A series of colored lanterns are arranged in the pattern ``red, red, green, yellow, yellow, red, red, green, yellow, yellow$$\cdots$$'' What color is the $$52^{\text{th}}$$ lantern?

red

green

yellow

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation

Since $$52\div(3+2)=10r2$$, the $$52^{\text{th}}$$ colored lantern is red.


Jin loves carrots! Yesterday she ate $$\frac{1}{2}$$ of her carrots, and today she ate $$\frac{2}{3}$$ of the remaining carrots. She then discovered that she had $$12$$ carrots left. Yesterday she must have started with  carrots.

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base

If $$12$$ carrots are left after Jin eats $$\frac{2}{3}$$ of today\textquotesingle s carrots, then $$12$$ carrots are $$\frac{1}{3}$$ of the carrots she started with today. So Jin began today with $$36$$ carrots. Since Jin ate $$\frac{1}{2}$$ yesterday, she started with $$2\times36$$ carrots.


This year, March $$19$$\textsuperscript{th} falls on a Thursday. What day of the week will it be in $$30$$ days?

Wednesday

Thursday

Friday

Saturday

Sunday

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time

$$30\div7=4 \text{R} 2$$, two days after Thursday, which is Saturday.


A $70\textbackslash\%$ alcohol solution contains $$120$$ g of water. How many g of solution are there?

$$200$$ g

$$300$$ g

$$400$$ g

$$500$$ g

Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems


It\textquotesingle s summer time! A beverage shop mixes $10$ bottles of apple and $20$ bottles of watermelon juice to make the new blended juice. The costs of a bottle of apple and a bottle of watermelon juice are $8$ and $11$ dollars, respectively. If the size of the bottle does not change, what is the cost of each bottle of the blended juice?

Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems

Total cost: $$10\times 8+11\times 20=300$$.  There are $$10+20=30$$ bottles, so each bottle of the blended juice should be $$300\div 30=10$$ dollars.


Irene mixes $$100$$ kilograms of dogfood that contains $$50\textbackslash\%$$ rice with $$400$$ kilograms of dogfood that contains $$80\textbackslash\%$$ rice. Find the percent concentration of the rice in the new mixture.

Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems


Chris and Debbie want to buy the same book, but they do not take enough money. Chris needs $$2$$ dollars and $$30$$ cents more to buy that book. Debbie needs $$3$$ dollars and $$80$$ cents more to buy that book. The sum of their own money is equal to the price of the book. How much is the book?

$$2$$ dollars and $$30$$ cents

$$4$$ dollars and $$60$$ cents

$$7$$ dollars and $$60$$ cents

$$3$$ dollars and $$80$$ cents

$$6$$ dollars and $$10$$ cents

Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems

$$2$$ dollars and $$30$$ cents + $$3$$ dollars and $$80$$ = $$6$$ dollars and $$10$$ cents


The average cost of a long-distance call in the USA in 1985 was 56 cents per minute, and the average cost of a long-distance call in the USA in 2018 was 2 cents per minute. Find the approximate percent decrease in the cost per minute of a long- distance call. (2007 AMC 8, Question \#6)

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems

The percent decrease is (the amount of decrease)/(original amount) the amount of decrease is $56-2=54$ so the percent decrease is $\frac{54}{56}$ which is about $ 96 \textbackslash\%$


There are $$2$$ inlets (namely $$\text{A}$$ and $$\text{B}$$) in a pool. If only inlet $$\text{A}$$ is open, it takes $$36$$ minutes to fill up the empty pool. If only inlet $$\text{B}$$ is open, it takes $$48$$ minutes to fill up the empty pool. Now, inlets $$\text{A}$$ and $$\text{B}$$ will be open in turns, according to such an order, open inlet $$\text{A}$$ for $$1$$ minute, $$\text{B}$$ for $$2$$ minutes, $$\text{A}$$ for $$2$$ minutes, $$\text{B}$$ for $$1$$ minute, $$\text{A}$$ for $$1$$ minute, $$\text{B}$$ for $$2$$ minutes $$\cdots$$ So on and so forth. How long, in the nearest minutes, does it take to fill up the empty pool?

None of the above

Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems


Joe lives on the $3$\textsuperscript{rd}~floor. He needs to spend $12$ minutes to move from the $4$\textsuperscript{th} floor to the $5$\textsuperscript{th} floor. How many minutes does he need to climb from the $1$\textsuperscript{st} floor to the $3$\textsuperscript{rd} floor?

Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems


Three people $$A$$, $$B$$, and $$C$$ have a total of $$$200$$. Given that the ratio of $${A}'$$ s total to $${B}'$$s total is $$4:3$$, and $$A$$ has $$$20$$ more than $$C$$, how much does $$C$$ have?

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio

Assume that $$C$$ borrows $$$20$$. Therefore, $$A:B:C = 4:3:4$$, for a total sum of $$11$$ increments, or $$$220$$. One increment is $$220\div 11=20$$ dollars. Therefore, $$C$$ has a total of $$4\times 20-20=60$$ dollars.


If $$29^{}\text{th}$$May is Monday, what day of the week is $$1$$\textsuperscript{st~}May ?

Sunday

Monday

Wednesday

Tuesday

Saturday

There are 29 days between $$29^{}\text{th}$$May and~ $$1$$\textsuperscript{st~}May.  Apart from $29$\textsuperscript{th} May itself, there are 28 days = 4 week.  Therefore,~~$$1$$\textsuperscript{st~}March is Monday.


Linda paid $$8$$ dollars for $$4$$ potatoes. How many dollars did Linda pay for the same kind of potatoes if she bought $$6$$ more of them? (adapted from $$2008$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$13$$)

Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable

Linda paid ＄$$8$$ for $$4$$ potatoes, $$8\div4=2$$, so we can know $$1$$ potatoes cost $$2$$ dollars. In total Linda should pay $$2\times10=20$$ dollars for $$10$$ potatoes.


There are $5$ people in Harry\textquotesingle s family with an average height of $168$ cm. The heights of Harry, Harry\textquotesingle s mom, Harry\textquotesingle s sister, and Harry\textquotesingle s brother are $170$ cm, $160$ cm, $162$ cm, and $175$ cm, respectively. What is the height of Harry\textquotesingle s dad?


Vera invited $$13$$ guests to her birthday party. She had $$2$$ pizzas, and each of them was cut into $$8$$ slices. Each person at the party ate one slice of pizza. How many slices of pizza were left over? (2015 Math Kangaroo Problem, Level 1-2, Question \#14)

Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division->Simple Multiplication Applications

There were $8\times2=16$ slices. $13+1=14$ slices of pizza were ate, so there were $16-14=2$ slices left.


If this is March, what month will it be $$1993$$ months from today?

January

February

March

April

Since $$12\times166 +1= 1992 + 1= 1993$$, the month will be April.


In $$1975$$ it was estimated that there were $$250000$$ lions in Africa.  Over $$40$$ years this figure has decreased by $$90\textbackslash\%$$.  What is the current estimate for the number of lions in Africa ?

A $$90\textbackslash\%$$ decrease means $$10\textbackslash\%$$ of $$250000 = 250000 \div 10 = 25000$$ of the lions remain.


Annie usually leaves her cell phone on. If her cell phone is on but she is not actually using it, the battery will last for $$36$$ hours. If she is using it constantly, the battery will last for only $$10$$ hours. Since the last recharge, her phone has been on $$20$$ hours, and during that time she has used it for $$120$$ minutes. If she only keeps using the phone $3$ hours more and then leaves the phone on, how many more hours will the battery last after she leaves the phone on? (Adapted from $$2004$$ AMC $$8$$ Problem, Question \#$$12$$)

Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Simple Work Word Problems

When not being used, the cell phone uses up $$\dfrac{1}{36}$$ of its battery per hour. When being used, the cell phone uses up $$\dfrac{1}{10}$$ of its battery per hour. Since Annie\textquotesingle s phone has been on for $$20$$ hours, of those $$18$$ simply on and $2$ being used, $$18\times\left(\dfrac{1}{36}\right)+2\times\left(\dfrac{1}{10}\right)=\dfrac{7}{10}$$ of its battery has been used up. To drain the remaining $$\dfrac{3}{10}$$, the phone can last for $$(\frac{3}{10}-3\times\frac1{10})\div \frac1{36}=0$$ more hours without being used.


A cow gives $24$ liters of milk each day. If the milkman sells $80$\% of the milk, how many liters of milk is left with him?


Patrick got into a lift. He went down six floors, up seven floors and then down eight floors. He was finally on the third floor. Which floor did Patrick get into the lift?

Overseas Competition->Knowledge Point->Word Problem Modules->Inverse Operation Problems->Inverse Operations


Together, Bob, Colin and Dave weigh $$195\text{kg}$$. Bob weighs $$9\text{kg}$$ more than Colin and $$6\text{kg}$$ more than Dave. How much does Bob weigh?

Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference->Sum and Differences Problems with multiple Variables


Helen said to Mary, "If you give me $$4$$ apples, I will have exactly as many apples as you." How many more apples does Mary have than Helen?

Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Difference and Multiple->Differences and Multiples of Two Variables->Differences and Integer Multiples


To make a pudding, you need $$2$$ ounces of flour and $$10$$ ounces of milk. You have $$10$$ ounces of flour and want to make as many puddings as possible. How much milk do you need?

$$20$$ ounces

$$30$$ ounces

$$40$$ ounces

$$50$$ ounces

$$60$$ ounces

The ratio of flour to milk is $$2:10$$ or $$1:5$$. With $$10$$ ounces of flour, you could make as many as $$5$$ puddings. At the same time, you need $$50$$ more ounces of milk. The ratio of flour to milk is $$10:50$$, or $$1:5$$.


NBA playoffs are held annually. The $62$\textsuperscript{nd~}NBA playoffs were held in $2008$. When Judy was $10$ years old, the $58$\textsuperscript{th}~NBA playoffs were held. When was Judy born?


Frank stands in line and has $$76$$ people behind him, If there are a total of $$110$$ people in line, how many people are there in front of Frank?

Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of one Character in a Line

If there are a total of $$110$$ people in line, subtract those behind Frank and Frank himself: $$110-76-1=33$$, the number in front of Frank.


A teacher distributes scorecards to students, if everyone gets $3$ cards, there will be a shortage of $12$ cards. If everyone gets $2$ cards, all these cards will just be divided. Then, how many students are there in total?

Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Basic Distribution Problems

If $2-1=1$ less card is given to students, the situation would transfer from \textquotesingle a shortage of $12$ cards\textquotesingle~ to \textquotesingle all cards are just divided\textquotesingle{} . Therefore. the shortage of $12$ cards is equal to the number of cards that everyone gets $1$ less card. So, there are in total $12\div1=12$ students.


Which date is $$100$$ days after November $$6\text{th}$$?

February $$14$$

February $$15$$

February $$16$$

February $$17$$

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time

It\textquotesingle s $$92$$ days $$\left( 30+31+31 \right)$$ from Nov. $$6$$ to Feb. $$6$$;~$$8$$ days later is $$100$$ days.


Karl Lecter has been collecting $$1\text{p}$$, $$2\text{p}$$ and $$5\text{p}$$ coins in a jar. All but $$10$$ of his coins are $$1\text{p}$$ coins, all but $$10$$ are $$2\text{p}$$ coins, and all but $$10$$ are $$5\text{p}$$ coins. How much money does he have?

Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method

All but $$10$$ of the coins are $$1\text{p}$$ coins, which tells us that the number of $$2\text{p}$$ and $$5\text{p}$$ coins adds up to $$10$$. Similarly, the total of the $$1\text{p}$$ and $$5\text{p}$$ coins is $$10$$ and the total of the $$1\text{p}$$ and $$2\text{p}$$ coins is $$10$$. He therefore has $$5$$ of each coin, giving a total of $$(5 \times1)+ (5 \times2)+(5\times5)=40\text{p}$$.


When I add together the number of sides of a quadrilateral, a trapezoid, and a parallelogram, I get a total of．

Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction

Quadrilaterals, trapezoids, and parallelograms each have $$4$$ sides each, so the total number of sides is $$4+4+4=12$$.


A ship was attacked by pirates. One by one the pirates climb a rope to get on the ship. The pirate captain was the $$8$$\textsuperscript{th}~pirate to climb in line, and there were as many pirates in front of him as behind him. How many pirates climbed the rope? (2015 Math Kangaroo Problem, Level 1 - 2, Question \#18)  $$\textasciitilde$$

The pirate captain was the $$8$$\textsuperscript{th}~pirate and there were as many pirates in front of him as behind him, which means there were $$7$$ pirates in front of him and there were also $$7$$ pirates behind him. The total number of pirates is~~$$7+7+1=15$$.


If $$28$$ January $$2000$$ falls on a Friday, which day of the week will $$28$$ January $2001$ fall on?

Thursday

Friday

Saturday

Sunday

Monday

$2000$ is a leap year and the period includes $29$ Feb, so there are $366$ days.  $366\div7=52$ R $2$  Friday $+$ $2$ days $\rightarrow$ Sunday


There are $$9$$ benches in the park, which have the same length. They are placed on one side of the road every $$7$$ meters from end to end. Given that the length of the road is $$74$$ meters, how long is the bench?

$$1$$ m

$$2$$ m

$$3$$ m

$$4$$ m

Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Straight Line Type with Objects on Both Sides

The $$9-1=8$$ intervals are $$7\times8=56$$ meters in total.  So, the sum of length of all the benches is $$74-56=18$$ meters and each of them is $$18\div9=2$$ meters.


Nancy did an experiment. She inserted a paper straw vertically into the bottom of a bottle of black ink. Then, she found that the length of the black part of the paper straw was exactly $12$ cm. She turned the straw upside down and inserted the other end vertically into the bottom of the bottle. She found that the length of the part not colored of the straw was exactly half of that of all the black parts. The paper straw was~\uline{~~~~~~~~~~}~cm.

Overseas Competition->Knowledge Point->Word Problem Modules

The black parts of the straw was $$12+12=24$$ cm, so the part not colored was $$24\div2=12$$ cm. Thus, the length of the straw was $$24+12=36$$ cm.


$A$, $B$ and $C$ start from the same place at the same time and chase a cyclist in front of them along the same road. The three cars catch up with him in $6$, $10$ and $12$ minutes respectively. Given that car $A$\textquotesingle s speed is $24$ kilometers per hour, car $B$\textquotesingle s speed is $20$ kilometers per hour. Find car $C$\textquotesingle s speed.

Overseas Competition->Knowledge Point->Word Problem Modules->Newton's Problem of Cows and Fields->Basic Newton's Problem of Cows and Fields->Finding the Number of Cows


Billy has three times as many llamas as lambs.  Milly has twice as many lambs as llamas.  They have $$17$$ animals in total.  How many of the animals are llamas?

Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Indefinite Equation Word Problems

Let Billy have $$b$$ lambs and $$3b$$ llamas. Let Milly have $$m$$ llamas and $$2m$$ lambs.  Therefore, as they have $$17$$ animals in total, $$4b + 3m= 17$$. The only positive integer solution of this equation is $$b= 2$$, $$m= 3$$. So the number of llamas is $$3b + m = 3 \times 2 + 3 = 6 + 3 = 9$$.


A $$25\textbackslash\%$$ salt solution contains $$75$$ g of water. How many g of solution are there?

$$100$$ g

$$25.5$$ g

$$25$$ g

$$102$$ g

Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems


At the red light, seven buses of the same length stop in a line. Given that the length of each bus is $$5$$ meters, and the distance between each two adjacent buses is $$2$$ meters, how long is the line?

$$35$$ m

$$49$$ m

$$47$$ m

$$54$$ m

Among the $$7$$ buses, there are $$7-1=6$$ intervals. So the answer is $$7\times5+2\times6=47$$ meters.


$$37$$ sakura trees were planted along one side of the road. The trees were planted at $$4m$$ intervals. After drivers complained the road was too pink, pineapple trees were planted on the other side of the road at $$6m$$ intervals. How many pineapple trees were planted, if there were sakura and pineapple trees at both ends of the road?

Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems

Number of sakura intervals = $$37-1 = 36$$  Length of road = $$36 \times 4 = 144m$$  Number of pineapple intervals = $$144m \div 6m = 24$$  Number of pineapple trees = $$24 + 1 = 25$$


Agnĳo has half as many apps as Sam who has a third as many apps as Naomi. Altogether, they have $$180$$ apps. How many apps does Sam have?

Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple

Let Agnijo have $$n$$ apps. Now Sam has $$2n$$, and Naomi $$6n$$. Therefore $$n+2n+6n = 9n = 180$$, and so $$n = 180\div9 = 20$$. Hence Sam has $$2\times20 = 40$$ apps.


In the amusement park, Jessie is playing with darts. For each time she hits the bullseye, she can win two toys. At the beginning she has $$3$$ toys and at the end she has $$23$$ toys. How many times did she hit the bullseye? (Adapted from 2006 Math Kangaroo Problem, Level 3-4, Question \#5)

Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable


October 10th, 2021 is Sunday. What day is October $$26$$th of the same year?~\uline{~~~~~~~~~~}~

Sunday

Monday

Tuesday

Wednesday

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates

$26-10=16$, $16\div7=2\textbackslash{} \rm R\textasciitilde2$,~ it\textquotesingle s Tuesday.


There are $$11$$ flags on one side of a road. The distance between neighboring flags is $$5$$ meters. Grace walked from the first flag to the last flag. How many meters did she walk? (Adapted from 2007 Math Kangaroo Problem, Level 3-4, Question \#5)

Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Straight Line Type with Objects on Both Sides->Planting Trees on Both Sides


Colin was preparing for the PE test. On the first day, he ran $1$ km. He decided that each day he would be running $100$ m more than the day before. How many meters did he run in total in the first $5$ days?

Overseas Competition->Knowledge Point->Word Problem Modules->Practical Application of Arithmetic Progression


In a mathematics contest with ten problems, a student gains $$5$$ points for a correct answer and loses $$2$$ points for an incorrect answer. If Olivia answered every problem and her score was $$29$$, how many correct answers did she have?

Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable

Suppose Olivia has $$x$$ correct answers. $$5x-2(10-x)=29$$, $$x=7$$.


Wendy had $$30$$ stickers. First, she gave Aiden three stickers. Then, she gave Terry $7$ stickers. Now, each of the three people had the same number of stickers. At the beginning, how many stickers did they have in total?

Overseas Competition->Knowledge Point->Word Problem Modules->Inverse Operation Problems

Now, Wendy had $30-3-7=20$ stickers. Then, all of them had $20\times3=60$ stickers, which was equal to the total number of stickers they had at beginning.


Bram bought $$60$$ beans for ＄$$3.00$$. At this price, $$100$$ beans cost．

If $$60$$ beans cost ＄$$3.00$$, then $$1$$ bean costs $$5$$￠and $$100$$ beans cost ＄$$5$$.


Historians say that William the Conqueror was born in $$1028$$. How many years ago was that?

The number of years from William\textquotesingle s birth is $$2018 - 1028 = 990$$.


A 20\% increase in the price of milk leads to a 10\% decrease in the quantity of cereal purchased. The cross-price elasticity of demand between milk and cereal is

-0.5 and the two goods are substitutes.

-0.5 and the two goods are complements.

0.5 and the two goods are complements.

-2 and the two goods are substitutes.

2 and the two goods are complements.

This is an application of the cross-price elasticity equation: \% change in QDx/\% change in Py. -0.10/0.2 = -0.5. A negative number means the goods are complements.


If one bag of chips costs $$75$$￠, then three of these bags cost ．

One bag costs $$75$$￠. Three such bags cost $$3\times $0.75=$2.25$$.


After Sally takes $20$ shots, she has made $40 \textbackslash\%$ of her shots. After she takes $5$ more shots, she raises her percentage to $52 \textbackslash\%$. How many of the last $5$ shots did she make? ( adapted from 2004 AMC 8, Question\#6)

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems

Sally made $0.4 * 20=8$ shots originally. Letting $x$ be the number of shots she made, we have $\frac{8+x}{25}=0.52$. Solving for $x$ gives us $x=5$


If $$1$$ August falls on Monday, which day of the week will $$12$$ September fall on?  Below is Chris\textquotesingle~answer.  Number of days from 1 Aug to 12 Sept: 31 + 12 = 43  43 $\div$ 7 = 6 R 1  Hence, 12 September is a Tuesday.  Is Chris\textquotesingle s answer correct? If not, what is the correct answer? ．

Sunday

Monday

Tuesday

Wednesday

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time

Number of days from $$1$$ August to $$12$$ September  $$=31+12-1$$  $$=42$$  $$42\div 7=6$$ weeks  Therefore, $$12$$ September will fall on \textbf{Monday}.


The owner of a bicycle store had a sale on bicycles(two-wheelers) and tricycles(three-wheelers). Each cycle had two pedals. When he counted the total number of pedals of the cycles, he got 50 . When he counted the total number of wheels of the cycles, he got 64 . How many tricycles were offered in the sale?

Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems

$50\div 2=25$  let $x$ be the number of bicycles, $y$ be the number of tricycles  $2x+3y=64$  $x+y=25$


Anna, Bridgit and Carol run in a $$100\text{m}$$ race. When Anna finishes, Bridgit is $$16\text{m}$$ behind her and when Bridgit finishes, Carol is $$25\text{m}$$ behind her. The girls run at constant speeds throughout the race. How far behind was Carol when Anna finished?

Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road

Carol finishes $$25$$ metres behind Bridgit, so she travels $$75$$ metres while Bridgit runs $$100$$ metres. Therefore she runs $$3$$ metres for every $$4$$ metres Bridgit runs. When Anna finishes, Bridgit has run $$84$$ metres, so that at that time Carol has run $$\frac{3}{4}\times 84$$ metres $$=63$$ metres. Hence Carol finishes $$\left( 100-63 \right)$$ metres $$= 37$$ metres behind Anna.


If $$6$$ cans of Sweet Stuff Soda all together contain $$96$$ teaspoons of sugar, then there are a total of teaspoons of sugar in $$15$$ cans.

Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value

If $$6$$ cans contain $$96$$ teaspoons of sugar, $$1$$ can contains $$96\div6 = 16$$ teaspoons of sugar. Thus $$15$$ cans contain $$16\times15 =240$$ teaspoons of sugar.


Given that January $$1$$st, $$2018$$ was Monday, on what day did January $$1$$st, $$2019$$ fall?

Tuesday

Monday

Sunday

Wednesday

$2018$ was a common year which had $365$ days. Thus, January $$1$$st, $$2019$$ fell on one day after Monday, which was Tuesday.


Three zebras take part in a contest. The winner is the zebra with the most number of stripes. QingLe has $$15$$ stripes, ChenXi has $$3$$ more than QingLe. QingLe has $$5$$ fewer stripes than YueYing. How many stripes does the winner have?

Overseas Competition->Knowledge Point->Word Problem Modules


In the yard there is an equal number of pigs, ducks and chickens. Together, they have $$144$$ legs. How many ducks are there in the yard?

Suppose there are $$x$$ ducks in the yard. Since there is an equal number of pigs, ducks and chickens, $$2x+4x+2x=144$$, $$x=18$$.


Paul was going to buy $$4$$ servings of ice cream, but he was $$80$$ cents short. So, he bought $$3$$ servings and had $$30$$ cents left. What was the price of one serving of ice cream?

$$70$$ cents

$$80$$ cents

$$90$$ cents

$$1$$ dollar

$$1$$ dollar $$10$$ cents

Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Basic Distribution Problems


A salt solution is made by mixing $100$ g of salt and $400$ g of water. Find the percent concentration of the mixture.

Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts->Calculating Price from Cost and Profit

$$100\div \left( 100+400\right) \times 100\textbackslash\% =20\textbackslash\%$$.  ~~


When $$4$$ kilograms of $$30\textbackslash\%$$ sugar water is mixed with some $$10\textbackslash\%$$ sugar water, it gives a mixture with a sugar concentration of $$26\textbackslash\%$$. How much $$10\textbackslash\%$$ sugar water is needed?~\uline{~~~~~~~~~~}~$$\text{kg}$$

Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems

Use the cross method $$\begin{matrix}30\textbackslash\%10\textbackslash\% \textbackslash\textbackslash{} \searrow \swarrow \textbackslash\textbackslash{} 26 \textbackslash\% \textbackslash\textbackslash{} \swarrow \searrow \textbackslash\textbackslash{} 16 \textbackslash\%4\textbackslash\% \textbackslash\textbackslash\end{matrix}$$ to see that the ratio of $$30\textbackslash\%$$ solution to $$10\textbackslash\%$$ solution is $$4:1$$. Therefore, $$1\text{kg}$$ of $$10\textbackslash\%$$ solution is needed.


Cindy has $$50$$ bookmarks. If she were to give $$6$$ bookmarks to each of her classmates, she would need $$10$$ more bookmarks. How many classmates does Cindy have?


A mixture of 30 liters of paint is $25 \textbackslash\%$ red tint, $30 \textbackslash\%$ yellow tint and $45 \textbackslash\%$ water. Five liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture? (2007 AMC 8, Question \#17 )

Since $30 \textbackslash\%$ of the original 30 liters of paint was yellow, and 5 liters of yellow paint were added to make the new mixture, there are $9+5=14$ liters of yellow tint in the new mixture. Since only 5 liters of paint were added to the original 30 , there are a total of 35 liters of paint in the new mixture. This gives $40 \textbackslash\%$ of yellow tint in the new mixture, which is (C) 40 .


Josh lives on the $6$\textsuperscript{th} floor. He needs to climb $24$ steps to move from the $2$\textsuperscript{nd~}floor to the $4$\textsuperscript{th} floor. How many steps does he need to climb from the $1$\textsuperscript{st} floor to the $6$\textsuperscript{th} floor?

Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems


Find the exact number of minutes after $3.00 \text{pm}$ when the minute and hour hands are first at $90^{\circ}$ to each other.

$$31 \frac{2}{11}$$

$$31 \frac{3}{11}$$

$$32 \frac{8}{11}$$

$$33 \frac{3}{11}$$

None of the above

The minute hand rotates $6^{\circ}$ per minute.  The hour hand rotates $\dfrac{1}{60}\times30^{\circ}=\left (\dfrac{1}{2}\right )^{\circ}$ per mimte.  Starting at $3$ O\textquotesingle clock, when the minute and hour hands are next perpendicular:  $$(90+90)\div(6-0.5)=\frac{360}{11}=32 \frac{8}{11}$$


The page numbers of a book are from $$1$$ to $$62$$. Tim adds up the $$62$$ page numbers. In his calculation, he misses a page number and the sum of remaining pages is $$1940$$. What is the missing page number~\uline{~~~~~~~~~~}~.


Suppose $50\textbackslash\%$ of $x$ equals $30\textbackslash\%$ of $y$. What percentage of $y$ is $x$ ? (adapted from 2020 AMC 8, Question 15)

$50\textbackslash\% \cdot x = 30\textbackslash\% \cdot y$  $ x = 0.6\cdot y$


Grandma made some cheese dumplings and some blueberry dumplings. Altogether, she made $$31$$ dumplings. If she had made $$11$$ more cheese dumplings, then there would be the same number of blueberry dumplings as cheese dumplings. How many cheese dumplings did grandma make? ($$2009$$ Math Kangaroo Problem, Levels $$1-2$$, Question \#$$19$$)

Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference


After the game, Owen is thirsty again. This time he gets a mixture of 3 liters of juice, which contain $25 \textbackslash\%$ of apple juice, $30 \textbackslash\%$ of mango juice, and $45 \textbackslash\%$ of water. $0.5$ liters of mango is added to the original mixture. What is the percent of mango in the new mixture? (Adapted from 2007 AMC 8, Question \#17 )


Grandma made some cheese dumplings and some blueberry dumplings. Altogether, she made $$31$$ dumplings. If she had made $$11$$ more cheese dumplings, then there would be the same number of blueberry dumplings as cheese dumplings. How many cheese dumplings did grandma make?


$$31 \frac{2}{11}$$

$$31 \frac{3}{11}$$

$$32 \frac{8}{11}$$

$$33 \frac{3}{11}$$

None of the above

The minute hand rotates $6^{\circ}$ per minute.  The hour hand rotates $\dfrac{1}{60}\times30^{\circ}=\left (\dfrac{1}{2}\right )^{\circ}$ per mimte.  Starting at $3$ O\textquotesingle clock, the minute hand rotates $\left (6t\right )^{\circ}$ and the hour hand rotates ~$$(90+ \frac{1}{2}t)^{ \circ }$$.  When the minute and hour hands are next perpendicular:  $$6t-\left (90+ \frac{1}{2}t\right )=90$$,  $$\frac{11}{2}t=180$$,  $$t= \frac{360}{11}=32 \frac{8}{11}$$.


Joann\textquotesingle s birthday in $$2020$$ was May $$10$$\textsuperscript{th}, which was Sunday. Elizabeth\textquotesingle s birthday in $$2020$$ was June $$21$$\textsuperscript{st}. On what day did Elizabeth\textquotesingle s birthday fall?

Thursday

Saturday

Sunday

Tuesday

It passed $$31-10 + 21 = 42$$ days in total. Since $$42 \div 7 = 6$$, it was Sunday.


Three zebras take part in a contest. The winner is the zebra with the most number of stripes. Runa has $$15$$ stripes, Zara has $$3$$ more than Runa. Runa has $$5$$ fewer stripes than Biba. How many stripes does the winner have?


Sara is $$5$$ years old and Mike is $$9$$. How old will Sara be when Mike is $$20$$ years old?

Their difference in age: $$9-5=4$$  When Mike is $$20$$, Sara is $$20-4=16$$


A $$15\textbackslash\%$$ sugar solution contains $$18$$ grams of pure sugar. How many grams of solution are there?

$$90$$ grams

$$100$$ grams

$$120$$ grams

$$150$$ grams

Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems

$$18\div15\textbackslash\% = 120$$ ounces.


The boundary of a lake is $$600\text{m}$$ long. Trees are planted at regular intervals of $$6\text{m}$$ round the lake. How many trees are planted round the lake?

Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Circular Paths

In the case of circular tracks,  number of intervals $$=$$ number of trees,  $$600\div 6=100$$,  $$100$$ trees are planted round the lake.


Given that January $$1$$st, $$2018$$ was Monday, on what day did January $$1$$st, $$2019$$ fall?

Tuesday

Monday

Sunday

Wednesday

$2018$ was a common year which had $365$ days. Thus, January $$1$$, $$2019$$ fell on one day after Monday, which was Tuesday.


A machine started printing posters at $$9.00 \rm a.m.$$ on Monday at the rate of $$1000$$ posters per hour. After every $$6$$ hours of printing, it was paused for an hour. How many posters were printed by $$\rm 11.00 a.m$$. the next day?

Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method


A shop purchased a kind of Lego at ＄$$125$$ each. It then sold them at ＄$$168$$ each. How much did the shopkeeper earn for $$5$$ Legos?


Jenny paid $15$ dollars for $3$ books. How many dollars should she pay in total for the same kind of books if she bought $5$ more of them?


There are $3600$ baby chickens on a farm. The number of hens on the farm is $\dfrac{8}{9}$~of the baby chickens, and the number of roosters is $\dfrac{1}{16}$~of the number of hens. How many roosters are there on the farm?

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base

Hens $=$ baby chickens $\times\dfrac{8}{9}$,  Roosters $=$ hens $\times\dfrac{1}{16}$,  We can write the formula as:~$3600\times\dfrac{8}{9}\times\dfrac{1}{16}=3200\times\dfrac{1}{16}=200$.


Students in the third grade lined up and formed a square array to perform a dance. Each side of the outermost layer had $37$ students. How many students in total are there on the outermost layer?

Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Squares->Solid Squares


The mushrooms picked by $2$ white rabbits in $3$ days will be eaten by $3$ gray rabbits in $4$ days. In how many days will $15$ gray rabbits eat up mushrooms picked by $5$ white rabbits in $6$ days?

The mushrooms picked by $2$ white rabbits in $3$ days will be eaten by $3$ gray rabbits in $4$ days, so the mushrooms picked by $1$ white rabbits in $1$ days will be eaten by $1$ gray rabbits in $2$ days.  Thus, the mushrooms picked by $5$ white rabbits in $6$ days will be eaten by $15$ gray rabbits in $4$ days.


Jimmy\textquotesingle s father brought Jimmy three pet dogs, and Jimmy could only keep one. How many dogs did Jimmy\textquotesingle s father want to take away?~(adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$3$$)


In a garage, the ratio of red cars to black cars is $$8:5$$, and the ratio of black cars to white cars is $$3:4$$. The minimum number of cars in the garage is．

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Complex Ratio Problems

The ratio of red cars to black cars is $$8:5=24:15$$; the ratio of black cars to  white cars is $$3:4 = 15:20$$. The minimum number of cars is $$24+15+20 =59$$.


In the Avengers League, there are $25$ superheroes. Six of the superheroes from the galaxy guard left. How many heroes are left?~(adapted from $$2007$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$6$$)

Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction

There are $25$ superheroes in total. After subtracting $6$, there are $25-6=19$ left.


In a verbal test, the average score of $$40$$ students is $$25$$. The lowest score is $$5$$. At most how many student(s) can get $$100$$ points?

Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems

Total points: $$40\times 25=1000$$.  To have as many $100$ points as possible, we should consider there are only two groups of students: everyone gets $5$ points in a group and everyone gets $100$ in the other group.  $$10\times 100=1000$$, so there must be less than $10$ people getting $100$ points.  If there are nine $100$s: $$9\times 100+31\times 5=1055\textgreater1000$$, which is impossible.  If there are eight $100$s:$$8\times 100+32\times 5=960\textless{}1000$$.  Thus, the answer is $$8$$.


If I write all $$26$$ letters of the English alphabet in alphabetical order $$62$$ times in a row, then the $$806$$th letter I write will be．

$$A$$

$$E$$

$$V$$

$$Z$$

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation

Since $$806\div 26=31$$, the $$806$$th letter Iwrite will be the last letter of the $$31$$st time I write the full alphabet; it will be a $$Z$$.


Amy mixes $$10$$ g of a $$20\textbackslash\%$$ sugar solution and $$40$$ g of a $$25\textbackslash\%$$ sugar solution together. After~\uline{~~~~~~~~~~}~of water evaporates, the percent concentration of solution is $40\textbackslash\%$.

$$15$$ g

$$18$$ g

$$20$$ g

$$25$$ g

Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants

$$10\times20\textbackslash\%+40\times 25\textbackslash\%=12$$ g.  $$(10+40)-12\div40\textbackslash\%=20$$ g.


A snail is climbing up from the bottom of a $15$-meter-deep well. It climbs up $3$ meters during the daytime, and slides down $1$ meter every night. How many days will it take to get out of the well?

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems

It climbs up $$3-1=2$$ meters actually everyday. It takes $$12\div 2 +1=7$$ days in total, and in the last day, it climbs up $3$ meters.


Annie had twice as many paper clips as Beth, After Beth had used $$15$$ paper clips, Annie had $$4$$ times as many as Beth. How many paper clips did Annie have?

Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Questions Involving Varying Multiples

Let the number of Annie\textquotesingle s and Beth\textquotesingle s be 2n and n. 2n=4(n-15), so n=30, 2n=30


It takes $$144$$ workers $$60$$ hours to paint a bridge. Working at the same rate, how many hours would $$108$$ workers require to do the job?

It takes $$144$$ workers $$60$$ hours to paint a bridge. That\textquotesingle s $$144\times60=8640$$ worker-hours. For $$108$$ workers, the job takes $$8640\div108=80$$ hours.


The speed of high-speed train is approximately $$350$$ kilometers per hour, while the walking speed of a person is approximately $$5$$ meters per second.  Approximately, how many times is the speed of a high-speed train faster than the walking speed of a person?．

$$2 $$

$$20 $$

$$70 $$

$$200 $$

Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples

The speed of high-speed train is approximately $$350$$ kilometers per hour, which is approximately $$100$$ meters per second. So its speed is roughly $$20$$ times faster than $$5$$ meters per second.


A gift store buys some gifts at＄$$125$$ each. It wants to earn＄$$25 $$ for each gift after a discount of $$25 \textbackslash\% $$. What is the selling price before the discount for each shirt?

$$160$$ dollars

$$180$$ dollars

$$190$$ dollars

$$200$$ dollars

Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts

$$\left( 125+25 \right)\div \left( 1-25 \textbackslash\% \right)=200$$ dollars.


Two motor-cyclists John and Kevin were $800 \text{km}$ apart and travelling towards each other at a constant speed. They started at the same time, meeting after $8$ hours. If Kevin started $1\dfrac{1}{2}$ hours later than John, they would be $70 \text{km}$ apart $8$ hours after John started. At what speed was John travelling in $\text{km/h}$?

$$51 \frac{2}{3}$$

$$52 \frac{1}{2}$$

$$53 \frac{1}{3}$$

None of the above

Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable


\textbf{Daniel is learning that five pennies spread out on his desk are the same number of coins as five pennies in a pile. According to Piaget, how old is Daniel likely to be?}

\textbf{4 years}

\textbf{8 years}

\textbf{13 years}

Overseas Competition->Knowledge Point->Word Problem Modules

\textbf{Daniel is learning conservation of number, a skill that Piaget believed children learn in the concrete operational stage}


Amy mixes $$30$$ g of a $$30\textbackslash\%$$ salt solution and $$20$$ g of a $$20\textbackslash\%$$ salt solution together. How many g of water should she add to the mixture to make it a $$10\textbackslash\% $$ solution?


Arrange $$28$$ balls to form a square.  One ball is placed at each corner of the square.  How many balls are there on each side of the square?~\uline{~~~~~~~~~~}~

Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Squares->Hallow Squares

Put $$1$$ ball in each corner ($$4$$ balls in total).  Remaining balls: $$28-4=24$$  $$24\div4=6$$  So, each side has $$1$$ ball at each corner and $$6$$ balls in the middle, giving a total of $$8$$ balls.


The average pocket money of the whole class is $91$ dollars. Each of the $24$ girls in the class has $92.5$ dollars on average. There are $18$ boys in the class, and their average pocket money is~\uline{~~~~~~~~~~}~dollars.

More than average: $$(92.5-91)\times24=36$$.  Each boy should have $$36\div18=2$$ dollars less than the average, so each of them has $91-2=89$ dollars.


$$\frac{3}{7}$$ of the passengers on the bus were adults and the rest were children. There were $$24$$ children. How many adults were there?

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base


When Teddy was $$5$$ years old, his father\textquotesingle s age was $$7$$ times his age. When his father is $$42$$ years old, how old will Teddy be?

Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->When..., When... Type Age Problems

$$7\times5=35$$,  His father was $$35$$ years old when Teddy was $$5$$ years old.  Age difference $=35-5=30$  $42-30=12$ years old  $\textasciitilde$  or  $\textasciitilde$  $$7\times5=35$$,  His father was $$35$$ years old when Teddy was $$5$$ years old.  $$42-35=7$$ years later  $$5+7=12$$ years old  $\textasciitilde$  Teddy will be $$12$$ years old when his father is $$42$$ years old.


The average height of all the teachers in Grape School is $168$. There are $5$ male teachers in Grape School with an average height of $180$. The average height of female teachers is $162$. How many female teachers are there?

Total height less than the average: $(180-168)\times5=60$.  Thus, there are $60\div(168-162)=10$ female teachers.


There are only lilies and roses in Bud\textquotesingle s garden. One third of the flowers are roses. There are 12 roses in total. How many flowers are there in Buds\textquotesingle s garden?


A shop purchased some tennis rackets at ＄$$150$$ each. It then sold them at ＄$$175$$ each. How much did the shopkeeper earn for $$10$$ rackets?

Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method


Little Pig is standing in a line. There are $$16$$ animals in the line and her position is the $$4$$\textsuperscript{th} counting from front to back. How many animals are behind her?~\uline{~~~~~~~~~~}~

Ms. Pig is included in the "$$4$$" , so there are $$16 - 4 = 12$$ animals behind her.


There are $5$ people in Linda\textquotesingle s family with an average weight of $56$ kg. The weights of Linda, Linda\textquotesingle s mom, Linda\textquotesingle s sister, and Linda\textquotesingle s brother are $45$ kg, $55$ kg, $50$ kg, and $60$ kg, respectively. What is the weight of Harry\textquotesingle s dad?


Della decides to buy some stationaries for her students. The price of two schoolbags is equal to the price of six notebooks, and the price of six pencilcases is equal to nine notebooks. Given that one schoolbag can be exchanged for four pens, how many pens can be exchanged for one pencilcase?

Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division

$$1$$ schoolbag$$=3$$ notebooks$$=4$$ pens,  and $$6$$ pencilcases$$=9$$ notebooks,  Then, $$2$$ pencilcases$$=3$$ notebooks$$=4$$ pens.  So, $$1$$ pencilcase$$=2$$ pens.


Suppose $20 \textbackslash\%$ of $x$ equals $40\textbackslash\%$ of $y$. What percentage of $y$ is $x$ ? (adapted from 2020 AMC 8, Question 15)

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems

$20 \textbackslash\% \cdot x = 40\textbackslash\% \cdot y$  $ x = 2 \cdot y$


Iate half an apple pie on Saturday and two thirds of the remainder on Sunday. What fraction of the pie was left for Monday?

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Understanding the Base

After I eat one half, half of the apple pie is left. Eating two thirds of this half leaves one third of one half of the pie, which is one sixth, for Monday.


If $$1000\textbackslash\%$$ of a certain number is $$100$$, the certain number is．

If $$1000\textbackslash\%$$ is $$100$$, then $$\left(\frac{1}{10}\right)\text{th}$$ of that, $$10$$, is $$100\textbackslash\%$$ of the number.


Jin loves carrots! Yesterday she ate $$\frac{7}{9}$$ of her carrots, and today she ate $$\frac{2}{7}$$ of the number of carrots she ate yesterday. She ate 14 carrots today. Yesterday she had started with  carrots.


A total of $$20$$ chickens and rabbits are caged together. If there are $$56$$ legs in total, how many chickens are there in the cage?

Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis

Suppose the number of chickens is $x$, so the number of rabbits is $(20-x)$.  $2x+(20-x)\times4=56$, $x=12$.


Ellie and Gloria have to interview a total of $$400$$ people. Ellie can interview $$60$$ people every week. If Gloria and Ellie work together, they can finish all the work in $$4$$ weeks. How many weeks will it take to finish interviewing everyone by Gloria herself?

Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems

Working together: $$400\div4=100$$ people every week  Gloria: $$100-60=40$$ people every week  $$400\div40=10$$ weeks  $\textasciitilde$


$50$ balloons are distributed to Ariel and seven other children. Each of them can get at least one balloon, and no two of them get the same number of balloons. For Ariel, what is the largest possible number of balloons she can get?

Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Problems Involving Extreme Value

The largest number of balloons Ariel can get is: $$50 -- (1 + 2 + 3 + 4 + 5+6+7) = 22$$, that is, $$22$$ balloons at most.


$$29$$ students came into the classroom in turn. The number of students that came in before Mike was $$5$$ more than the number of students who came in after him. Which place did Mike come in? (Adapted from 2015 Math Kangaroo Problem, Level 3 - 4, Question \#13)

Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Order of one Character

The sum of the number of students that came in before Tom and the number of students that came in after him is $29 - 1 = 28$. The number of students that came in before Mike was $(28 + 6) \div 2 = 17$, so Mike was the eighteenth.


A $$15\textbackslash\%$$ sugar solution contains $$18$$ ounces of pure sugar. How many ounces of solution are there?

$$90$$ ounces

$$100$$ ounces

$$120$$ ounces

$$150$$ ounces

Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems

$$18\div15\textbackslash\% = 120$$ ounces.


My first day of vacation is May $$10$$. My last day of vacation is May $$20$$ of the same year. How many days of vacation do I have?

$$ 10 $$

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time


The sum of two numbers is $$71$$. The difference of the two numbers is $$9$$. Find the bigger number.

Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference


For a quarter ($$25$$￠), Pat can play a video game for $$5$$ minutes.  How many quarters does Pat need to play for an hour?

For a quarter ($$25$$￠), Pat can play a video game for $$5$$ minutes.  The number of $$5$$-minute intervals in $$1$$ hour is $$60 \div 5 = 12$$.


The teacher has $$14$$ sweets. She wants to give eight students the same number of sweets. How many more sweets should she prepare? (adapted from $$2020$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$16$$)

$$14=8+6$$, ~In this equation, $$8$$ means everyone can get $$1$$ sweet. There are $$6$$ sweets left, the teacher also needs $$8-6=2$$ sweets.


Given that May $$16$$ of a certain year is a Monday, what day of the week will July $$8$$ fall on in the same year?

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday


$$\frac{1}{4}$$ of the beads in a box are blue. $$\frac{1}{3}$$ of the blue beads are small. lf there are $$700$$ small blue beads, how many beads are there altogether in the box?

$\frac{1}{4}\times\frac{1}{3}=\frac{1}{12}$ of the total beads are small blue beads.  $700\times12=8400$


Nick bought $20$ apples from the supermarket. $40$\% of them were red and $60$\% of them were green. How many red apples did he buy?


Famer $$A$$ had $$1233$$ ducks. He had three times as many ducks as Farmer $$B$$. Farmer $$B$$ had $$199$$ more ducks than Farmer $$C$$. How many ducks did Farmer $$C$$ have?

Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Word Problems Involving Comparing and Ordering

Farmer B\textquotesingle s duck: $$1233 \div3 = 411$$  Farmer C\textquotesingle s duck: $$411-199=212$$


Given that June $$14$$, $$2012$$ was Thursday, what day was June $$14$$, $$2014$$?

Monday

Tuesday

Friday

Saturday

Sunday

It would pass $365+365=730$ days, which means June $$14$$, $$2014$$ was two days after Thursday. It was Saturday.


There are some apples and $8$ pears in a basket, each of them are green or yellow. There are three more apples than the total number of green fruit. There are $6$ yellow pears. How many yellow apples are there in the basket?


Starting with some gold coins and some empty treasure chests, I tried to put $$9$$ gold coins in each treasure chest, but that left $$2$$ treasure chests empty. So instead I put $$6$$ gold coins in each treasure chest, but then I had $$3$$ gold coins left over. How many gold coins did I have? ．

Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable

Suppose $x$ is the number of treasure chests. Thus the number of gold coins can be represented as $$9(x-2)$$ or $$6x + 3$$. So, $$9(x-2)=6x+3$$, $$x=7$$. There are $$9\times (7-2)=45$$ gold coins.


There were $$27$$ children in a class.  There were twice as many boys as girls.  How many boys were there?

$$21$$ boys

$$18$$ boys

$$16$$ boys

$$14$$ boys

$$9$$ boys

Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple


On a map $4\text{cm}$ represents $50\text{km}$. The distance between town A and town B is $14\text{cm}$. A car leaves town A and travels towards town B at $35$km per hour. How long does it take the car to travel to town B?

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units

If $$4\textasciitilde\text{cm}$$ represents $$50\textasciitilde\text{km}$$, $$2\textasciitilde\text{cm}$$ represents $$25\textasciitilde\text{km}$$. So, their actual distance apart is $$14\div2\times 25=175\textasciitilde\text{km}$$. $175\div35=5$ hours.


Students guess that Norb\textquotesingle s age is $$24$$, $$28$$, $$30$$, $$32$$, $$36$$, $$38$$, $$41$$, $$44$$, $$47$$, and $$49$$. Norb says, "At least half of you guessed too low, two of you are off by one, and my age is a prime number." How old is Norb? ($$2011$$ AMC $$8$$ problem, Question \#$$21$$)

Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems

If at least half the guesses are too low, then Norb\textquotesingle s age must be greater than $$36$$.  If two of the guesses are off by one, then his age is in between two guesses whose difference is $$2$$. It could be $$31$$, $$37$$, or $$48$$, but because his age is greater than $$36$$, it can only be $$37$$ or $$48$$.  Lastly, Norb\textquotesingle s age is a prime number so the answer must be $$37$$.


Joan needs $$250$$ pounds of metal with $$27\textbackslash\%$$ silver. If Joan combines one metal with $$23\textbackslash\%$$ silver, and another with $$43\textbackslash\%$$ silver,how much of each metal does Joan need respectively?

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base


Ten years ago, the sum of the ages of my mother and father was $$71$$. What is the sum of their ages today?

Ten years ago, the sum of the ages of my mother and father was $$71$$. Each has aged $$10$$ years, so the sum of their ages is now $$91$$.


If I start with $2$, and begin to count in $$3$$s, my $50^{}\text{th}$ number will be~\uline{~~~~~~~~~~}~.

Overseas Competition->Knowledge Point->Word Problem Modules->Practical Application of Arithmetic Progression


In the yard there is an equal number of pigs, ducks and chickens. Together, they have $$144$$ legs. How many ducks are there in the yard?

Suppose there are $$x$$ ducks in the yard. Since there is an equal number of pigs, ducks and chickens, $$2x+4x+2x=144$$, $$x=18$$.


Emma is $9$ years old. Anna is $12$ years old. Peter is older than Emma but younger than Anna. How old is Peter?

Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems


Some kangaroos are lining at bakery. Tom is the third kangaroo from the back, and the fifth from the front. How many kangaroos are there lining up in total?

Overseas Competition->Knowledge Point->Word Problem Modules


Henderson has $$9$$ sweets more than Flora. After teacher Johnny gave each of them $$7$$ more sweets, they have a total of $$43$$ sweets. How many sweets does Flora has at first?


If today is a Tuesday, then $$15$$ days ago was a.

Saturday

Sunday

Monday

Wednesday

Today is Tues. $$14$$ days ago was Tues. $$15$$ days ago was Mon.


In a jar of red, green, and blue marbles, all but $$6$$ are red marbles, all but $$8$$ are green, and all but $$4$$ are blue. How many marbles are in the jar?

Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Multivariate Linear Equation Word Problems

Suppose there are $$x$$ red marbles, $$y$$ green marbles and $$z$$ blue marbles. Thus, we can get  $$\begin{cases} x+y=4① \textbackslash\textbackslash{} y+z=6②\textbackslash\x+z=8③\end{cases}$$,  ①$$+$$②$$+$$③: $$2x+2y+2z=18$$, $$x+y+z=9$$.


In a jar of red, green, and blue marbles, all but $$16$$ are red marbles, all but $$18$$ are green, and all but $$14$$ are blue. How many marbles are in the jar? ．

Suppose there are $$x$$ red marbles, $$y$$ green marbles and $$z$$ blue marbles. Thus, we can get  $$\begin{cases} x+y=14① \textbackslash\textbackslash{} y+z=16②\textbackslash\x+z=18③\end{cases}$$,  ①$$+$$②$$+$$③: $$2x+2y+2z=48$$, $$x+y+z=24$$.


Sanjay let me finish his box of mints.  He had eaten $$\frac{5}{8}$$ of them.  If $$36$$ mints were left for me, how many mints were there in the box at the start?

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base


On a map of England and Wales the distance between St Ives in Cornwall and St Ives in Cambridgeshire measures $$18\text{cm}$$. In reality the distance between the two towns is about $$450\text{km}$$.  Which of the options below is the scale of the map?

The scale of the map is $$18\text{cm} : 450\text{km}$$; converting the actual distance to centimetres, this is equivalent to $$18 : 450 \times 1000 \times 100 = 18 : 45 000 000$$. Simplifying gives a scale of $$1 : 2 500 000$$.


None of the above

Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples


There are $$300$$ students in Think Primary School. Three-tenths of the students are in year $$5$$ and three-fifths of the year $$5$$ students are girls. How many year $$5$$ girls are there in Think Primary School?

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages


The five-digit number $411A2$ is a multiple of $9$. What digit does A represent?

None of the above

Overseas Competition->Knowledge Point->Word Problem Modules->Applying of Multiplication and Division

From the Divisibility Rule of $9$, the sum of the digit of 411A2 must be divisible by $9$.  $4 + 1 + 1+ 4 + 2 = 8 + A$  Hence A = $1$.


Iron Man\textquotesingle s flying speed is $$12,250$$km/h, which is $$25$$ times the speed of a regular airplane. What is the speed of the airplane?

Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples

The speed of the airplane is~$12250\div25=490$km/h.


I am threading blue and purple beads onto a necklace in the ratio $$2 : 5$$. I use $$98$$ beads in total. How many more purple beads than blue do I use?

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio

The ratio $$2 : 5$$ means that $$2$$ in $$7$$ beads are blue and $$5$$ in $$7$$ purple. Since $$98 \div 7 = 14$$, there are $$28$$ blue and $$70$$ purple beads, hence $$70 - 28 = 42$$ more purple than blue.


If Pip was 10 years old 5 years ago, how old will he be 7 years from now?


Harry planted some trees around a $20$m by $20$m square garden. If there are trees planted at each of the $4$ corners, and the distance between every $2$ trees is $5$m, at least how many trees did Harry plant?

Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Circular Paths->Planting Trees (circular path)

$20 \div 5 = 4$ intervals on each side  $4+1=5$ trees on each side  $4\times5-4=16$


There is a basket of peaches. Three students take turns to take peaches. Sana takes $2$ less than the half of peaches. Joann takes $2$ more than half of the remaining peaches. Now, there are $5$ peaches in the basket. How many peaches are there in the basket at beginning?


Mother\textquotesingle s Day in $$2020$$ was May $$10$$th, which was Sunday. Father\textquotesingle s Day in $$2020$$ was June $$21$$st. On what day did Father\textquotesingle s Day fall?

Thursday

Saturday

Sunday

Tuesday

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time

It passed $$31-10 + 21 = 42$$ days in total. Since $$42 \div 7 = 6$$, which means the Father\textquotesingle s Day fell on Sunday as well.


Andy has $$6$$ candies.  Bob has twice as many candies as Andy.  Chloe has $$4$$ times as many candies as Andy.  How many candies do they have altogether?


James wants to make $5$ cakes. Each day he makes one cake. He made the first cake on Tuesday. What day of the week will it be when he makes the last cake? (Adapted from 2011 Math Kangaroo Problem, Level 3-4, Question \#2)

Wednesday

Thursday

Friday

Saturday

Sunday


Half a loaf of bread costs $$6$$ pence more than one-fourth of a loaf of bread. How many pence does a whole loaf of bread cost? ($$1998$$ Math Kangaroo Problem, Level $$3-4$$, Question \#$$14$$)

One-fourth of a loaf of bread is "$$1$$ unit". Half a loaf of bread is "$$2$$ units".  One-fourth of a loaf of bread: $$6 \div (2-1) =6$$. A whole loaf of bread: $$6 \times 4 =24$$.


Many years ago, $$1^{\text{st}}$$ of May was a Friday. Which day of the week was $$23^{\text{rd}}$$ of May in that year?

Thursday

Friday

Saturday

Sunday

Monday

First Friday: 　　　$$1^{\text{st}}$$ of May  Second Friday: 　　$$8^{\text{th}}$$ of May  Third Friday: 　　　$$15^{\text{th}}$$ of May  Fourth Friday: 　　$$22^{\text{nd}}$$ of May  $$23^{\text{rd}}$$ of May was a \textbf{Saturday} in that year.


There are stools and chairs in the room. Each stool has $$3$$ legs, and each chair has $$4$$ legs. Altogether there are $$17$$ legs. How many chairs are there in the room?

Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis

If there are five stools, the chairs have $17-3\times5=2$ legs, which is not applicable. If there are four stools, the chairs have $17-3\times4=5$~ legs, which is also not applicable. If there are three stools, the chairs have $17-3\times3=8$ legs, which implies that there are $8\div4=2$ chairs and is applicable according to the question.


The cost of my algebra book is $$200\textbackslash\%$$ of that of my geometry book.  The cost of my geometry book is $$\frac{4}{3}$$ that of my calculus book. If my calculus book costs ＄$$21$$, how much do all $$3$$ books cost together?

The cost of the calculus book is ＄$$21$$. The cost of my geometry book is ＄$$21\times \left(\frac{4}{3}\right)=$$＄$$28$$. My algebra book costs ＄$$28 \times2 =$$＄$$56$$. All $$3$$ books cost ＄$$21+$$＄$$28 +$$＄$$56 =$$＄$$105$$ in total.


There are $$18$$ chocolates in Swee Tuth\textquotesingle s box, $$2$$ each of $$9$$ flavours. She likes only $$6$$ of the flavours. If she picks a chocolate at random, what is the probability of her getting one she doesn\textquotesingle t like?

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate

Out of $$18$$ chocolates there are $$6\times2=12$$ of the flavours that she likes. So the probability of Swee Tuth getting one she doesn\textquotesingle t like is $$\frac{6}{18} =\frac{1}{3}$$.


Maddie is $$2$$ years older than Lola, and Lola is $$6$$ years younger than Ellie.  How much older is Ellie than Maddie?

$$2$$ years

$$3$$ years

$$4$$ years

$$5$$ years

$$6$$ years

Ellie is $$6$$ years older than Lola, and Maddie is $$2$$ years older than Lola. Therefore Ellie is $$4$$ years older than Maddie.


Some students are going to an amusement park. If each student carries $9$ bottles of water in his or her backpack, there will be $2$ students carrying nothing; if one of the students carries $2$ bottles of water and the rest students carry $8$ bottles each, all the bottles of water can be carried to the park. There are~\uline{~~~~~~~~~~}~bottles of water in total that need to be carried.

Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Distribution Conversion Problems

Solve the problem as a problem of surplus and shortage. If each student carries $9$ bottles, there will be a shortage of $9\times2=18$ bottles;  if each student carries $8$ bottles, there will be a shortage of $8-2=6$ bottles. Therefore, there are $(18-6)\div(9-8)=12$ students and $12\times9-18=90$ bottles of water.


In a certain calendar year, there are more Mondays than Fridays, and more Sundays than Wednesdays. Which day of the week is $$1^{}\text{st}$$ March in that year?

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday


A worm is staying at the bottom of a well with a depth of $$13$$ metres. If it climbs up $$4$$ metres in the daytime and slips down $$1$$ metres at night, which day will it climb up to the ground?

The $$4$$th day

The $$5$$th day

The $$6$$th day

The $$7$$th day

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems

It climbs up $$4$$ metres in the day time and slips down $$1$$ metre at night, so it climbs up $$3$$ metres in a whole day. For the first $$3$$ days, it climbs $$9$$ metres. During the day time of the forth day, it climbs $$4$$ metres and reaches the ground. Then it needs four days to climb up to the ground.


A jacket was on sale. The original price was ＄$$180$$, and Peter bought it at ＄$$135$$. What was the discount rate?

Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts


Justin said to his mom, "If I had planted three times as many flowers as I planted, I would have planted $48$ more flowers than I have planted now." How many flowers did Justin plant?

Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple


Ella and George are lining up for dinner. Ella is sitting in the fifth from the front of the line, and George is sitting at the sixth from the end of the line. George and Ella are standing together. How many people are there in total?~(adapted from 2001 Math Kangaroo Problem, Level 3-4, Question \#13)

Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of Two Characters in a Line


There are $20$ children lining up outside a theme park. John is the $14$\textsuperscript{th}~ person counting from the front of the line and Mary is the $2$\textsuperscript{th}~person counting from the back of the line. How many children are standing in line between John and Mary?

Overseas Competition->Knowledge Point->Word Problem Modules

Mary is the $$20-2+1=19$$\textsuperscript{th} person in the line, so there are $$19-14-1=4$$ children are between them.


A mixture of $80$ liters of paint is $20 \textbackslash\%$ red tint, $30 \textbackslash\%$ yellow tint and $50 \textbackslash\%$ water. $20$ liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture? (adapted from 2007 AMC 8, Question \#17 )

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems

The original mixture contains $80 \times 30\textbackslash\% = 24$ liters of yellow tint.  $$20$$ liters of yellow tint is added to the mixture, the new mixture now has $24+20=44$ liters of yellow tint.  New percent of yellow =$\frac{44}{80+20} =44\textbackslash\% $


None of the above


A $30\textbackslash\%$ sugar solution contains $12$ g of pure sugar. How many g of solution are there?

$30$ g

$40$ g

$50$ g

$60$ g

Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems


Felix and Marmalade are two cats. Together they weigh $$10\text{kg}$$.  Felix weighs $$4\text{kg}$$ less than Marmalade. How much does Marmalade weigh?

$$7 \text{kg}$$

$$14 \text{kg}$$

Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference


Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction


My mom\textquotesingle s birthday is on Sunday, and my dad\textquotesingle s birthday is $$55$$ days later. On what day of the week will my dad\textquotesingle s birthday be? ．

$$ $$Sunday$$ $$

$$ $$Monday$$ $$

$$ $$Tuesday$$ $$

$$ $$Thursday$$ $$

$$ $$Saturday$$ $$

After $$1$$ day, it is Monday; after $$2$$ days, it is Tuesday; after $$3$$ days, it is Wednesday $$\cdots$$ After $$8$$ days, it is still Monday, and the period is $$7$$ days. $$55\div 7=7$$(weeks) $$\rm R$$ $$6$$ (days). The birthday is Saturday.


Sammy\textquotesingle s mom is $$6$$ years older than his dad. Right now, his dad is $$27$$ years old. How old was his mother $$10$$ years ago?

Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Difference of Ages

Now, his dad is $27$ years old, his mom is $$6$$ years older than his dad, so his mom is $33$ years old. $10$ years ago, his mom was $33-10=23$ years old.


Find the exact number of minutes after $3.00 \text{pm}$ when the minute and hour hands are first at $90^{\circ}$ to each other.

$$31 \frac{2}{11}$$

$$31 \frac{3}{11}$$

$$32 \frac{8}{11}$$

$$33 \frac{3}{11}$$

None of the above

Overseas Competition->Knowledge Point->Distance Word Problems->Clock Problems

The minute hand rotates $6^{\circ}$ per minute.  The hour hand rotates $\dfrac{1}{60}\times30^{\circ}=\left (\dfrac{1}{2}\right )^{\circ}$ per mimte.  Starting at $3$ O\textquotesingle clock, the minute hand rotates $\left (6t\right )^{\circ}$ and the hour hand rotates ~$$(90+ \frac{1}{2}t)^{ \circ }$$.  When the minute and hour hands are next perpendicular:  $$6t-\left (90+ \frac{1}{2}t\right )=90$$,  $$\frac{11}{2}t=180$$,  $$t= \frac{360}{11}=32 \frac{8}{11}$$.


Given that October $$10$$th, $$2018$$ was Wednesday, on what day will October $$10$$th, $$2022$$ fall?

Monday

Tuesday

Wednesday

Thursday

During this period, $$2020$$ is a leap years. Therefore, October $$10$$, $$2022$$ is $$1+2+1+1=5$$ days after Wednesday, which is Monday.


The average cost of a long-distance call in the USA in 1985 was 56 cents per minute, and the average cost of a long-distance call in the USA in 2018 was 2 cents per minute. Find the approximate percent decrease in the cost per minute of a long- distance call. (adapted from 2007 AMC 8, Question \#6)

The percent decrease is (the amount of decrease)/(original amount) the amount of decrease is $56-2=54$ so the percent decrease is $\frac{54}{56}$ which is about $ 96 \textbackslash\%$


At which of these times is the angle between the minute hand and the hour hand of a clock equal to $$150^{}\circ$$?

At all the times given, the minute hand is pointing to $$12$$. When the minute hand is pointing to $$12$$ and the angle between the hands is $$150^{}\circ$$, the hour hand has turned $$\frac{150}{360}= \frac{5}{12}$$ of a complete turn. Therefore the hour hand will point at $$5$$ and the time will be $$5\text{pm}$$. (There are other times when the angle between the hands is $$150^{}\circ$$ but, of these, only at $$7\text{pm}$$ does the minute hand point to $$12$$ and $$7\text{pm}$$ is not one of the times given.)


In $$4$$ hours Rob drove $$120 \text{km}$$. He drove at an average rate of $$\text{m/min}$$.


SASMO 2015 P2 Q10  John is 5 years old this year. His sister is 2 years old. What is the sum of their age after 3 years?

Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems


Jack was able to sell $30$\% of his vegetables before noon. If he had 200 pounds of vegetables in the morning, how many pounds of vegetables was he able to sell by noon?

$200 \times 30$\%=$60$,  He was able to sell $60$ pounds of vegetables by noon.


I am going to travel $$200\text{km}$$ at a rate of $$60\text{km}$$ per hour. How many minutes will my trip take?

Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road

I am going to travel $$200\text{km}$$ at $$60\text{km}$$ per hour. Since $$60\text{km}$$ per hour is the same as $$1\text{km}$$ per minute, my trip will take $$200$$ minutes.


Last year, at the school where Gill teaches Mathematics, $$315$$ out of the $$600$$ pupils were girls. This year, the number of pupils in the school has increased to $$640$$. The proportion of girls is the same as it was last year.  How many girls are there at the school this year?

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base

Last year, the fraction of girls at the school was $$\frac{{315}}{{600}}=\frac{{63}}{{120}}=\frac{{21}}{{40}}$$. This year, there are $$40$$ more pupils at the school, but the proportion of girls has remained the same. So there are $$21$$ more girls at the school this year, making a total of $$315+21=336$$.


Chloe is buying candies at a grocery store. She can either spend $8$ dollars on a $15$ ounce bag or $12$ dollars on a $20$ ounce bag. Which is a better buy?

$15$ ounce bag

$20$ ounce bag

Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value


Jin loves carrots! Yesterday she ate $$\frac{1}{4}$$ of her carrots, and today she ate $$\frac{2}{7}$$ of the number of she ate yesterday. She ate 10 carrots today. Yesterday she have started with  carrots.

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base


Tom scored a basket at the end of the third quarter of a basketball game between the Lakers and the Warriors. At that point, what fraction of the whole game remained to be played?

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate

Basketball games consist of four quarters. Tom\textquotesingle s scoring at the end of the third quarter implies that there is one quarter left, which is equivalent to 1/4 of the entire game.


Five positive integers (not necessarily all different) are written on five cards. Boris calculates the sum of the numbers on every pair of cards. He obtains only three different totals: 57, 70 and 83. What is the largest integer on any card?

Let the five integers be a, b, c, d and e with a ≤ b ≤ c ≤ d ≤ e. The smallest total is 57, which is an odd number so b ≠ a. Similarly, the largest total is 83, which is also an odd number so d ≠ e. Hence we now have a \textless{} b ≤ c ≤ d \textless{} e and a + b = 57 and d + e = 83. Only one possible total remains and so b = c = d with c + d = 70. This gives c = d (= b) = 35 and therefore e, the largest integer, is 83 − 35 = 48 (whilst a = 22).


The average cost of a long-distance call in the USA in 1985 was 44 cents per minute, and the average cost of a long-distance call in the USA in 2005 was 11 cents per minute. Find the approximate percent decrease in the cost per minute of a long- distance call. (adapted from 2007 AMC 8, Question \#6)

The percent decrease is (the amount of decrease)/(original amount) the amount of decrease is $44-11=33$ so the percent decrease is $\frac{33}{44}$ which is about $(\mathbf{c}) 75 \textbackslash\%$


James lives on the second floor, and Paul lives in the same building but has to walk up five times as many stairs as James. There are no stairs to the entrance of the building. On which floor does Paul live? (Adapted from 2000 Math Kangaroo Problem, Level 3-4, Question \#4)

On the $$2^{\rm nd}$$ floor

On the $$3^{\rm rd}$$ floor

On the $$4^{\rm th}$$ floor

On the $$5^{\rm th}$$ floor

On the $$6^{\rm th}$$ floor

Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Straight Line Type with Objects on Both Sides->Taking the Stairs


Amy mixes $$10$$ grams of a $$20\textbackslash\%$$ sugar solution and $$40$$ grams of a $$25\textbackslash\%$$ sugar solution together. After~\uline{~~~~~~~~~~}~of water evaporates, the percent concentration of solution is $40\textbackslash\%$.

$$15$$ grams

$$18$$ grams

$$20$$ grams

$$25$$ grams

Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants

$$10\times20\textbackslash\%+40\times 25\textbackslash\%=12$$ grams.  $$(10+40)-12\div40\textbackslash\%=20$$ grams.


Greta was $$110\text{cm}$$ tall $$2$$ years ago, when she was $$10\text{cm}$$ taller than her brother. They both have grown, but now Greta is $$10\text{cm}$$ shorter than her brother. If her brother grew $$40\text{cm}$$ in those two years, Greta is now$$\text{cm}$$ tall.

Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction

Greta was $$110\text{cm}$$ tall $$2$$ years ago, when she was $$10\text{cm}$$ taller than her brother. Her brother was $$100\text{cm}$$ then. Now Greta is $$10\text{cm}$$ shorter than her brother. If her brother grew $$40\text{cm}$$, he is now $$140\text{cm}$$. Greta is now $$130\text{cm}$$ tall.


The average weight of $4$ students in Class $A$ is $37$ kilograms. The average weight of $11$ students in Class $B$ is $41$ kilograms. The total weight of $5$ students in Class $C$ is $161$ kilograms. What is the average weight of the students in the $3$ classes?

$36$ kilograms

$38$ kilograms

$40$ kilograms

$43$ kilograms

Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems


Cici and Kiki took the same quiz. They agreed on the following rules: a person got $10$ points for a correct answer and lost $5$ points otherwise (getting a wrong answer or skipping a question). They each answered $10$ questions and together got $95$ points. If Cici got $15$ more points than Kiki, how many questions did Kiki answer correctly?

Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis

Kiki got $(95-15)\div2=40$ points. If she answered all the questions correctly, she would have gotten $100$ points. Hence, she skipped or got $(100-40)\div(10+5)=4$ wrong answers and she answered $10-4=6$ questions correctly.


Amy and Bella bought some cookies in the ratio of $$3:4$$. Bella gave $$9$$ cookies to Amy. Then the ratio of the number of cookies Amy had to that of Bella was $$1:1$$. How many cookies did they have at first?

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Ratio Word Problems with Invariant Sums

Total number of cookies both of them had did not change.  Make total the same number of units by finding LCM.  Before $\to$ $A:B:Total$ $\to$ $3:4:7$ $\to$ $6:8:14$  After $\to$ $A:B:Total$ $\to$ $1:1:2$ $\to$ $7:7:14$  $1u=9$  $14u=14\times9=126$ cookies at first (and also in the end) in total.


Alex, John and Sam went to buy oranges. Alex paid $\textbackslash$20$, John paid $\textbackslash$15$, and Sam only paid $\textbackslash$5$. They bought $120$ oranges altogether. They divided them in proportion to the amount of money each of them had paid. How many oranges did John get?

None of the above

Overseas Competition->Knowledge Point->Word Problem Modules->Applying of Multiplication and Division


If $$3^{}\text{th}$$February is Monday, what day of the week is $$27$$\textsuperscript{th~}February?

Sunday

Monday

Wednesday

Thursday

Saturday

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time

We can count backward by days or by weeks. Count a few weeks back to find that $$22$$\textsuperscript{nd} February is a Monday. Then count a few days back to find that $$24$$\textsuperscript{th~}February is a Wednesday.


The speed of high-speed train is approximately $$350$$ kilometres per hour, while the walking speed of a person is approximately $$5$$ metres per second.  Approximately, how many times is the speed of a high-speed train faster than the walking speed of a person?．

$$2 $$

$$20 $$

$$70 $$

$$200 $$

Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples

The speed of high-speed train is approximately $$350$$ kilometres per hour, which is approximately $$100$$ metres per second. So its speed is roughly $$20$$ times faster than $$5$$ metres per second.


Martha had ＄$$1.50$$. She bought $$12$$ caramels at $$5$$￠ each. How many chocolate mints at $$10$$￠ each can she buy with the money she has left?

Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts

Martha had ＄$$1.50$$. She bought $$12$$ caramels at $$5$$￠ each, spengding  $$60$$￠ and leaving her with $$90$$￠. With $$90$$￠, she can buy $$90 \div 10 =9$$ mints at $$10$$￠ each.


Balloons are sold in packets of $$5$$, $$10$$, and $$25$$. Marius buys exactly $$70$$ balloons. What is the smallest number of packets he can buy? (2017 Math Kangaroo Problem, Level 3 - 4, Question \#11)

Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division->Simple Multiplication Applications


Three hens and four rabbits are in a cage. How many legs do they have?~(adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$4$$)

Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method

A hen has two legs and a rabbit has four legs, so three hens have six legs and four chickens have sixteen legs.  $6+16=22$


A police spots a burglar from $$480$$ m apart. The burglar immdiately runs away at a speed of $$8$$ m/s and the police starts chasing him at $$12$$ m/s at the same time. At this rate, how long will it take the police to catch the burglar?

$$24$$ seconds

$$40$$ seconds

$$1$$ minutes

$$2$$ minutes

Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road

The distance between them is $$480$$ m, and the difference between their speeds is $$12-8=4$$ m/s. It takes $$480\div4=120$$ seconds to catch the burglar, which is $$2$$ minutes


At the 2013 Winnebago County Fair a vendor is offering a "fair special" on sandals. If you buy one pair of sandals at the regular price of $\textbackslash$ 50$, you get a second pair at a $40 \textbackslash\%$ discount, and a third pair at half the regular price. Javier took advantage of the "fair special" to buy three pairs of sandals. What percentage of the $\textbackslash$ 150$ regular price did he save? (2013 AMC 8, Question \#12)

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems

First, find the amount of money one will pay for three sandals without the discount. We have $\textbackslash$ 50 \times 3$ sandals $=\textbackslash$ 150$. Then, find the amount of money using the discount: $50+0.6 \times 50+\frac{1}{2} \times 50=\textbackslash$ 105$. Finding the percentage yields $\frac{105}{150}=70 \textbackslash\%$ To find the percent saved, we have $100 \textbackslash\%-70 \textbackslash\%=(\text{B}) 30$


There was a $15$-meter long corridor in the school. The teacher asked Jack to put a flowerpot on the corridor every three meters. How many flowerpots did Mike put?~(adapted from $$2008$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$7$$)

Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Planting no Trees on either Side (straight line type)->Cutting the Ropes

The corridor is divided into $15\div3=5$ segments. The number of flowerpots is one more than that of the segments, so $5+1=6$.


The original price of a pair of shoes was $$\textbackslash$85$$. Then, it was sold at a discount of $$20\textbackslash\%$$. What was the price of the pair of shoes after the discount?

After discount, price became $100\textbackslash\%-20\textbackslash\%=80\textbackslash\%$ of original price.  $\textbackslash$85\times80\textbackslash\%=\textbackslash$85\times0.8=\textbackslash$68$


Julia has eaten one-quarter of the pizza.  What is the ratio of the number of pizza that remain to the number Julia has eaten?

$$3:1 $$

$$1:4 $$

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units

Julia has eaten one-quarter of the pizza. So three-quarters of the pizza remain.  Therefore the required ratio is $$\frac{3}{4}:\frac{1}{4}=3:1$$.


In a certain quiz show there are the following rules: every participant has $$10$$ points at the beginning and has to answer $$10$$ questions. For each correct answer, the participant earns $$1$$ point, and for each incorrect answer, the participant loses $1$ point. Mrs. Smith had $$14$$ points at the end of this quiz show. How many correct answers did she give? ($$2011$$ Math Kangaroo Problem, Level $$3-4$$, Question \#$$17$$)

Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis->Basic Type->Non-typical Types

Full score: $10+10\times1=20$.  Smith gets $(20-14)\div(1+1)=3$ questions wrong, and $10-3=7$ questions correct.


My mom\textquotesingle s birthday is on Sunday, and my dad\textquotesingle s birthday is $$55$$ days after it. On what day of the week will my dad\textquotesingle s birthday be? ($$1999$$ Math Kangaroo Problem, Levels $$3-4$$, Question \#$$9$$)

Sunday

Monday

Tuesday

Thursday

Saturday

$$55\div7=7 \text{R}6$$. It is Saturday.


Penelope paid＄$$24.58$$ for pens and pencils. If pens cost $$9$$￠ each and pencils cost $$4$$￠ each, at most how many pens did Penelope purchase?

Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division

Continue subtracting $$4$$￠ from $$2458$$￠ until the difference is a multiple  of $$9$$. This happens when the difference is $$2430$$￠ which is $$270 \times 9$$￠.


The selling price of a sofa set is ＄$$5500$$ and the profit percentage is $$10\textbackslash\%$$ for each set sold. If the cost of the sofa set is not changed, what is the new profit percentage if raising the profit to ＄$$1800$$?


A worm is at the bottom of a well with a depth of $$11$$ metres. If it climbs up $$3$$ metres in the day and slips down $$1$$ metre at night, how many days will it take the worm to climb up to the ground?

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems

It climbs up $$3$$ meters in the day time and slips down $$1$$ meter at night, so it climbs up $$2$$ meters in a whole day. For the first $$4$$ days, it climbs $$8$$ meters. During the day time of the fifth day, it climbs $$3$$ meters and reaches the ground. Then it needs five days to climb up to the ground.


Bowen has $$40$$ ounces of a $$25\textbackslash\%$$ sugar solution. After~\uline{~~~~~~~~~~}~of water evaporates, the percent concentration of the solution is $$40\textbackslash\%$$. (Evaporate: the water turns from liquid into vapor and is no longer in the solution anymore.)

$$15$$ ounces

$$12$$ ounces

$$9$$ ounces

$$6$$ ounces

Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants


Patrick gets $80 \textbackslash\%$ on a 10 -problem test, $60 \textbackslash\%$ on a 20 -problem test and $50 \textbackslash\%$ on a 30 -problem test. If the three tests are combined into one 60 problem test, which percent is closest to her overall score? (adapted from 2006 AMC 8, Question \#12)

$80 \textbackslash\% \cdot 10=8$, $60\textbackslash\% \cdot 20=12$, $50\textbackslash\% \cdot 30=15$  Adding them up gets $8+12+15=35$. The overall percentage correct would be $\frac{35}{60} \approx 0.58$.


Gawel lives on the 2\textsuperscript{nd} floor, and Pawel lives in the same building but has to walk up twice as many stairs as Gawel. There are no stairs to the entrance of the building. On which floor does Pawel live?

on the $2$\textsuperscript{nd} floor

on the $3$\textsuperscript{rd} floor

on the $4$\textsuperscript{th} floor

on the $5$\textsuperscript{th} floor

on the $6$\textsuperscript{th} floor

Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems

Gawel lives on the second floor, so he only needs to walk up one floor.  Pawel has to walk up twice as many stairs as Gawel, so he needs to walk up two floors. So, Pawel lives on the $3$\textsuperscript{rd} floor.


Ben stands in line and has $$76$$ people behind him, If there are a total of $$110$$ people in line, how many people are there in front of Ben?

Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of one Character in a Line

If there are a total of $$110$$ people in line, subtract those behind Ben and Ben himself: $$110-76-1=33$$, the number in front of Ben.


A jacket was on sale. The original price was ＄$$180$$, and Peter bought it at ＄$$135$$. What was the discount?


The sum of two numbers is $$800$$. The smaller number is $$356$$.  What is the greater number?

Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples

Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Addition and Subtraction of Whole Numbers->Adding and Subtracting within 10000->Subtraction of 3-digit Numbers


There are $$20$$ chickens and rabbits in the case, and the total number of legs is $$48$$. How many rabbits in this case?

Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis

If all were rabbits,  $20\times 4= 80$  the total number of legs would be $$$80$$.  $80- 48=32$  The difference is $$$32$$.  $4-2=2$  $32\div 2=16$  $20-16=4$


A sugar solution is made by mixing $$10$$ ounces of sugar and $$15$$ ounces of water. Find the percent concentration of the solution.

Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems


Mother baked $$40$$ cookies. She gave $$8$$ cookies to her friend and packed the rest equally into bottles. She put $$4$$ cookies in each bottle. How many bottles did she use?

Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable


Julian started reading a book with $$348$$ pages. He read $$6$$ pages on each day from Monday to Friday and $$11$$ pages on each day on Saturday and Sunday. He started reading on a Thursday. On which day of the week did he finish reading the book? ．

Friday

Saturday

Sunday

Monday

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time

Thursday to Sunday $$\rightarrow 6\times 2+11\times 2=34$$ pages  $$348-34=314$$  $1$ week (Monday to Sunday) $$\rightarrow 11\times 2+6\times 5=52$$ pages  $6$ weeks $$\rightarrow 52\times6=312$$ pages  After reading another $312$ pages in $6$ weeks, Julian has another $(314 -- 312) = 2$ pages left to read. It will now be a Monday and Julian can finish reading the last $2$ pages.


$5$\% of the students at Hamilton Middle School have red hair. There are $800$ students at Hamilton Middle School. How many students at Hamilton Middle School have red hair?

$800 \times 5$\%=$40$,  $40$ students at Hamilton Middle School have red hair.


My pay is the same every day I work. I worked \emph{every} day in $$1992$$, even weekends. In March, I earned ＄$$930$$. I earned for all of $$1992$$.

Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value

In March, there are $$31$$ days. I earned ＄$$930 \div 31$$, which is ＄$$30$$ each day. For all of $$1992$$, I earned $$366\times$$ ＄$$30 =$$＄$$10980$$.


Zosia is drawing kangaroos. The first one is blue, the next one green, the one after it red, the fourth one yellow, and then again blue, green, red, yellow, and so on, in the same order. What color will the seventeenth kangaroo be? (2003 Math Kangaroo Problem, Level 3-4, Question \#4)

$$$$Blue

$$$$Green

$$$$Red

$$$$Black

$$$$Yellow

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation

A group of the blue one, the green one, the red one, and the yellow one is repeating. $17 \div 4 = 4R1$, so the seventeenth one is blue.


William is 15 years old, and his sister is 23 years old. How old will his sister be when William is 23 years old?

Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems


Luna, Lily, and Lucy are talking about their ages. $6$ years ago, Luna was born, and Lily was $5$ years old. This year, the sum of ages of these $3$ people is $33$. When Luna was born, how old was Lucy?

Six years ago, the sum of ages of Luna, Lily, and Lucy was $33-6\times3=15$. Lucy was $15-0-5=10$ years old.


Jack mixed $200$ g of $10\textbackslash\%$ salt solution, $200$ g of $15\textbackslash\%$ salt solution, and $400$ g of $20\textbackslash\%$ salt solution together. What is the percent concentration of salt solution at this time?

Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems->Calculating Solution from Solute and Solvent

$$\frac{200\times 10\textbackslash\%+200\times 15\textbackslash\%+400\times 20\textbackslash\%}{200+200+400}\times 100\textbackslash\%=16.25\textbackslash\%$$.


After Sally takes 20 shots, she has made $75 \textbackslash\%$ of her shots. After she takes 10 more shots, she drops her percentage to $60 \textbackslash\%$. How many of the last 5 shots did she make? (adapted from 2004 AMC 8, Question\#6)

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems

Sally made $0.75 * 20=15$ shots originally. Letting $x$ be the number of shots she made, we have $\frac{15+x}{30}=0.6$. Solving for $x$ gives us $x=3$


Crystal and Angela had a poem recitation game. Each poem in their game earned $$2$$ points. Crystal recited $$7$$ poems and Angela recited $$11$$ poems. How many more points than Crystal did Angela earn?~(adapted from $$2021$$ Math kangaroo, Level $$1-2$$, Question \#$$14$$)

Overseas Competition->Knowledge Point->Word Problem Modules

Angela recited $$11-7=4$$ poems more than Crystal.  There are 4$$\times$$2$$=8$$ points


A test is with a full score of $100$ points. Five students in a group wants to reach an average of $92$ points. If everyone scores a different whole number, the lowest score among them could be~\uline{~~~~~~~~~~}~.

Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems


Given that April $$15$$, $$2011$$ was Friday, what day was May $$11$$, $$2011$$?

Thursday

Saturday

Tuesday

Wednesday

Counting from April $$15$$, $$2011$$, after $30-15=15$ days it will be April $$30$$, $$2011$$. After $11$ days, it will be May $$11$$, $$2011$$. In total, there are $15+11=26$ days. $26\div 7 =3R5$, which means May $$11$$, $$2011$$ was Wednesday.


The perimeter of a cuboid is $180$. What is the largest volume?

Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Problems Involving Extreme Value


A worm is staying at the bottom of a well with a depth of $$10$$ metres. If it climbs up $$3$$ metres in the daytime and slips down $$2$$ metres at night, which day will it climb up to the ground?

The $$6$$th day

The $$7$$th day

The $$8$$th day

The $$9$$th day

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems


A train travels from Exeter to Cambridge at a~ speed of $$55km/h$$. Given that Cambridge is $$420km$$ away from Exeter, How far is the train away from Cambridge after setting off for 5 hours?

Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road


In the teachers\textquotesingle{} lounge there are $$6$$ tables with $$4$$ chairs by each one, $$4$$ tables with $$2$$ chairs by each, and $$3$$ tables with $$6$$ chairs by each. How many chairs are there in the lounge? (2003 Math Kangaroo Problem, Level 3-4, Question \#5)

Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division->Simple Multiplication Applications


Helga is climbing stairs in such a way that she goes up $$2$$ steps at a time. She is standing on the third step now. On which step will she be after she moves up $$3$$ times?

Moving up $3$ times is $6$ steps. Now she is on the third step, after moving up $6$ steps, she is on the ninth step.


If today is Tuesday, what day of the week will be 86 days later?

Wednesday

Thursday

Friday

Saturday

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates

$$86\div 7=12\cdots \cdots 2$$．  2 days later will be Thursday.


Last month, the price of a couch increased by $\textbackslash$600$. During a sale this month, the couch was offered at a $25\textbackslash\%$ discount. John bought the couch at $\textbackslash$2250$ at the sale. What is the percentage decrease in the cost of the couch as compared to the original price of the couch before the discount?

None of the above.

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages

Price before discount $=\frac{100}{75}\times\textbackslash$2250=\textbackslash$3000$  Original price of the couch before increase $=\textbackslash$3000-\textbackslash$600=\textbackslash$2400$  Price decrease $=\textbackslash$2400-\textbackslash$2250=\textbackslash$150$  Percentage decrease $=\frac{\textbackslash$150}{\textbackslash$2400}\times100\textbackslash\%=6.25\textbackslash\%$


Anna is lining up to get some ice-cream. Counting from the front, she is the $$4$$\textsuperscript{th}~in the line. Counting from the back, she is the $$7$$\textsuperscript{th}. How many people are there lining up?~\uline{~~~~~~~~~~}~


Jerry starts a savings account with ＄$$7,000$$ at a bank. The interest rate is $$3\textbackslash\%$$ per year. How much interest will he earn in his savings account at the end of the second year?

Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Interest Problems

$$7000\times \left( 1+3\textbackslash\% \right)\times \left( 1+3\textbackslash\% \right)-7000=426.3$$.


A bookstore purchases some story books at ＄$$22$$ each. If the bookstore wants to earn ＄$$11$$ for each book, what is the selling price of each book?

Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts


There are four books on my shelf. The almanac and the dictionary together weigh $$4310\text{g}$$. The biography and the cookbook together weigh $$2325\text{g}$$. If the almanac and the biography together weigh $$2795\text{g}$$, what is the weigh of the cookbook and dictionary together?

Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Including and Excluding

The almanac, the dictionary, the biography, and the cookbook together weigh $$4310\text{g}+2325\text{g=6635g}$$. Since the almanac and the biography together weigh $$2795\text{g}$$, the cookbook and the dictionary together weigh $$6635\text{g}-2795\text{g=3840g}$$.


There are $72$ balloons in the shop. Pip bought $$\frac49$$ of them. The shop left~\uline{~~~~~~~~~~}~balloons.

Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base