the sum of the lengths $$\left\textbar{} P{{A}\_{1}} \right\textbar+\left\textbar{} P{{A}\_{2}} \right\textbar+\left\textbar{} P{{A}\_{3}} \right\textbar+\left\textbar{} P{{A}\_{4}} \right\textbar+\left\textbar{} P{{A}\_{5}} \right\textbar$$ is minimal. Then：．

$$P$$ may be any point between $$A\_2$$ and $$A\_{4}$$

$$P$$ may be any point between $$A\_1$$ and $$A\_5$$

Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Planning->Planning on Location->Equally Important for Every Points


Jola has four candles. Each of her candles burns itself our within three hours. Jola lit two candles and placed them next to an open window. $$30$$ minutes later the wind blew out one candle, and another hour later the wind blew out another candle. Then Jola closed the window and lit all four candles. How long after this moment will the last candle burn out?

$$1\text{ hr }30\text{ min}$$

$$2\text{ hr}$$

$$3\text{ hr}$$

$$7\text{ hr }30\text{ min}$$

$$8\text{ hr}$$


A certain box contains $$15$$ balls that are coloured red and blue (both colours on each ball), $$12$$ balls that are coloured blue and green, and $$9$$ balls that are coloured green and red. What is the smallest number of balls that must be selected to guarantee that you have at least seven balls that share a colour?

Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems

N/A.(US $$2006$$ Math kangaroo Problems, Level $$9-10$$, Question \#$$19$$)


How many small squares we need at least in the big square?


15. Jensen and Benny had $328$ cookies. If Jensen gave Benny $36$ cookies, Jensen would have thrice as many cookies as Benny. How many cookies did Jensen have?~\uline{~~~~~~~~~~}~


Fill the operation signs "$$+$$" or~"$$-$$" in the squares below to make the equation true.  $$4\square 3\square 2\square1=8$$

Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)->Filling the Symbol in the Equations


9. Raymond and Victor had the same amount of money at first. After Raymond spent $$$12$$, Victor had 4 times as much money as Raymond in the end. How much money did each of them have at first?


Junlong spent $$150min$$ reading a storybook. Express the time spent in hours and minutes.

$$2 \space h \space50 \space min$$

$$2 \space h \space30 \space min$$

$$1 \space h \space50 \space min$$

$$1 \space h \space30 \space min$$

Overseas Competition->Knowledge Point->Combinatorics->Time Problem


Green went out to travel on May $27$, $2022$. There are $31$ days in May. It took him $6$ days to reach the destination. When did he reach the destination?

on May $31$

on June $1$

on June $2$

on June $3$

on June $5$


Which set of signs $$+$$ and $$-$$ needs to be placed in the boxes to make the expression true?  $$4\square 3\square 2\square 1=8$$


An object is moving to the west at a constant speed. Three forces are exerted on the object. One force is 5 N directed due north, and another is 5 N directed due west. What is the magnitude and direction of the third force if the object is to continue moving to the west at a constant speed?

$5\sqrt{3}$~N, directed northwest

$5\sqrt{3}$~N, directed southeast

$5\sqrt{2}$~N, directed northwest

$5\sqrt{2}$~N, directed southeast

Overseas Competition->Knowledge Point->Combinatorics->Directions and Coordinates


If four identical equilateral triangles are put together to form a new shape, which of these can be the shape they form?

$$$$rectangle

$$$$trapezium

$$$$square

$$$$parallelogram

$$$$pentagon

Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem->Jigsaw


Johnson arrives at the office at $$10:30am$$ everyday. If it takes him $$55$$ minutes to go to the office, at what time does he set off from home office?


Mia is going to watch a movie tomorrow. The movie will start at $$10:45$$ am, and end at $11:55$ am. How long will the movie last?


A boy named Peter has as many brothers as sisters. His sister Ann has twice as many brothers as sisters. How many children are there in the family?


How should the time half past six in the evening be written?


What is the biggest number of matchsticks to form 6 triangels?

Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math->Fun Math Problems->Matchstick Problems


In a riding competition, the horses started at three-minute intervals.  The first horse started at $$10:45$$.  The $$18\text{th}$$ horse took $$13$$ minutes to complete the course.  At what time did the $$18\text{th}$$ horse finish?

Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation


The square roots of \sqrt{16} are~\uline{~~~~~~~~~~}~.

4 or -4

2 or -2

Overseas Competition->Knowledge Point->Combinatorics->Magic Square


Which equation or inequality describes real numbers whose distance from $-5$ is less than or equal to $13$ units?

$\textbar x-5\textbar{} \leq 13$

$\textbar x+5\textbar{} \leq 13$

$\textbar x-13\textbar{} \leq 5$

$\textbar x+13\textbar{} \leq 5$


The $+$, $−$, $\times$, $\div$ signs have been left out of the following sum:  $6\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} 3\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} 10\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} 2=23$  Which of the following expressions has the correct signs?

$6+3 \times 10 − 2$

$6 \div 3 + 10 \times 2$

$6 \times 3 + 10 \div 2$

$6 − 3 + 10 \div 2$


Ben thought of a way to replace numbers with graphs, $$\triangle = 1$$, $$\bigcirc = 3$$, $$\square = 5$$. For example, $$\bigcirc\triangle\square =315$$. What is the code of "$$\triangle\square\square\triangle\bigcirc$$"?


Jonathan has $$4$$ regular dice. Each dice has numbers from $$1$$ to $$6$$. Which of the following could not be the sum of the numbers on top of the $$4$$ dice?

All the above numbers are possible sum


Bud has six number cards: $\boxed{1}, \boxed{2}, \boxed{3}, \boxed{7}, \boxed{8}, \boxed{9}$.  How many cards can she choose at most to ensure that no two of chosen cards sum to $10$?


9. $3$ chocolate cookies, $2$ almond cookies and a strawberry cookie cost $$$41$$. A chocolate cookie cost  $$$2.20 $$ more than a strawberry cookie. A strawberry cookie cost $$$1.10$$ more than an almond cookie. How much did a strawberry cookie cost?~\uline{~~~~~~~~~~}~

Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math


Nancy, Katie, John, and Reed were reading the same book. They each finished reading $\frac{5}{7}, \frac{5}{9}, \frac{5}{6}$ and $\frac{5}{8}$ of the book, respectively. Who finished reading more pages?

Nancy

Katie

John

Reed

Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem


Using $$7$$, $$6$$, $$5$$, $$4$$ in order and addition and subtraction signs we can make $$10$$, as shown below.  $$7-6+5+4=10$$  Fill in the gaps below with either addition or subtraction signs to make $$12$$.  $$7$$~ ~ ~ $$6$$~ ~ ~ $$5$$~ ~ ~ $$4$$~ ~ ~ $$=12$$


In the calculation, $$1\textasciitilde\textasciitilde2\textasciitilde\textasciitilde3\textasciitilde\textasciitilde4\textasciitilde\textasciitilde5\textasciitilde\textasciitilde6\textasciitilde\textasciitilde7=0$$, you can fill in one of the four operations $$+$$, $$-$$,~$\times$,~$\div$~and brackets in each of the gaps. Which of the following choices is the correct filling?

$1\times2+\left( 3-4\right)\times5+6-7=0$

$\left( 1+2-3\right)\times4\times5\times6\times7=0$

Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)


Matt, Will and Tiger are predicting the outcome of a tournament, which only has $$4$$ teams.  \textbf{Matt: "Team $$A$$ will be the $$1$$\textsuperscript{st}, and Team $$B$$ will be the $$4$$\textsuperscript{th}."~}  \textbf{Will: "Team $$B$$ will be the $$2$$\textsuperscript{nd}, and Team $$C$$ will be the $$3$$\textsuperscript{rd}."}  \textbf{Tiger: "Team $$A$$ will be the $$2$$\textsuperscript{nd}, and Team $$D$$ will be the $$4$$\textsuperscript{th}."}  After the tournament, it turns out they are all half-right and half-wrong. What is the ranking of Team $$D$$?


2019 AMC 8/ Problem 18  The faces of each of two fair dice are numbered 1, 2, 3, 5, 7 and 8. When the two dice are tossed, what is the probability that their sum will be an even number?


As Hans wrote a problem on the board, he forgot one digit. What he wrote was: $$23+31+2+12=94$$. What digit did he forget to write?

Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (horizontal forms)


Which of the following points is in Quadrant $III$?

Overseas Competition->Knowledge Point->Combinatorics->Directions and Coordinates->Coordinates


It is $$9:00pm:$$ now, what was the time $$33$$ minutes before?


One evening, Sarah started her homework at half past four.  She finished it at twenty minutes to six.  How long did her homework take?

$$1$$ hour $$10$$ minutes

$$1$$ hour $$50$$ minutes

$$50$$ minutes

$$1$$ hour $$30$$ minutes

$$1$$ hour $$20$$ minutes


Express~$\dfrac{4}{6}$ in its simplest form.


$$454\text{g}$$ is the same as $$1\textasciitilde\text{lb}$$ in weight. Hannah has bought a $$5\textasciitilde\text{lb}$$ turkey which needs cooking. The instructions state that it needs to be cooked for $$55\min $$ per $$\text{kg}\textasciitilde+$$ a further $$25\min $$.  Approximately how long does the turkey need to cook for?  Choose the answer.

$$2 \frac{1}{2}$$ hours

$$1 \frac{1}{2}$$ hours

$$2 \frac{3}{4}$$ hours

$$2$$ hours

$$2 \frac{1}{4}$$ hours


15. Stephen is facing east. After turning~\uline{~~~~~~~~~~}~$$^{\circ}$$ in the clockwise direction, he will be facing south-west.


Kanga is 1 year and 3 months old now. In how many months will Kanga be 2 years old?


In the following Cryptarithm, each letter represents $$1$$ one-digit number. Find the three-digit number represented by `$$ABC$$'．  $$\begin{matrix}\& \& 8 \& 8\& \boxed C \textbackslash\textbackslash{} \&\&5\& \boxed B \&4 \textbackslash\textbackslash{} + \&\&\boxed A\&1 \&7 \textbackslash\textbackslash{} \hline \&2~\&0 \&2 \&1\textbackslash\textbackslash{} \end{matrix}$$

Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles


Alice snd Bob picked the marbles from a bag without looking. The bag contains $2$ blue marbles and $1$ red marble. Each picked $1$ marble only. After each saw the colour of their own marble,  Alice said: "I know the colour of your marble!"  If Alice is telling the truth and she is correct, what is the colour of the marble each one got?

Alice - Blue, Bob - Blue

Alice - Red, Bob - Blue

Alice - Blue, Bob - Red

Alice - Red, Bob - Red

None of the above

Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning


Pip is practicing for a marathon. He starts running at $$9:00$$ am and he stops at $$12:00$$ noon for lunch. After Pip has enough rest, he continues the run at $$2:00$$ pm and finishs the run at $$5:00$$ pm. How long has Pip run in total?

$$3$$ hours

$$5$$ hours

$$6$$ hours

$$8$$ hours


From $1$ to $40$, How many integers can be chosen at most to ensure that no two of chosen numbers sum to $35$?

Overseas Competition->Knowledge Point->Combinatorics->Constructing and Proving


$$86-3\square=48$$  What is the missing digit?


Eddie, Joe and Ken measured the height of a building using different methods. They got $\frac{81}{4}$ meters, $20.142857$ meters, and $20\frac{1}{10}$ meters, respectively. Order their results from least to greatest (using their names).

Eddie, Joe, Ken

Joe, Ken, Eddie

Ken, Joe, Eddie

Eddie, Ken, Joe

Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value


There are $5$ gift boxes of different sizes.  The red box is bigger than the white box.  The yellow box is bigger than the white box.  The black box is smaller than the red box.  The blue box is bigger than the yellow box but smaller than the black one.  Which box is the biggest?

The red one.

The black one.

The yellow one.

The white one.

The black one.

Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Comparing


12.John had thrice as much money as Melissa. After John gave Melissa $$$140$$, they had an equal amount of money left. How much money did each of them have at first?


A student always tells the truth on Mondays and Tuesdays but always tells lies on Saturdays. On the other days of the week he tells the truth or tells lies, at random. For six consecutive days he was asked what his first name was, and he gave the following answers, in order: Jack, Bill, Jack, Bill, Peter, Bill. On what day of the week did he answer Peper?

Wednesday

Thursday

Friday

Saturday

Sunday


There are some people living on the island of lies. Half of them only tell lies on Wednesday, Friday and Saturday. The other half only tell lies on Tuesday, Thursday and Sunday. One day, all of the people living on the island said that they would tell the truth the next day. What day of the week was that day?

Tuesday

Wednesday

Friday

Saturday

Sunday

Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning using Hypothesis->Truth or Lie


Put the digits $$0$$, $$1$$, $$2$$ and $$3$$ in the squares and the sum of the formula is $$15$$. which number can\textquotesingle t "$$0$$" be combined with?  $$\square \square +\square \square = 15 $$.

$$1$$ or $$2$$

$$2$$ or $$3$$


If $1st$ December fall on a Thursday, which day of the week will $7th$ November fall on?

Sunday

Monday

Tuesday

Wednesday

Thursday

Overseas Competition->Knowledge Point->Combinatorics->Time Problem


It is $$11:33am$$ now, what will be the time $$2$$ hours $$14$$ minutes later?


2020 AMC 8/ Problem 23  Five different awards are to be given to three students. Each student will receive at least one award. In how many different ways can the awards be distributed?


Andrew takes $$15$$ minutes to wash up in the morning, $$20$$ minutes to have his breakfast, $$6$$ minutes to pack his school bag, $$8$$ minutes to walk to his friend\textquotesingle s house before going to the school together. From his friend\textquotesingle s house to the school, it will need $$26$$ minutes. The school rules require you to arrive at $$8.00 \rm{a.m.}$$ every morning, what\textquotesingle s the latest time he needs to leave his house?

$$6.45 \rm{a.m.}$$

$$7.00 \rm{a.m.}$$

$$7.26 \rm{a.m.}$$

$$7.34 \rm{a.m.}$$

None of the above


9.What is the size of $$\angle AOB$$?~\uline{~~~~~~~~~~}~$$^{\circ}$$


A train leaves London at $17:13$ and arrives at Bristol at $19:09$, having been delayed by $11$ minutes owing to the wrong type of snow.  How long does the journey normally take when there are no delays?

$2$ hours $7$ minutes

$126$ minutes

$1$ hour $45$ minutes

$115$ minutes

$2$ hours $16$ minutes


How many $3$-digit numbers can be formed using the digits $0,1,2$ if no digit can be repeated?

Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (vertical forms)->Counting Different Ways to Fill Number Puzzles


David wants to prepare a meal with $$5$$ dishes using a stove with only $$2$$ burners. The times needed to cook the $$5$$ dishes are $$40$$ min, $$15$$ min, $$35$$ min, $$10$$ min and $$45$$ min. What is the shortest time in which he can do it? (He may only remove a dish from the stove when it is done cooking.) (2017 Math Kangaroo Problem, Level 3-4, Question \#15)

$$60$$ min

$$70$$ min

$$75$$ min

$$80$$ min

$$85$$ min


Amy started cooking at $$11:10$$ A.M.. After she cooked, she had eating for an hour and 15 minutes, and it was $2:25$ P.M. How long had she cooked?

$$1$$ h $$15$$ min

$$1$$ h $$25$$ min

$$1$$ h $$50$$ min

$$2$$ h

$$2$$ h $$10$$ min


We place the signs $$+$$, $$-$$ and $$=$$ between the digits: $$4$$ $$8$$ $$3$$ $$3$$ $$6$$ $$9$$ in such a way that an equality is made. The sequence of the signs is: ．

Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)->Adjacent Numbers can be formed into Multi-Digit


Tom is having a race with $9$ other people. If he just went past Jerry who was in $5th$ place, which position is Tom in right now?


~\uline{~~~~~~~~~~}~$\div4\textbackslash{} =\textbackslash{} 8\textbackslash{} R1$


From $1$ to $40$, how many integers must be chosen at least to ensure that there are two of chosen numbers sum to $35$?


It is $$13:48$$ now, what will be the time $$75$$ minutes later?


Tucker must finish his homework at $$16:20$$ If it takes him $$129$$ minutes to finish the homework, at what time should he start to do his homework?


When it is $$8:00am$$ in London, it is $$5:00pm$$ in Japan. Today is $17^{th}$~November, Vicky lives in London and she wants to call her parents in Japan after she finishs her work at $$10:00pm$$. What is the time and date in Japan when her parents receive the phone call?

$$7:00pm $$~$17^{th}$~November

$$1:00am$$~$18^{th}$ November

$$7:00am$$~$18^{th}$ November


Aria, Evelyn and Camila sit at a round table. They study in primary $$2$$, $$3$$ and $$4$$. The primary $$4$$ girl is on Camila\textquotesingle s left. The primary $$3$$ is on Aria\textquotesingle s right. Who is the primary $$2$$ girl？

Aria

Evelyn

Camila

Impossible to determine

None of the above


The perimeter of a square is 36cm. What is its area?


$$95-2\square=\square9$$  Jack\textquotesingle s calculator displays the sum entered and the answer.  The calculator works correctly except that one digit always appears as a blank space.  What is the missing digit?

N/A.  revise from (GL Assessment book$$2$$《Paper $$6$$》 $$6$$ years Question \#$$3$$)


In a card game, there are $$4$$ types of colour cards and $$3$$ functional cards with no colour. If there are $$9$$ red cards, $$16$$ yellow cards, $$8$$ green cards and $$5$$ blue cards, How many cards should I draw to ensure that I get $$5$$ cards in the same colour?

Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems


The time in Thornsburg is $$6$$ hours ahead of London. The time in London is $$8.27$$ pm. What is the time in Thornsburg?  Choose the answer.

$$2.27$$ pm

$$02.27$$ pm

$$14.27$$ am

Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation


It\textquotesingle s 11:05 now. Tom is waiting for the bus. The next bus will arrive in 7 minutes. It takes 95 minutes from this station to the terminal. When will Tom arrive at the terminal?


In the equation $$KAN-GAR=OO$$ each letter represents a certain digit (different letters represent different digits, the same letters represents the digits). Find the largest possible value of the number $$KAN$$ ．


There are $$5$$ children in a family. Dannie is $$3$$ years older than Edmud, but $$4$$ years younger than Bella. Amy is $$3$$ years older than Cindy and Cindy is $$2$$ years older than Dannie. Who of them is the eldest?

Amy

Bella

Cindy

Dannie

Edmud

Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions->Complex Reasoning


On a bookshelf there are 50 mathematics and physics books. No two physics books stand side by side, but every mathematics book has a mathematics book next to it.  What is the least possible number

The number of mathematics books is at least 32.

The number of physics books is at most 17.

There are 3 mathematics books standing together.

If the number of physics books is 17, then one of them is the first or the last on the shelf.

Among any 9 consecutive books, at least 6 are mathematics books.


Which set of signs $$+$$ and $$-$$ needs to be placed in the boxes to make the expression true?  $$4\square 3\square 2\square 1=8$$

Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)->Filling the Symbol in the Equations

N/A. (US $$2005$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$20$$)


Bud returns from the shops at $$2:15$$ pm, $$3$$ hours $$40$$ minutes after she left her hourse. At what time did she leave her house?

$$10:35$$ am

$$11:25$$ am

$$11:35$$ am

$$1:25$$ pm

$$5:55$$ pm


Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math


A concert has two $$40$$-minute parts and has a few commercials between them. The concert started at $$2:00$$ PM and ended at $$3:35$$ PM. How long did the commercials last for in total?

$$30$$ min

$$20$$ min

$$15$$ min

$$10$$ min


Three fund managers invested in stocks. Jack bought 66 stocks, Wendy bought 40, and Leo bought 23. Jack and Wendy both bought 17 of the same stocks, Wendy and Leo bought 13 of the same, and Leo and Jack bought 9 of the same. All three of them bought 6 of the same stocks.~ How many stocks in total did the three managers purchase?


Fill in the blanks with digits so that the equality is true: $$45\times $$\_$$3=3$$\_ \_ \_. The sum of the four digits placed in the blanks is:．

equal to $$20$$

equal to $$21$$

equal to $$17$$

more than $$21$$

less than $$17$$


A movie started at $$2.45 \text{p.m.}$$ It ended at $$4.30 \text{p.m.}$$ How long did the movie last? ．

$$1 \space \text{h} \space 25 \space \min $$

$$1 \space \text{h} \space 45 \space \min $$

$$2 \space \text{h} \space 15 \space \min $$

$$2 \space \text{h} \space 45 \space \min $$


Susan had dinner with her family. She started cooking at $$3:25$$ P.M. and cooked for $2$ hours and $45$ minutes. They finished eating at $8:50$ P.M., how long did they eat?

$$1$$ h $$50$$ min

$$2$$ h $$50$$ min

$$3$$ h

$$3$$ h $$15$$ min

Overseas Competition->Knowledge Point->Distance Word Problems->Bus Departure Time Word Problems


A certain town is inhabited only by knights and liars. Knights always tell the truth and liars always lie. One day, several of the townspeople met in a room and three of them made the following statements:  $$\bullet$$ First person: "There are no more than three of us in the room. Each of us is a liar."  $$\bullet$$ Second person: "There are at most four people in the room, Not every one of us is a liar."  $$\bullet$$ Third person: "There are five people in the room. Three of us are liars."  How many people were in the room and how many of them were liars?

$$3$$ people, $$1$$ liar

$$4$$ people, $$1$$ liar

$$4$$ people, $$2$$ liars

$$5$$ people, $$2$$ liars

$$5$$ people, $$3$$ liars


- $$\star$$ is the smallest $$4$$-digit number that can be created using all the digits $$2, 0, 2$$ and $$1$$.  - $$\diamond$$ is the largest $$4$$-digit number that can be created using all the digits $$2, 0, 2$$ and $$1$$.  Find the value of $$\diamond - \star$$.

None of the above


Misa went to the leisure centre.  She used the gym for $$50$$ minutes and then went swimming for $$25$$ minutes.  How long did she exercise altogether?

$$1$$ hour and $$15$$ minutes

$$1.15$$ hours

$$7$$ hours and $$5$$ minutes

$$7.5$$ hours

$$7$$ hours and $$50$$ minutes


We place the signs $$+$$, $$-$$ and $$=$$ between the digits: $$4$$ $$8$$ $$3$$ $$3$$ $$6$$ $$9$$ in such a way that an equality is made. The sequence of the signs is~\uline{~~~~~~~~~~}~. ($$2006$$ Math Kangaroo Problem, Level $$1-2$$, Question \#$$24$$)


This year, May $6$ falls on a Friday. What day of the week will it be in $25$ days?

Tuesday

Wednesday

Thursday

Friday

Sunday


Four pirates Jack, Jimmy, Tom and Sanchi a gold coin. Jack said, "I got 11 less gold than Jimmy, 15 more than tom one, 20 less than Sanchi indivual. "So, Sanji got  gold coins.


Candace woke up at 6 a.m. She spent 30 minutes showering and another 50 minutes getting ready for work. When she left the house, she realised that her clock was 15 minutes slower. What was the actual time Candace left her house?

6.55 a.m.

7.20 a.m.

7.35 a.m.


Grace is taller than Ann, but shorter than Tania. Irena is taller than Kate, but shorter than Grace. Which of the girls is the tallest?

$$$$Grace

$$$$Ann

$$$$Kate

$$$$Irena

$$$$Tania


Alex arrives at school at $$8.30$$ a.m. and leaves at $$4.15$$ p.m.  For how many minutes is he at school?


The points $$A=(6,7)$$, $$B=(7,6)$$, $$C=(-6,-7)$$, $$D=(7,-7)$$ and $$E=(7,-6)$$ are marked on a coordinate grid. Which line segment is parallel to the $$x$$-axis?

$$\overline{AD}$$

$$\overline{BE}$$

$$\overline{BC}$$

$$\overline{CD}$$

$$\overline{AB}$$


The time now is $$16:56$$ and Archie\textquotesingle s $$12$$-hour digital clock shows $$4:56 \rm{P.M}$$. He realizes that the digits of his digital clock are increasing consecutive order. When the time is $$12:17 \rm{P.M.}$$ or $$\rm{A.M.}$$, the clock will show $$12:17 \rm{P.M.}$$ or $$\rm{A.M.}$$ respectively. How many minutes later will Archie\textquotesingle s clock show digits again in consecutive order?

$$507$$ minutes

$$458$$ minutes

$$467$$ minutes

$$407$$ minutes

None of the above


Marysia leaves her house at $$6:55$$ and arrives at school at $$7:32$$. Zosia needs $$12$$ minutes less than Marysia to get to school. Yesterday Zosia showed up at school at $$7:45$$. What time did she leave her house?

At $$7:07$$

At $$7:20$$

At $$7:25$$

At $$7:30$$

At $$7:33$$


What is the least possible number of children in the Kowalski family if each of the children has at least one brother and at least one sister?


What should 5: 21 a.m. be written in the 24-hour clock?

5: 21 a.m.

5: 21 p.m.

5: 21

17: 21