The number of apples in basket $$A$$ was $$\frac{13}{19}$$ of that in basket $$B$$. After $$10$$ apples were taken out from basket $$A$$ and were put in basket $$B$$, the number of apples in basket $$A$$ became $$\frac{1}{3}$$ of that in basket $$B$$. How many apples were there in basket $$A$$ and basket $$B$$, respectively, in the beginning? ．

$$13$$ apples in basket $$A$$; $$19$$ apples in basket $$B$$

$$26$$ apples in basket $$A$$; $$19$$ apples in basket $$B$$

$$26$$ apples in basket $$A$$;~$$38$$ apples in basket $$B$$

$$19$$ apples in basket $$A$$; $$13$$ apples in basket $$B$$

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

The total number of apples in basket $$A$$ and basket $$B$$ is constant. In the beginning, $$A: B=13:19$$; now, $$A: B=1:3=8:24$$ (the total number of portions is still $$32$$). By comparison, the number of portions in basket $$A$$ decreases by $$5$$, and the number of portions in basket $$B$$ increases by $$5$$, so each portion is $$10\div5=2\text{kg}$$. Formerly, there were $$13\times2=26$$ apples in basket $$A$$ and $$19\times2=38$$ apples in basket $$B$$. So, the answer is $$C$$.


The average cost of a long-distance call in the USA in 1985 was 50 cents per minute, and the average cost of a long-distance call in the USA in 2008 was 5 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)

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 $50-5=45$ so the percent decrease is $\frac{45}{50}$ which is ~$ 90 \textbackslash\%$


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$$ $$

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

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.


If $$10$$ February $$2013$$ falls on Friday, which day of the week will $$10$$ February $2014$ fall on?

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday


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?

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

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 $$1 : 2 500 000$$.


A mixture of $$30$$ litres of paint is $$25\textbackslash\%$$ red tint, $$30\textbackslash\%$$ yellow tint and $$45\textbackslash\%$$ water. Five litres of yellow tint are added to the original mixture. What is the percentage of yellow tint in the new mixture?

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

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 $$40$$.


Rick and Roy each stands at different ends of a straight road that is $$2021$$m long. They run toward each other. Rick\textquotesingle s speed is $$21\text{m/s}$$ and Roy\textquotesingle s speed is $$22\text{m/s}$$. They will meet in~\uline{~~~~~~~~~~}~seconds. ($$2016$$ Math League.com contest problem, $$5$$th Grade, Question \#$$26$$)

Overseas Competition->Knowledge Point->Word Problem Modules


If $$13^{}\text{th}$$February is Friday, what day of the week is $$1$$\textsuperscript{st~}February?

Sunday

Monday

Wednesday

Thursday

Saturday

We can count backward by days or by weeks. Count a few weeks back to find that February $$6$$ is a Friday. Then count a few days back to find that February $$1$$ is a Sunday.


To defeat a dragon, Matthias has to cut off all the dragon\textquotesingle s heads. If he can cut off $$3$$ of the dragon\textquotesingle s heads, one new head immediately grows. Matthias defeats the dragon by cutting off $$17$$ heads in total. How many heads did the dragon have at the beginning?

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

$17\div3=5R2$, so Matthias has $5$ groups of $3$ cuts, which means $5$ new heads grew. Thus, there are $17-5=12$ heads originally.


Gabriel wrote his name $$100$$ times in the sand. What was the $$100\text{th}$$ letter he wrote? ．

$$a$$

$$b$$

$$r$$

$$i$$

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

The $$1\text{st}$$ letter Gabriel wrote was $$G$$, and every $$7\text{th}$$ letter after was $$G$$.  The $$99\text{th}$$ letter he wrote was $$G$$, and the $$100\text{th}$$ was an"$$a$$."


At the $2018$ Tompkins County Fair a vendor is offering a "fair special" on hats. If you buy one hat at the regular price of $\textbackslash$ 30$, you get a second hat at a $40\textbackslash\%$ discount, and a third pair at half the regular price. James took advantage of the "fair special" to buy three hats. What percentage of the $\textbackslash$ 90$ regular price did he save? (adapted from 2013 AMC 8, Question \#12)

First, the amount of money one will pay for three hats without the discount $=\textbackslash$ 90$. Then, find the amount of money using the discount: $30+0.6 \times 30+\frac{1}{2} \times 30=\textbackslash$ 63$. Finding the percentage yields $\frac{63}{90}=70\textbackslash\%$ To find the percent saved, we have $100 \textbackslash\%-70\textbackslash\%= 30\textbackslash\%$


The sales tax rate in Bergville is $$6\textbackslash\%$$. During a sale at the Bergville Coat Closet, the price of a coat is discounted $$20\textbackslash\%$$ from its ＄$$90.00$$ price. Two clerks, Jack and Jill, calculate the bill independently. Jack rings up ＄$$90.00$$ and adds $$6\textbackslash\%$$ sales tax, then subtracts $$20\textbackslash\%$$ from this total. Jill rings up ＄$$90.00$$, subtracts $$20\textbackslash\%$$ of the price, then adds $$6\textbackslash\%$$ of the discounted price for sales tax. What is Jack's total minus Jill's total?

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

The price Jacks rings up is $$(90.00)(1.06)(0.80)$$. The price Jill rings up is $$(90.00)(0.80)(1.06)$$. By the commutative property of multiplication, these quantities are the same, and the difference is $$(\text{C})$$＄$$0$$.


The distance between Exeter and London is $$175$$ miles. Sam left Exeter at $$10:00$$ on Tuesday for London. Morgan left Exeter~ for London at $$13:00$$ the same day. They travelled on the same road. Sam\textquotesingle s average speed was $$25$$ miles per hour, and Morgan\textquotesingle s average speed was $$50$$ miles an hour. At what time did Sam and Morgan meet?

$25\times3=75$miles  $75\div (50-25)=3$h  $13+3=16$  They meet at $16:00$.  revise from ($$2017$$ Junior Mathematical Challenge Question \#$$25$$)


There were $$31$$ runners competing in a race. The number of runners who finished before John is four times smaller than the number of runners who finished later than John. At what place did John finish?

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


Gary will be three times as old as Harry $$4$$ years from now. If Harry is $$5$$ years old now, how old will Gary be in $$4$$ years?

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

Harry is $$5$$ years old now; he\textquotesingle ll be $$9$$ in $$4$$ years.  Gary is thus $$3\times9=27$$ years old


Bowen has $$40$$ grams 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.)

$$15$$ grams

$$12$$ grams

$$9$$ grams

$$6$$ grams

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


Mike makes $5$ cakes every minute. He works for $16$ minutes. How many cakes does he make altogethe?

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


Luis has 7 apples and 2 bananas. He gives 2 apples to Yuri who, in return gives bananas to Luis. Then Luis has as many apples as bananas. How many bananas did Yuri give to Luis?

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


Alice\textquotesingle s first day in Caterpillar Club was Tuesday. She wants to throw a party on her 40th day in the club. If Alice attends the club everyday, on which day of the week will the party be?

Friday

Saturday

Sunday

Monday

None of the above

40th day = 39th day after first day joining.  39 days/7 = 5 weeks R 4 days. 4 days after Tues is Saturday.


A fifth-grade class has $8$ boys and $10$ girls. What is the ratio of boys to girls?.


Emily was $$6$$ years old last year, and her sister was $$6$$ years old six years ago. What is the age difference between Emily and her sister today?

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

Emily was $$6$$ years old last year , which means Emily is $7$ years old this year. Her sister was~ $$6$$ years old six years ago, which tells us her sister is~ $12$ years old this year, so the age difference is $5$ today.


Gill is now 27 and has moved into a new flat. She has four pictures to hang in a horizontal row on a wall which is 4800 mm wide. The pictures are identical in size and are 420 mm wide. Gill hangs the first two pictures so that one is on the extreme left of the wall and one is on the extreme right of the wall. She wants to hang the remaining two pictures so that all four pictures are equally spaced. How far should Gill place the centre of each of the two remaining pictures from a vertical line down the centre of the wall?

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


David and Billy are on the bus together. They sit in the same column. There are $5$ people in front of David, Billy is in the middle. There are $10$ people behind Billy, and David is in the middle. How many people in this column? (adapted from2004 Math Kangaroo Problem, Level 3 - 4, Question \#19)

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


How many pieces can we get if we break a wooden stick in $8$ places? (Adapted from 1999 Math Kangaroo Problem, Level 3-4, Question \#3)

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


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


There are twice as many boys in a room as girls. If $$5$$ boys leave the room, there would be an equal number of boys and girls in the room. How many boys were in the room at first?

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

The number of boys that leave the room must equal the number of boys that remain. Since $$5$$ boys leave, there are $$5$$ boys still in the room for a total of $$10$$ boys.


There are twelve rooms in a building and each room has two windows and one light. Last evening, eighteen windows were lit. In how many rooms was the light off? (2016 Math Kangaroo Problem, Level 1-2, Question \#14)

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


There were $$31$$ runners competing in a race. The number of runners who finished before John is $18$ less than the number of runners who finished later than John. At what place did John finish? (Adapted from 1998 Math Kangaroo Problem, Level 3 - 4, Question \#13)


A basket with $$5$$ watermelons weighs $$3250$$ grams. If $$3$$ of the watermelons were taken out, the remaining weight would be $$1510$$ grams. What is the weight (in grams) of the basket?

$$350$$ grams

$$1160$$ grams

$$1740$$ grams

$$870$$ grams

None of the above

Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Equivalent Substitution in Equation Word Problems->Replacement of Equivalent Substitution


In a magic land, a monkey wants to climb a tree of $180$ m. The monkey can make one of the two kinds of climb each day: $6$ m up or $10$ m up. Beginning at the ground , at least how many days will the monkey need in order to rest on the branch of $108$ m high?

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


$4$ years gao, the sum of Cathy\textquotesingle s and Larry\textquotesingle s ages was $$20$$. What is the sum of their ages this years?

Overseas Competition->Knowledge Point->Word Problem Modules


$$75$$ out of $$100$$ apples are \textbf{not} rotten. What percentage of the apples are rotten?

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

$$\frac{75}{100}=75 \textbackslash\%$$,  $$100\textbackslash\%-75\textbackslash\%=25\textbackslash\%$$,  $$25\textbackslash\%$$ of the apples are rotten.


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


How many times does it take to cut a rope into $$5$$ pieces? The rope can\textquotesingle t be folded.

It depends on how long the rope is.


Amy has $12$ candies and Nancy has $33$ candies. How many candies do they have in total?


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

$$70$$ pence

$$80$$ pence

$$90$$ pence

$$100$$ pence

110 pence

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


Luke and Matthew ran a lemonade stand on Saturday. They agreed that Matthew would get $65$\% of the profit because the lemonade stand was his idea. They made a profit of $60$ dollars. How much money did Luke make?

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


Alan is $5$ years old, his mother is $18$ years older than him, and his father is $2$ years older than his mother. How old is his father?~(adapted from $$2005$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$7$$)

Alans\textquotesingle{} mother is $18$ years older than him, his mother is $23$ years old.  His father is two years older than his mother, so he is $25$ years old.


On Monday morning, a snail fell down a well which is $$5$$ metres deep. During the day, it climbs up $$2$$ metres, and during the night it slides down $$1$$ metre. On what day of the week will the snail get out of the well?

$$$$Tuesday

$$$$Wednesday

$$$$Thursday

$$$$Friday

$$$$Monday

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


$$37$$ 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. If there were sakura and pineapple trees at both ends of the road, how many pineapple trees were planted? ．

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 = $$24 + 1 = 25$$


Fatimah has $$3$$ bags of marbles. There are $$291$$ marbles in each bag. How many marbles does Fatimah have in all?


I ate lunch every day of my $$12$$-week summer break. I ate lunch out-doors only on every Saturday, Sunday, and Tuesday. I ate lunch in-doors ondays.

I ate lunch every day of my $$12$$-week summer break. I ate lunch out-doors only on every Saturday, Sunday, and Tuesday. I ate lunch in-doors $$4$$ days each week. In $$12$$ weeks, that\textquotesingle s $$12\times 4=48$$ days.


Bella and her brother agreed to share a pizza which was cut into $15$ slices. Bella ate $40$\% of the pizza. How many slices did she eat?


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: $$2x+2y+2z=18$$, $$x+y+z=9$$.


Cecilia and her dad are climbing stairs from the first floor. They start at the same time, and each of them keeps her or his speed of climbing unchanged. When Cecilia arrives at the third floor, her dad arrives at the fifth floor. When Cecilia arrives at the eighth floor, which floor does her dad arrive at?


After Sally takes 20 shots, she has made $50 \textbackslash\%$ of her shots. After she takes 5 more shots, she raises her percentage to $60 \textbackslash\%$. How many of the last 5 shots did she make? (adapted from 2004 AMC 8, Question\#6)

Sally made $0.5\times 20=10$ shots originally. Letting $x$ be the number of shots she made, we have $\frac{10+x}{25}=0.60$. Solving for $x$ gives us $x=$ $(E)5$


Irene mixes $$100$$ grams of dogfood that contains $$50\textbackslash\%$$ rice with $$400$$ grams 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


The average cost of a long-distance call in the USA in 1985 was 41 cents per minute, and the average cost of a long-distance call in the USA in 2005 was 7 cents per minute. Find the approximate percent decrease in the cost per minute of a long- distance call. (2007 AMC 8, Question \#6)

The percent decrease is (the amount of decrease)/(original amount) the amount of decrease is $41-7=34$ so the percent decrease is $\frac{34}{41}$ which is about $(\mathbf{E}) 80 \textbackslash\%$


Mike has $$160$$ grams of a $$3\textbackslash\%$$ salt solution and Danni has an $$8\textbackslash\%$$ salt solution. If Danni gives $$200$$ grams of her solution to Mike, they will have the same amount of pure salt in their solutions. How many grams of solution did Danni have in the beginning?

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

$$160\times3\textbackslash\%+200\times8\textbackslash\%=20.8$$ ounces.  $$20.8\div8\textbackslash\%+200=260+200=460$$ ounces.


At the 2017 King County Fair a vendor is offering a "fair special" on hats. If you buy one hat at the regular price of $40$ dollars, you get a second hat at a $10 \textbackslash\%$ discount, and a third pair at half the regular price. James took advantage of the "fair special" to buy three hats. What percentage of the $120$ dollars regular price did he save? (adapted from 2013 AMC 8, Question \#12)

First, find the amount of money one will pay for three hats without the discount. We have $\textbackslash$ 40 \times 3$ hats $=\textbackslash$ 120$. Then, find the amount of money using the discount: $40+0.9 \times 40+\frac{1}{2} \times 40=\textbackslash$ 96$. Finding the percentage yields $\frac{96}{120}=80 \textbackslash\%$ To find the percent saved, we have $100 \textbackslash\%-80 \textbackslash\%=(\text{B}) 20$


My aunt can fold $$16$$ paper cranes in $$4$$ minutes. My uncle can fold $$15$$ paper cranes in $$5$$ minutes. How long would it take them to fold $$42$$ cranes if they work together at those rates?

$$6$$ minutes

$$9$$ minutes

$$12$$ minutes

$$13$$ minutes

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

My aunt can fold $$4$$ paper cranes in $$1$$ minute. My uncle can fold 3 paper cranes in $$1$$ minute. Together they fold $$7$$ paper cranes in $$1$$ minute. It takes them $$42\div7 = 6$$ minutes to fold $$42$$ paper cranes.


On the farm, there are $$5$$ sheep, $$5$$ hens, $$2$$ dogs, $$2$$ cats, and the farmer. How many legs are there altogether? (2006 Math Kangaroo Problem, Level 1-2, Question \#15)

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


If $$11$$th November 2031 is a Tuesday, what day of the week will $$11$$th November 2032 be?

Tuesday

Wednesday

Thursday

Friday

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


An average of $$40$$ campers sign up for each of the $$6$$ sports at camp. If each camper signs up for exactly $$3$$ sports, how many campers are there?

Since $$40\times 6=240$$, $$240$$ campers have signed up for the $$6$$ sports, and each camper is counted $$3$$ times. There are $$240\div 3=80$$ campers in all.


Al ran twice as far as Bob ran. They ran a total off $$18\rm km$$. How far did Al run?

$$3\rm km$$

$$6\rm km$$

$$9\rm km$$

$$12\rm km$$

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

Al ran twice as far as Bob. Split $$18\rm km$$ into two parts, one twice the other, to see that Bob ran $$6\rm km$$ and Al ran twice as far, $$12\rm km$$.


David has $$15$$ more candies than Andy at the beginning. David has $$3$$ candies more than Andy after giving some candies to Andy. How many candies does Debbic give to Aiden?

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


Adam paid ＄$$6$$ for $$15$$ buns. How many dollars did Tom pay for the same kind of buns if he bought $$5$$ more of them? (2008 Math Kangaroo Problem, Level 1-2, Question \#13)

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

There are $$3$$ groups of $$5$$ buns in $$15$$ buns: $$15\div 5=3$$, so $$5$$ buns cost $$6\div 3=$$＄$$2$$.  In total, Tom bought $$15 + 5 = 20$$ buns, which is $$4$$ groups of $$5$$ buns. So, Tom paid $$4\times 2 =$$＄$$8$$.


If $$20$$ years ago Allen was half as old as he is today, how old was he $$10$$ years ago?

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

If $$20$$ years ago Allen was half as old as he is today, then today he is $$40$$. Thus, $$10$$ years ago he was $$30$$.


A teacher distributes scorecards equally to students, and there is a surplus of $8$ cards. If $2$ more cards are given to each student, all the cards will be distributed. Then there arestudents in the class in total.

If $2$ more scorecards are given to each student, all the cards are distributed. Therefore, the class has $8\div2=4$ students.


Ryan buys a watch on sale for $$20\textbackslash\%$$ off in a shopping mall. He has an additional $$200-$$dollar coupon since he is a member of this shopping mall. The sales tax in his city is $$5\textbackslash\%$$, and he paid $$\textbackslash$2730$$ for this watch. What was the original price of the watch?

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


Workers want to plant some trees between houses. There are $17$ houses on one side of a road. Workers want to plant three trees between every two adjacent houses. How many trees do they need to plant?

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


A sum of $$\textbackslash$459$$ was shared among $$5$$ boys and $$14$$ girls. Each girl received $$\textbackslash$16$$.  How much did each boy get?

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

Girls $=14\times\textbackslash$16=\textbackslash$224$  Boys $=\textbackslash$459-\textbackslash$224=\textbackslash$235$  Each boy $=\textbackslash$235\div5=\textbackslash$47$


The radius of a coin is $$3\text{cm}$$. When $$4000$$ of these coins are placed side by side in a straight line, how long would this line be?

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

The length of the line is $$4000\times 2\times 3\text{cm=}24000\text{cm=}240\text{m}$$.


Alicia, Bryant, and Charles work for a software company and they want to write a particular computer program. Alicia and Bryant first write $\frac{1}{3}$ of the program in $6$ days. Then Bryant and Charles write $\frac{1}{4}$ of the remaining program in $2$ days. In the end three of them work together to finish the program in $5$ days. How many days will it take if Alicia works on the program by herself?

Overseas Competition->Knowledge Point->Word Problem Modules

In the second part, Bryant and Charles can write $\left( 1-\frac{1}{3} \right) \times \frac{1}{4}=\frac{1}{6}$ of the program in 2 days. Therefore, they can write $\frac{1}{6} \div 2 =\frac{1}{12}$ in one day. There is still $1-\frac{1}{3}-\frac{1}{6}=\frac{1}{2}$ left.  Now in the last part, they work together and finish in $5$ days. They can write $\frac{1}{2} \div 5=\frac{1}{10}$ in one day. Therefore, Alicia can write $\frac{1}{10}-\frac{1}{12}=\frac{1}{60}$ in one day, which means she needs $60$ days to complete.


A gardener has a box of bulbs to plant in a garden. The garden has three sections.  She plants 1/2~of the bulbs in the first section.  She plants 3 /4~of the remaining bulbs in the second section.  She has 6 bulbs left, which she plants in the third section.  How many bulbs were in the box at the start?

1- 1/2 - 1/2 x 3/4=1/8，1/8 means 6 bulbs, so in total there are 6~$\div$~1/8=48 bulbs.


John is 8 years and 3 months old. Alice is 102 months old. Cindy has been alive for 4380 days. Who is the oldest?

John

Alice

Cindy


As a Grade 1 student, Jenny saw thirteen seats in a row in the class, and she didn\textquotesingle t know which one belonged to her. The teacher told her that there were seven students behind her seat. So which seat should she sit?(Adapted from 2015 Math Kangaroo Problem, Level 1-2, Question \#18)  ~\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}


A clothing store bought some shirts at＄$$96$$ each. It wants to earn＄$$24 $$ for each shirt after a discount of $$20 \textbackslash\% $$. What is the selling price before the discount for each shirt?

$$100$$ dollars

$$120$$ dollars

$$150$$ dollars

$$180$$ dollars

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

$$\left( 96+24 \right)\div \left( 1-20 \textbackslash\% \right)=150$$ dollars.


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.


$$1$$ similar skirt and $$3$$ similar blouses cost $$$75$$. If each skirt costs twice as much as each blouse, how much will each skirt cost?

Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Equivalent Substitution in Equation Word 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


Six friends went to hike together and agreed to share the bill equally. However, James forgot to bring his wallet, so each of his five friends paid an extra of $10.2$ dollars to cover James\textquotesingle~portion. How much did they have to pay in total?

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

Everyone should pay $10.2\times5=51$ dollars. $51\times 6=306$


Of $$60$$ people at a school board meeting, $$24$$ are men. The ratio of women to men at the meeting is．

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


Water from the first faucet fills the swimming pool in $36$ hours. Water from each of the two other faucets fills the same swimming pool $4$ times faster. In how many hours will the swimming pool be filled if all three faucets are opened?

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

The efficiency of the first faucet is $\frac1{36}$ and that of the other two is $\frac4{36}$.  Thus it takes $1\div (\frac1{36}+\frac4{36}\times2)=4$ hours to fill the pool.


My vacation will start three weeks and two days after yesterday. If today is Tuesday, my vacation will start on what day?

Monday

Tuesday

Wednesday

Thursday

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

Three weeks after yesterday, which was a Monday, is a Monday also. Two days after a Monday is a Wednesday.


Mina put $12$ potted plants in a row from one end to the other end of the corridor. They were placed at an equal distance from one another. The distance between the first and the fifth potted plant was $28$ m. Mina went along the corridor from the first pot to the last pot. How many meters did she walk?


There are $6$ boxes each contains only oranges, apples, or pears. The boxes weigh $$15$$, $$16$$, $$18$$, $$19$$, $$20$$, and $$31$$ kg, respectively. If the total weight of apples is half of that of pears, and there is only one box of oranges, what is the weight of the box of oranges.

The total weight of all the boxes is $15+16+18+19+20+31=119$ kg. The weight of pears is twice that of apples, so excluding the box of orange, the weight of the remaining boxes should be divisible by $3$. Only removing $20$, the remaining weight is divisible by $3$.


A shop purchased some basketballs at ＄$$60$$ each. It then sold them at ＄$$75$$ each. How much did the shopkeeper earn for $$10$$ basketballs?


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 left 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.


Seventh grade students from a school line up and form a square array. There are $196$ students in the outermost layer. How many students in total are there in this array?

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

The number of students on each side of the outermost layer was $$196\div 4+1=50$$ students. The total number of students in the array was $$50\times 50=2500$$.


Given March $$25$$ of a certain year is Monday, what day of the week would May $$1$$ fall on this year? ．

Tuesday

Wednesday

Thursday

Friday

$(31-25+30+1=37$  $37\div7=5R2$  Exactly $5$ weeks from $25$ Mar, it will also be a Monday; another $2$ days later will be a Wednesday


A mixture of 45 liters of paint is $20 \textbackslash\%$ red tint, $30 \textbackslash\%$ yellow tint and $50 \textbackslash\%$ 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 )

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

Since $30 \textbackslash\%$ of the original 45 liters of paint was yellow, and 5 liters of yellow paint were added to make the new mixture, there are $13.5+5=18.5$ liters of yellow tint in the new mixture. Since only 5 liters of paint were added to the original 45 , there are a total of 50 liters of paint in the new mixture. This gives $ 37\textbackslash\%$ of yellow tint in the new mixture, which is (C) 37 .


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

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

The $$8$$\textsuperscript{th} means there are $$7$$ people in front of him. So there are also $$7$$ people behind him. The total number of pirates can be calculated: $$7+7+1=15$$.


A $$12$$-metre long steel pipe was cut into few pieces. The length of each piece is $$3$$ metres. It takes $$18$$ minutes to complete the whole process. How long does it take to cut a $$12$$-metre pipe into $$6$$-metre sections?

$$6$$ minutes

$$9$$ minutes

$$12$$ minutes

$$18$$ minutes

None of the above


A city council decided to put lanterns on both sides of a river. The distance between any two neighbouring lanterns on each side must be $11$ metres. The length of the river is $132$ metres. The distance between the first and the last lantern on each side must be also $132$ metres. How many lanterns will there be in total?

None of the above

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

132/11 = 12 lanterns  12 lanterns + 1 = 13 lanterns  13 x 2 = 26 lanterns.


Nine bus stops are equally spaced along a certain bus route. The distance between the first stop and the third stop is $$600$$ m. How long is the bus route? ($$2004$$ Math kangaroo Problem, Level $$5-6$$, Question \#$$9$$)

$$1800$$ m

$$2100$$ m

$$2400$$ m

$$2700$$ m

$$3000$$ m

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

Each interval is $600\div2=300$ m. There are $9-1=8$ intervals in total, so the bus route\textquotesingle s length is $300\times8=2400$ m.


A ship is being attacked by pirates. One by one the pirates climb a rope to get on the ship. The pirate captain is the $$8$$\textsuperscript{th} in line, and there are as many pirates in front of him as there are behind him. How many pirates are in line to climb the rope?（）


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 in the outermost layer?


On Think Planet, each Thinkyear has $8$ Thinkmonths and each Thinkmonth has $6$ Thinkweeks. How many Thinkweeks are there in one quarter of a Thinkyear?


When asked about his age, my uncle said "If you multiply my current age by $2$, then subtract the product by $6$, divide the answer by $2$ and then add $8$, the final answer is $38$." My uncle\textquotesingle s age isyears old．

Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems->Finding the Working Hours


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


After a test, teacher Valeria collects the data of the scores. Given that:  The average score of class $A$ is $76$.  The average score of class $B$ is $84$.  The average score of class $C$ is $89$.  The average score of class $A$ and $B$ is $79$.  The average score of all the three classes is $81$.  There are $40$ students in class $A.$ What is the ratio of number of students of class $B$ to that of $C$?

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


Ala, Lenka and Miso went out for dessert. Lenka paid $$4$$ dollars and $$50$$ cents for three scoops of ice cream. Miso paid $$3$$ dollars and $$60$$ cents for two cookies. How much did Ala pay for one scoop of ice cream and one cookie? (2011 Math Kangaroo Problem, Level 3 - 4, Question \#6)

$3$~dollars and~$30$~cents

$4$~dollars and~$80$~cents

$5$~dollars and~$10$~cents

$6$~dollars and~$30$~cents

$8$~dollars and~$10$~cents

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

$4$ dollars and $50$ cents are equal to $450$ cents, so one scoop of ice cream costs $450 \div 3 = 150$ cents. $$3$$ dollars and $$60$$ cents are equal to $360$ cents, so one cookie costs $360 \div 2 = 180$ cents. Thus, Ala should pay $ 150 + 180 = 330$ cents for one scoop of ice cream and one cookie. $330$ cents are equal to $3$ dollars and $30$ cents, so the answer is $A$.


Danni bought a painting for £$$42$$ last year. She sold it this year for £$$55$$. How much did she earn?

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


There are $38$ chickens and rabbits in a farm in total. The number of ducks is $2$ more than five times that of rabbits. How many ducks are there in the farm?

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


A fruit shop brought in some fruit. A quarter of them were sold last week. This week another $120$ kilograms were sold. One third of the original fruit is left now. How many kilos of fruit did the fruit shop buy?

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


Nicole has a $$500$$ ml bottle of mouthwash. Every morning, she uses two capfuls of mouthwash. Each capful contains $$4$$ ml of mouthwash.  If Nicole open a new bottle of mouthwash on $$12$$ April, on which of these dates will she use up the whole bottle of mouthwash?

$$12$$ June

$$13$$ June

$$14$$ August

$$15$$ August

Overseas Competition->Knowledge Point->Word Problem Modules

Nicole uses $$4\times2=8$$ ml of mouthwash every day.  $$500\div8=62$$ R $$4$$  So, $$62$$ days after $$12$$ April, the bottle of mouthwash will become empty.  There are $$18$$ remaining days in April and $$31$$ days in May.  $$62-18-31=13$$


A bag of toffee is $5$ dollars, a bag of cotton candy is $3$ dollars, and a bag of orange candy is $12$ dollars. Now, the candy shop decides to mix $25$ bags of toffee, $60$ bags of cotton candy, and $15$ bags of orange candy for $100$ bags of assorted candy. What should be the price of the assorted candy in dollars to keep the total revenue unchanged?

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

Total revenue: $25\times 5+60\times 3+15\times 12=485$ dollars  A bag of assorted candy: $$485\div 100=4.85$$ dollars


Jill is now $$14$$ years old. Jack is now $$6$$ years older than Jill was $$2$$ years ago. How old is Jack now?

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

Jill is now $$14$$. Two years ago, she was $$12$$. Since Jack is now $$6$$ years older than Jill was $$2$$ years ago, Jack is now $$12 + 6= 18$$.


Mr. Ronald sold $$300$$ burgers on Monday. He sold $$133$$ fewer burgers on Tuesday.  How many burgers did he sell on Tuesday?


To make coleslaw Cathy uses twice as much carrot (by weight) as cabbage. She then adds half as much yoghurt as cabbage. A pot of Cathy\textquotesingle s coleslaw weighs $$175\text{g}$$. How many pots of coleslaw can she make with a $$2 \text{kg}$$ cabbage?

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

The ratio by weight of carrot: cabbage:yoghurt$$=2:1:0.5$$ which we can double to give $$4:2:1$$. We can see that here $$2$$ represents the amount of cabbage and we want $$2 \text{kg}$$ of cabbage, so there will be $$4+2+1=7\text{kg}$$ of coleslaw altogether. Therefore the number of pots is $$7000\div 175 =40$$.


In a traditional Chinese novel, there are $108$ heroes, three of whom are women. How many male heroes are there in this novel？(adapted from $$2007$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$6$$)

There are $108$ heroes in total. Subtract three heroines to get the number of male heroes. That is $108-3=105$.


A total of $$46$$ bicycles and tricycles are in the garage. If there are $$100$$ wheels in total, there should be~\uline{~~~~~~~~~~}~tricycles in the garage.

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


Amanda is $$7$$ years old last year. In $$2$$ years times, she is double of her sister\textquotesingle s age. What is the sum of their age this year?

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


If I have $$2500$$ quarters, then I have．

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

Every $$4$$ quarters is ＄$$1$$; the number of dollars I have is $$2500\div 4=$$＄$$625$$.


Bud needs to recite 120 words for a dictation in a week (7 days). She plans to recite 15 words everyday. Can she be fully prepared for the test?

Yes, she can.

No, she can\textquotesingle t.


Two plums and one cherry weigh $$80\text{g}$$. One cherry and one plum weigh $$50\text{g}$$. What is the weight of four plums?

Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Equivalent Substitution in Equation Word Problems

Let the mass of one plum and the mass of one cherry be $$p \text{g}$$ and $$c\text{g}$$ respectively.  Then $$2p +c=80$$ and $$p+c=50$$. We can deduce that $$p=80-50= 30$$, and so four plums weigh $$120 \text{g}$$.  Revise from ($$2017$$ Primary Mathematics Challenge-February, Question \#$$18$$)


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. $$5x-2(10-x)=29$$, $$x=7$$.


On Kellin\textquotesingle s $$13$$th birthday, Allen was four times her age. On Kellin\textquotesingle s $$24$$st birthday, how old was Allen?

$$ 52 $$

$$ 63 $$

$$ 74$$

On Kellin\textquotesingle s $$13$$th birthday, Allen was four times her age, that is $$52$$. It is then eleven years until Kellin\textquotesingle s $$24$$st birthday, so Allen\textquotesingle s age at that time was $$52 +11 =63$$.


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: $$2x+2y+2z=18$$, $$x+y+z=9$$.


Hailey is $$6$$ years old and Xavier is $$7$$ years old this year. What is the sum of their ages after $$10$$ years?


Water from the first faucet fills the swimming pool in $20$ hours. Water from each of the three other faucets fills the same swimming pool $3$ times faster. In how many hours will the swimming pool be filled if all three faucets are opened?

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

The efficiency of the first faucet is $\frac1{20}$ and that of the other two is $\frac3{20}$.  Thus it takes $1\div (\frac1{20}+\frac3{20}\times3)=2$ hours to fill the pool.


A red kangaroo and a gray kangaroo weigh $$139\textasciitilde\text{kg}$$ altogether. The red kangaroo weighs $$35\textasciitilde\text{kg}$$ less than the gray kangaroo. How much does the gray kangaroo weigh?

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


I ate half of 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


In a group of $$48$$ children, the ratio of boys to girls is $$3:5$$. How many boys must join the group to make the ratio of boys to girls $$5:3$$?

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

Initially there are $$48$$ children of whom $$\frac{3}{8}$$ are boys and $$\frac{5}{8}$$ are girls, so there are $$18$$ boys and $$30$$ girls. When more boys join, there are still $$30$$ girls but now they form $$\frac{3}{8}$$ of the total. So the total number of pupils is now $$\frac{8}{3}\times30= 80$$, of whom $$80-30=50$$ are boys. Hence the number of boys joining is $$50-18=32$$.


Lucy joined a math test which had the scoring rules below: for any correct answer, she got $5$ points; for any skipped or wrong answer, she lost $7$ points. There were $20$ problems in total. When she finished the test, she got only $4$ points. How many problems did she answer correct?

Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems

The total points is $20\times5=100.$ If there was one wrong anwser, she would lose $5+7=12$ points.  $(20\times5-4)\div(7+5)=8$, so she got $20-8=12$ problems correct.


Nathan has $$4$$ red shirts, $$6$$ yellow shirts and $$8$$ white shirts. What fraction of his shirts are white? Give your answer in its simplest form.

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

White shirts $$=8$$  Total shirts $$=4+6+8=18$$  Fraction of shirts that are white $$=\frac{8}{18}=\frac{4}{9}$$


An empty truck weighs $$2000$$ kg. After the truck was loaded, the freight (that is, the load) made up $$80\textbackslash\%$$ of the weight of the loaded truck. At the first stop one fourth of the freight was unloaded. What percent of the loaded truck\textquotesingle s weight did the freight make up after that? ($$2003$$ Math Kangaroo Problem, Level $$7-8$$, Question \#$$17$$)

$$20\textbackslash\% $$

$$ 60\textbackslash\%$$

Actually, we don\textquotesingle t need the weight of the empty truck.  Suppose the weight of the loaded truck before the first stop is $5x$ kg, and the weight of the feight is $4x$ kg. After the first stop, $4x \times \frac14=x$ kg of freight is unloaded. Now, the freight weighs $4x-x=3x$ kg, and the loaded truck weighs $5x-x=4x$ kg. Thus, the percent is $\frac{3x}{4x}=\frac34=75\textbackslash\%$.


Jodie has just begun to read a $$160$$-page book. If she reads $$20$$ pages every day, she will finish the book in ．

$$8$$ days

$$18$$ days

$$20$$ days

$$80$$ days

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

Jodie has just begun to read a $$160$$-page book. If she reads $$20$$ pages every day, she will finish the book in $$160 \div 20 =8$$ days.


Tadek has $$7$$ zloty (unit of money) more than Witek. Witek has $$10$$ zloty less than Karol. Witek and Karol have $$28$$ zloty together. How much money does Tadek have?

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

Witek has $$(28 - 10) \div 2 = 9$$ zloty, so Tadek has $$9 + 7 = 16$$ zloty.


Ben and Ken have some books. After Ben sends $4$ books to Ken, he has $1$ book less than Ken. Which of the following is true?

Originally, Ben had $3$ books more than Ken.

Originally, Ben had $4$ books more than Ken.

Originally, Ben had $1$ books less than Ken.

Originally, Ben had $9$ books more than Ken.

Originally, Ben had $7$ books more than Ken.

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


David and Billy are on the bus together. They sit in the same column. There are $5$ people in front of David, Billy is in the middle. There are $10$ people behind Billy, and David is in the middle. How many people in this column? (adapted from2004 Math Kangaroo Problem, Level 3 - 4, Question \#19)

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


Chloe and Zoe are both students in Ms. Demeanor\textquotesingle s math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to $90\textbackslash\%$ of the problems she solved alone, but overall $60\textbackslash\%$ of her answers were correct. Zoe had correct answers to $70\textbackslash\%$ of the problems she solved alone. What was Zoe\textquotesingle s overall percentage of correct answers? (adapted from 2017 AMC 8, Question \#14)

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

Assume the total amount of problems is $100$ per half homework assignment, since we are dealing with percentages, and not values.  Then, we know that Chloe got $90$ problems correct by herself, and got $120$ problems correct overall.  We also know that Zoe had $70$ problems she did correct alone.  We can see that the total amount of correct problems Chloe and Zoe did was $120-90=30$. Therefore Zoe has $30+70=100$ problems out of $200$ problems correct. Thus $\frac{100}{200} = 50$ percent.


In the enchanted garden of the Green King, there are apple trees that grow golden apples. Every day, $$5$$ golden apples become ripe on each tree, and at the end of each day they fall from the trees. Today, the Green Gardener has picked up $$20$$ ripe apples that fell under the trees last night. How many enchanted trees are there in the garden?（$$2005$$ Math Kangaroo Problem, Levels $$1-2$$, Question \#$$1$$）

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

$$5$$ apples fall down from each trees. "Each"~is a sign of division. So, the answer is $$20\div5=4$$.


Add the number of days in January March, April, May, June, July, August, September, October, November and December.

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

The only missing month is February. The sum will be either $$365$$ - $$28$$ or (in leap years) $$366$$ - $$29$$. Both are equal to $$337$$．


Some cows live on a grassland. $10$ cows can eat all grass in $9$ days. $12$ cows can eat all grass in $7$ days. The amount of new grass that grows each day is constant. $24$ cows can eat all grass in~\uline{~~~~~~~~~~}~days.

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

Suppose a cow can eat $1$ m\textsuperscript{2}~of grass each day.  The amount of new grass that grows each day: $(9\times10-12\times7)\div(9-7)=3$ m\textsuperscript{2}.  The amount of grass originally: $$90-9\times 3=63$$ m\textsuperscript{2}.  $$24$$ cows can eat all grass in $$63\div \left( 24\times1-3 \right)=3$$ days.


The distance between Exeter and London is $$175$$ miles. Sam left Exeter at $$10:00$$ on Tuesday for London. Morgan left London for Exeter at $$13:00$$ the same day. They travelled on the same road. Up to the time when they met, Sam\textquotesingle s average speed was $$25$$ miles per hour, and Morgan\textquotesingle s average speed was $$35$$ miles an hour.  At what time did Sam and Morgan meet?

Overseas Competition->Knowledge Point->Word Problem Modules

Sam left Exeter three hours before Morgan left London, and travelled $$3\times 25$$ miles $$=75$$ miles in the three hours to $$13:00$$. So at $$13:00$$, the distance between Sam and Morgan was $$ \left( {175-75} \right) $$ miles $$=100$$ miles.  Let the time in hours between $$13:00$$ and the time at which Sam and Morgan met be $$t$$.  Then $$25t+35t=100$$. So $$t=\frac{{100}}{{60}}$$ hours $$=100$$ minutes $$=1$$ hour $$40$$ minutes. So Sam and Morgan met at $$14:40$$.


Some students are lining up at the cafeteria. Ellie is the third from the back and the seventh from the front. How many students are there lining up in total?


A bridge is built across a river. One quarter of the bridge is over the left bank of the river and one third of the bridge is over the right bank. The river is $$120\text{m}$$ wide. How long is the bridge?

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

The river is $$120\text{m}$$ wide and represents $$\left( 1-\frac{1}{4}-\frac{1}{3} \right)=\frac{5}{12}$$ of the length of the bridge. Therefore $$\frac{1}{12}$$ of the length of the bridge is $$24\text{m}$$. Hence the total length of the bridge is $$12\times 24\text{m}=288\text{m}$$.


There are $$40$$ guests queueing to enter a party. Every $$4^{\rm th}$$ guest in the queue receives a balloon and every $$6^{\rm th}$$ guest in the queue receives a mask. How many guests receive both a balloon and a mask?~\uline{~~~~~~~~~~}~

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

Every 12th guest receives both a mask and a balloon. Hence, the 12th, 24th and 36th guest receive both.


Daniel raises some ducks and dogs. All the ducks and dogs have $18$ legs and $5$ pairs of wings in total. How many ducks and dogs are there in total?

$5$ pairs of wings means there are $5$ ducks, so there are $18-5\times2=8$ legs for dogs, which is $8\div4=2$. Thus, there are $2+5=7$ animals.


There were $$31$$ runners competing in a race. The number of runners who finished before John is four times smaller than the number of runners who finished later than John. At what place did John finish?

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


The number of ounces of water needed to reduce $$9$$ ounces of shaving lotion containing $$50\textbackslash\%$$ alcohol to a lotion containing $$30\textbackslash\%$$ alcohol is: ($$1953 $$ AHSME Problem, Question \#$$9$$)

Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Solving Concentration Problems with Equations

Solution $$1$$.  Say we add $$N$$ ounces of water to the shaving lotion. Since half of an $$9$$ ounce bottle of shaving lotion is alcohol, we know that we have $$\dfrac{9}{2}$$ ounces of alcohol. We want $$\dfrac{9}{2}=0.3(9+N)$$ (because we want the amount of alcohol, $$\dfrac{9}{2}$$, to be $$30\textbackslash\%$$, or $$0.3$$, of the total amount of shaving lotion, $$9+N$$). Solving this, we find that $$9=0.6(9+N)\Rightarrow9=5.4+0.6N\hspace{0pt}\Rightarrow3.6=0.6N\hspace{0pt}\Rightarrow6=N$$. So, the total amount of water we need to add is $$6$$.  Solution $$2$$.  The concentration of alcohol after adding $$n$$ ounces of water is $$\dfrac{4.5}{9+n}$$.  To get a solution of $$30\textbackslash\%$$ alcohol, we solve $$\dfrac{4.5}{9+n}=\dfrac{3}{10}$$  $$45=27+3n$$  $$18=3n$$  $$6=n\Rightarrow6$$.


In the Adventure Park, 30 children took part in two of the adventures. 15 of them participated in the "moving bridge" contest, and 20 of them went down the zip-wire. How many of the children took part in both adventures?

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

There are 30 children.  15 of them participated in the "moving bridge" contest.  This means that the other 15, who did not participate in the "moving bridge" surely went down the zip-wire.  In fact 20 went down the zip-wire; therefore, 20-15=5 of the 15 "moving bridges\textquotesingle{} " participants must have also gone down the zip-wire.


When Lucy was born, Cathy was $23$ years old. The sum of their ages $3$ years later will be $45$. How old will be Cathy $3$ years later?

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

Suppose that Lucy will be $x$ years old $3$ years later, Cathy will be $$(x+23)$$ years old. $x+(x+23)=45$, so $x=11$. Thus, Cathy will be $11+23=34$ years old $3$ years later.


When Kerr was born, Barry was $13$ years old. The sum of their ages $5$ years later will be $51$. How old will be Barry $5$ years later?

Suppose that Lucy will be $x$ years old $5$ years later, Cathy will be $$(x+13)$$ years old. $x+(x+13)=51$, so $x=19$. Thus, Cathy will be $13+19=32$ years old $5$ years later.


A store sells cakes for $10 each, at the following discounts.  \textbf{① $1 off each every Wednesday.}  \textbf{② Buy three or more, $1 off each.}  If both rules are met at same time, the price can be reduced together.  How much will Tracy pay for 4 cakes at this store on Tuesday?

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


If $2\text{cm}$ represents $50\text{km}$ on a map and the distance between two towns on this map is $7.5\text{cm}$, then their actual distance apart is ．

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

If $$2\textasciitilde\text{cm}$$ represents $$50\textasciitilde\text{km}$$, $$1\textasciitilde\text{cm}$$ represents $$25\textasciitilde\text{km}$$. So, their actual distance apart is $$7.5\times 25=187.5\textasciitilde\text{km}$$.


There are $10$ benches on one side of a road. Brown wants to put $1$ pot of flowers between every two adjacent benches. How many pots of flowers does he need to prepare?

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


Cagney can frost a cupcake every $$30$$ seconds and Lacey can frost a cupcake every $$60$$ seconds. Working together, how many cupcakes can they frost in $$5$$ minutes? (Adapted from $$2012$$ AMC $$10\rm A$$ Problem, Question \#$$11$$)

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

In $$300$$ seconds ($$5$$ minutes), Cagney will frost $$\dfrac{300}{30}=10$$ cupcakes, and Lacey will frost $$\dfrac{300}{60}=5$$ cupcakes. Therefore, working together they will frost $$10+5=\boxed{(\text{B})15}$$ cupcakes.


Owen attends a basketball shooting game. He gets $70 \textbackslash\%$ on $10$ one-point shots , $80 \textbackslash\%$ on $10$ two-points shots and $90 \textbackslash\%$ on $10$ three-points shots. Compare Owen\textquotesingle s score with the total points possible, which percent is closest to his overall score? (Adapted from 2006 AMC 8, Question \#12)

$70 \textbackslash\% \cdot 10=7$ $80 \textbackslash\% \cdot 20=16$ $90 \textbackslash\% \cdot 30=27$ Adding them up gets $7+16+27=50$. The overall percentage correct would be $\frac{50}{60}=\frac{5}{6}=5 \cdot 16 . \overline{6}=83 . \overline{3} \approx(\mathbf{D}) 83$.


There are five kangaroo mothers, six kangaroo babies, and one kangaroo father. Each kangaroo mother should take care of the same number of kangaroo babies. How many kangaroo babies should kangaroo father take care of? (adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$6$$)

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

The key point is that each kangaroo mother needs to take care of the same number of kangaroo babies. So $6$ (number of kangaroo baby) $$\div$$ $5$ (number of kangaroo mother)$=1\ldots\ldots1$, and the remaining one is taken care of by kangaroo father.


There are twice as many boys in a room as girls. If $$5$$ boys leave the room, there would be an equal number of boys and girls in the room. How many boys were in the room at first?

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

The number of boys that leave the room must equal the number of boys that remain. Since $$5$$ boys leave, there are $$5$$ boys still in the room for a total of $$10$$ boys.


Pamela, Pearl, and Polly went to buy some toys. Pamela paid $$2$$ dollars and $$70$$ cents for three identical dolls. Pearl paid $$3$$ dollars and $$40$$ cents for two identical toy cars. How much did Polly pay for one doll and one toy car? (Adapted from 2011 Math Kangaroo Problem, Level 3-4 , Question \#6)

$2$ dollars and $80$ cents

$2$ dollars and $70$ cents

$2$ dollars and $60$ cents

$2$ dollars and $50$ cents

$2$ dollars and $40$ cents

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

$$2$$ dollars and $$70$$ cents=$270$ cents  $$3$$ dollars and $$40$$ cents=$340$ cents  One doll costs $270\div3=90$ cents.  One toy car costs $340\div2=170$ cents.  $170+90=260$ cents = $2$ dollars $60$ cents.


A police spotted a burglar from $$100\text{m}$$ apart. The burglar immdiately runs away at a speed of $$4\text{m/s}$$ and the police starts chasing him at $$8\text{m/s}$$ at the same time. At this rate, how long will it take the police to catch the burglar?

$$1 $$ minute

$$25 $$ seconds

$$30$$ seconds

$$15$$ seconds

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

The distance between them is $$100$$ m, and the difference between their speeds is $$12-8=4000$$ m/h. It takes $$100\div4000\times60=1.5$$minutes to catch the burglar, which is $$90$$ seconds


A sugar solution is made by mixing $$7$$ grams of sugar and $$21$$ grams of water. Find the percent concentration of the solution.

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


Two plums and one cherry weigh $$80\text{g}$$. Two cherries and one plum weigh $$70\text{g}$$. What is the weight of four plums?

Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Equivalent Substitution in Equation Word Problems

Let the mass of one plum and the mass of one cherry be $$p \text{g}$$ and $$c\text{g}$$ respectively.  Then $$2p +c=80$$ and $$2c+p=70$$. Hence $$3p +3c=150$$, and $$p+c=50$$. But since $$2p+c=80$$, we can deduce that $$p=80-50= 30$$, and so four plums weigh $$120 \text{g}$$.


A total of $$32$$ chickens and rabbits are caged together. If there are $$90$$ legs in total, how many chickens and rabbits are in the cage, respectively?

$20$; $12$

$13$; $19$

$18$; $14$

$19$; $13$

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

Suppose all the animals in the cage are chickens: there should be $$2\times 32=64$$ legs. However, $$90-64=26$$ legs are missing because we counted $$26\div2=13$$ rabbits as chickens. Hence, there are $$13$$ rabbits and $$32-13=19$$ chickens.


Anna is $$10$$ years old and the age of her mother is $$4$$ times that of Anna. How old will Anna\textquotesingle s mother be when Anna\textquotesingle s mother is twice as old as Anna? (Adapted from $$2007$$ Math kangaroo Problem, Level $$5-6$$, Question \#$$20$$)

Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Varying Multiples in Age Problems

The age difference between them is $(4-1)\times10=30$, which stays the same forever. Then, when Anna\textquotesingle s mother is twice as old as Anna, Anna should be $30$ years old, then her mom should be $30\times2=60$.


Some students are buying a boardgame together. If each person pays $$$60$$, they need another $$$60$$ for payment. If each person pays $$$70$$, they will have $$$10$$ left. How much is the boardgame?

Overseas Competition->Knowledge Point->Word Problem Modules

Number of students: $$(60+10)\div (70-60)=7$$  Price of boardgame: $$60\times7+60=480$$．


In a speed skating competition, $$10$$ skaters reached the finish line. The number of skaters that came in before Tom was $$3$$ less than the number of skaters who came in after him. Which place did Tom end up in? (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 skaters that came in before Tom and the number of skaters that came in after him is $10 - 1 = 9$. The number of skaters that came in before Tom was $(9 - 3) \div 2 = 3$, so Tom was the fourth one.


There is a tournament at the pool, First, $$13$$ children signed up and then another $$19$$ children signed up, Six teams with an equal number of members each are needed for the tournament, At least how many more children need to sign up so that,the six teams can be formed．

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

The total number of children is $$13+19=32$$, To form six teams with the same number of children in each team, we divide $$32$$ by $$6$$, $$32\div6=5$$$$\rm R$$$$2$$, The remaining $$2$$ children will need $$4$$ more children to form the sixth team.


Bob and Wilson are standing in line. Bob knows that there are $$5$$ people in front of him. Wilson knows that there is a total of $$12$$ people in the line. If Bob is just in front of Wilson, how many of the people in the line are behind Wilson? (Adapted from 2017 Math Kangaroo Problem, Level 1-2, Question \#14)


Mother\textquotesingle s Day in $$2020$$ was May $$10^{\rm th}$$, which was a Sunday. Father\textquotesingle s Day in $$2020$$ was June $$21^{\rm st}$$. On what day of the week did Father\textquotesingle s Day fall?

Monday

Tuesday

Wednesday

Sunday

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

There are in total $$21 + 21 = 42$$ days from May $$11$$ to June $$21$$. Since $$42 \div 7 = 6$$, with no remainder, the Father\textquotesingle s Day falls on Sunday as well.


If today is Monday, then $63$ days from today will be．

$$$$Monday

$$$$Tuesday

$$$$Friday

$$$$Sunday

If today is Monday, every $$7$$ days is another Monday.


A store sells cakes for $10 each, at the following discounts.  \textbf{① $1 off each every Wednesday.}  \textbf{② Buy three or more, $1 off each.}  If both conditions are met at same time, the price can be reduced together.  How much will Tracy pay for 4 cakes at this store on Tuesday?


A balloon ride can take at most $$3$$ people at a time. If $$41$$ people want to fly in the balloon, the least number of rides needed is．

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

A balloon ride can take \emph{at most}~$$3$$ people at a time. If $$41$$ people want to fly in the balloon, the least number of rides needed is $$41 \div3$$, rounded \emph{up} to $$14$$.


Andy spent $$5$$ dollars on $$15$$ biscuits. How much would it cost if Andy bought six more of them? (adapted from $$2008$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$13$$)

Fifteen cookies for five dollars means three cookies for one dollar. Six more cookies cost $$2$$ dollars. $$5+2=7$$~ dollars in total.


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

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


One of my two brothers is $$4$$ years older than the other. If the sum of their ages is $$38$$, the older brother isyears old.

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

One of my two brothers is $$4$$ years older than the other. If they were the same age, they\textquotesingle d each be $$19$$. Thus, one is $$17$$ and the other is $$21$$.


Lee is $14$ years old and Lay is $41$ years old. How many years ago, Lay\textquotesingle s age is exactaly $4$ times Lee\textquotesingle s age?

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


Which of the following equations represents the situation: John drinks $x$ cups of boba everyday on weekdays and $2$ cups of boba everyday on the weekends.

The boba that John drinks during weekdays: $$5x$$  The boba that John drinks during weekends: $$2\times 2 =4$$  The total boba that John drinks during a week: $$5x+4$$


Granny and the triplets Cara, Cate and Chris all have their birthdays today.  The ages of all four of them total $$120$$ years.  Granny is $$5$$ times as old as each of the triplets.  When were the triplets born?

Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Sums and Multiples in Age Problems

Given that Granny is $$5$$ times older than each of the three triplets, we know that the age of each triplet is $$120\div (5+3)= 15$$. So Cara, Cate and Chris were born in $$2007$$.


Nick has $83$ books and Steven has $140$ books. Starting from tomorrow, Nick will buy $8$ books and Steven will buy $5$ books every day. How many days later will they have the same number of books?

Never


In a basket, there are $60$ bananas. $20$\% of them are rotten. How many bananas are in good condition?

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


There are $$7$$ numbers with an average of $$79$$. After eliminating a number, the average of the remaining numbers is $$84$$. What is the eliminated number?

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


If today is Saturday, what day of the week will be 100 days later?

Sunday

Friday

Monday

Thursday

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

$$100\div7=14$$$$\cdots \cdots 2$$,  So 2 days later is Monday.


Some zoo animals are standing in an array to prepare for the Zoo Olympics. The fox, Bob, finds that no matter whether he counts from front to back, back to front, left to right, or right to left, he is always the $$3$$\textsuperscript{rd} in line. How many animals are there in the array?~\uline{~~~~~~~~~~}~

Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number of People in a Rectangular Array

$$3+3-1=5$$.  Since each row and column has $$5$$ animals, there are $$5\times5=25$$ animals in total.


The sum of two natural numbers is equal to $$77$$. If the first number is multiplied by $$8$$ and the second by $$6$$, then those products are equal. The larger of these numbers is~\uline{~~~~~~~~~~}~. ($$2004$$ Math Kangaroo Problems, Level $$5-6$$, Question \#$$20$$)

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

Suppose one of the numbers is $x$. $8x=6(77-x)$, $x=33$. Thus, these two numbers are $33$ and $44$. The larger one is $44$.


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

Thursday

Saturday

Sunday

Tuesday

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.


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


Ella says:" I can run $18\text{km}$ every hour."  Vivian says: " Haha, I am the faster runner because I can run $100\text{m}$ every $21\text{s}$."  Vivian\textquotesingle s statement is~\uline{~~~~~~~~~~}~because it only takes Ella~\uline{~~~~~~~~~~}~$\text{s}$ to run $100\text{m}$.

correct, 200

correct, 60

wrong, 20

wrong, 10

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


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?

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.


There were $$31$$ runners competing in a race. The number of runners who finished before John is four times smaller than the number of runners who finished later than John. At what place did John finish? ($$1998$$ Math Kangaroo Problem, Level $$3-4$$, Question \#$$13$$)

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


Mike has a bookcase with three layers, and the ratio of books placed on the upper, middle and lower layers is $$5:6:4$$. Given that there are $$240$$ books on the middle level,  books should be removed from middle level and added to the lower level so that the number of books on each level can be exactly the same.

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

Lower level: $$240\div6\times4=160$$,  The number of books to be added to the lower level: $$(240-160)\div2=40$$.  So, the answer is $$\text{B}$$.


Tom and Jerry have to mail $$2000$$ envelopes for a new marketing campaign. Jerry can mail $$120$$ envelopes per hour. With Tom\textquotesingle s help, they can get the job done in $$10$$ hours. How long will it take Tom to finish the job by himself?

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

Working together: $$2000\div10=200$$ envelopes per hour.  Tom: $$200-120=80$$ envelops per hour, $$2000\div80=25$$ hours.


A series of colored lanterns are arranged in the pattern: red, red, red, yellow, yellow, red, red, red, yellow, yellow $\cdots$ The $$50$$\textsuperscript{th} lantern is~\uline{~~~~~~~~~~}~.

red

yellow

Since $$50\div(3+2)=10$$ which has no remainder, the $$50^{\text{th}}$$ colored lantern is yellow.


In a farm, there is an equal number of cows, sheep, and chickens. These animals have $250$ legs in total. How many sheep are there?

Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems

Group $1$ of each kind of animals together, and there are $4+4+2=10$ legs in each group. There are $250\div10=25$ groups, so there are $25$ sheep.


If Kelly was 12 years old 4 years ago, how old will she be 8 years from now?

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


There are $$20$$ students in a class lining up for recess. Mike is the $$7$$\textsuperscript{th} counting from front to back. How many students are behind Mike? What is his position counting from back to front?

$$12$$, $$13^{\rm th}$$

$$13$$, $$14^{\rm th}$$

$$13$$, $$12^{\rm th}$$

$$14$$, $$13^{\rm th}$$

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

The number of students behind Mike plus the position of Mike equals the total number of students in the class. So there are $$13$$ students behind Mike: $$20-7=13$$. However Mike is not included in these $$13$$ students, which means Mike is the $$14$$\textsuperscript{th} student counting from back to front.


The ratio of your pears to oranges is $$3:7$$, and you have $$15$$ pears. How many oranges do you have?

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


$$10$$ trees are planted at equal distance along a river. The distance between the $$1^{st}$$ and the $$3^{rd}$$ tree is $$20$$ metres. What is the distance between the $$7^{th}$$ and $$9^{th}$$ tree?

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

They are having the same number of intervals.


The average of John and Leo's ages is Kelly's age. The average of Kelly and Mila's ages is Leo's age. Of the four children, John is the youngest and Mila the oldest. The average of John and Mila's ages is 11.  What is the total of the ages of Kelly and Leo?


Marcus has $$75$$ toy cars. $$\frac{1}{5}$$ of his toy cars are black, $$\frac{2}{15}$$ of the remainder are white, and the rest are grey. He hasmore black toy cars than white toy cars.

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

$75\div5=15$ toy cars are black.  $15\times4=60$ toy cars are white or grey.  $60\div15\times2=8$ toy cars are white.  He has $15-8=7$ more black toy cars than white toy cars.


Miya is $3$ years old this year, and her brother is $3$ years older than her. How old her brother will be $2$ years later?~(adapted from $$2005$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$7$$)

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

When Miya is $3$, her brother is $6$, so $2$~years later, her brother is  $8$.


Five years ago, Jennifer\textquotesingle s age was five times Jason\textquotesingle s age. Now, Jennifer\textquotesingle s age is four times Jason\textquotesingle s age. How old is Jennifer now?

None of the above

Let Jason\textquotesingle s age five years ago be 1 unit. Then Jennifer\textquotesingle s age was 5 units.  Now, Jason\textquotesingle s age is 1 unit + 5 and Jennifer\textquotesingle s age is 5 units + 5. We also know that Jennifer\textquotesingle s age is four times Jason\textquotesingle s age or 4 x (1 unit + 5) = 4 units + 20.  Then:~  5 units + 5 = 4 units + 20  5 units - 4 units = 20 - 5  1 unit = 15  Jennifer is 5 units + 5 = 5x15 + 5 = 80 years old now.


The number of weeks in $$139$$ days is most nearly equal to．

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

The number of weeks in $$139$$ days is most nearly $$140\div 7=20$$.


When Patience asked her Granddad how old he was, he answered, "I am $$34$$ now and will be $$33$$ on my birthday." She looked confused so he added, "After being $$50$$ for a year I started counting backwards on each birthday. " How old will he actually be on his birthday?

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

When Granddad would have claimed to be $$49$$ he was actually $$51$$, $$48$$ when he was actually $$52$$- in every case his claimed age and his real age have a total of  $$100$$. So this year his age is $$100-33=67$$.


None of the above

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


In the window of Bradley\textquotesingle s Bicycle Bazaar there are some unicycles, some bicycles and some tricycles. Laura sees that there are seven saddles in total, thirteen wheels in total and more bicycles than tricycles.  How many unicycles are in the window?


Red and green dragons lived in a cave. Each red dragon had $$6$$ heads, $$8$$ legs, and $$2$$ tails. Each green dragon had $$8$$ heads, $$6$$ legs, and $$4$$ tails. There were $$44$$ tails altogether, and there were $$6$$ less green legs than red heads. How many red dragons lived in the cave? ($$2003$$ Math Kangaroo Problems, Level $$5-6$$, Question \#$$29$$)

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

Suppose there are $x$ red dragons and $y$ green dragons. $2x+4y=44$ and $6x-6y=6$. We can get that $y=7$ and $x=8$. Thus, there are $8$ red dragons.


$$12$$, $$13$$

$$13$$, $$14$$

$$13$$, $$12$$

$$14$$, $$13$$


A bookstore purchases $$20$$ story books for ＄$$820$$. If the bookstore wants to earn ＄$$12$$ for each book, what is the selling price of each book?

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


Henry starts to read a $$290$$-page book on a Monday. He reads four pages every day except on Sundays when he reads $$25$$ pages. He will read the book starting from page~\uline{~~~~~~~~~~}~next Monday.


There are $$10$$ blind boxes on the desk, and each blind box contains two toys. Now there are $$16$$ toys in hands. How many blind boxes remain？(adapted from $$2010$$ Math Kangaroo Problem, Level $$1-2$$, Question \#$$15$$)

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

$$16$$ toys means $$8$$ blind boxes are opened.  There are $$10$$-$$8$$=$$2$$ blind boxes that have not been opened.


A salt solution is made by mixing $$8$$ ounces of pure salt and $$32$$ ounces of water. Find the percent concentration of the solution.

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


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.


If February is a month that contains Friday $$13^{}\text{th}$$, what day of the week is February $$1$$st?．

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 February $$6$$ is a Friday. Then count a few days back to find that February $$1$$ is a Sunday.


Grandpa suggested dividing all the peanuts between the family members in the following way: one person would get $5$ kilos, two people would get $4$ kilos each, four people would get $2$ kilos each, one person would get $6$ kilos, and one person would not get any peanuts. Grandma suggested dividing the peanuts equally among all of the family members. How many people would get more peanuts in grandma\textquotesingle s suggestion than grandpa\textquotesingle s? (adapted from 2005 Math Kangaroo Problem, Level 5-6, Question \#14)

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

Grandma\textquotesingle s suggestion: $(1\times 5 + 2\times 4+4\times 2+1\times 6+1\times 0)\div(1+2+4+1+1) = 27\div9=3$  Thus, there are $4+1=5$ people get more peanuts.


Study the pattern below. The $$100^{}\rm {th}$$ letter is  .  $$A A B B C A A B B C A A B B C A A \cdots$$

$$A$$

$$B$$

$$C$$

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


Given that May $2$nd of a given year is a Thursday, what day is May $29$th of the same year?

Saturday

Wednesday

Thursday

Tuesday

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

$29-2=27$ days later, it will be May $29$th. $27\div7=3R6$, which means May $29$th is Wednesday.


A $$16$$-quart radiator is filled with water.Four quarts are removed and replaced with pure antifreeze liquid.Then four quarts of the mixture are removed and replaced with pure antifreeze.This is done a third and a fourth time.The fractional part of the final mixture that is water is．

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


On a map of the Andes, if $2$ $\text{cm}$ represents $6000$ $\text{km}$, then  ~represents $300$ $\text{km}$ .

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

If $2$ $\text{cm}$ represents $6000\text{km}$, $1\text{cm}$ represents $3000\text{km}$, and $0.1\text{cm}$ represents $300\text{km}$.


My sister runs $$10\text{km}$$ per hour, and I run $$2\text{km}$$ in $$15$$ minutes. If we both run for $$2$$ hours, my sister will run$$\text{km}$$ farther than I will.

Overseas Competition->Knowledge Point->Word Problem Modules

I run $$2\text{km}$$ in $$15$$ minutes, or $$8\text{km}$$ in $$1$$ hour. In $$2$$ hours, I will run $$16\text{km}$$ and my sister will run $$20\text{km}$$. She will run $$4\text{km}$$ farther than I will.


In 2010 about 120 million digital still cameras were sold worldwide.  By 2018 this number had decreased by 85\%.  About how many million digital still cameras were sold in 2018?

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


Monica arrived in the Kangaroo Camp on July 25th in the morning and left the camp on August 3rd in the afternoon. How many nights did she sleep in the camp?

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

July has 31 days. She arrive on morning of July 25.  From July 25 to 31, there are 7 nights that she slept in the camp.  Then she slepft for 2 days in August, since she left on the afternoon Aug 3 already.  Hence, 2=7=9


There are three books Chinese, Math, and English. Sissy wants to put them in the bookcase. How many ways are there for the three books to put? List out all the ways.

List out all the possible ways in order.  $C A E$  $C E A$  $A C E$  $A E C$  $E C A$  $E A C $


In a fruit stall, there are 25 apples. There are 9 fewer apples than oranges. How many oranges are there in the fruit stall?


Chloe has＄$$7$$. She is going to buy $$6$$ pens, and each costs $90$ cents. She also buys a certain number of pencils, and each costs $$50$$ cents. How many pencils at most can she buy? (Adapted from 2007 Math Kangaroo Problem, Level 3-4, Question \#4)


Isabella must take four $100$-point tests in her math class. Her goal is to achieve an average grade of $95$ on the tests. Her first two test scores were $97$ and $91$. After seeing her score on the third test, she realized she can still reach her goal. What is the lowest possible score she would have made on the third test?

Isabella wants an average grade of $95$ on her $4$ test; this also means that she wants the sum of her test scores to be at least $95\times 4=380$ (if she goes over this number, she\textquotesingle ll be over the goal!). She\textquotesingle s already taken two tests, which sum to $97+91=188$, which means she needs $380-188=192$ more points to achieve her desired average. In order to minimize the score on the third test, we assume that Isabella will receive all $100$ points on the fourth test. Therefore, the lowest score on the third test would be $192-100=92$.


\textbf{In the setting of the previous problem, about what percent of the variation in the number of service calls is explained by the linear relation between number of service calls and number of machines?~}

None of the above

\textbf{Can't tell from the information given}


Otto the octopus needs $$2$$ tentacles to juggle up to $$3$$ balls.  If Otto uses all $$8$$ tentacles, Otto can juggle up to  balls.

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

Otto needs $$2$$ tentacles to juggle up to $$3$$ balls. Using $$8=4\times2$$ tentacles, Otto can juggle up to $$4\times3 = 12$$ balls.


Lucy was $$20$$ years old when Bill was $$12$$. Now, Bill is $$17$$ years old. How old is Lucy?

The age difference between Lucy and Bill is $$20~-- 12 = 8$$, which will not change. Thus, Lucy is $$17 + 8 = 25$$ years old.


Olivia has $32$ clothes, $4$ of them are yellow, $10$ are blue, $13$ are purple, and the others are white. Suddenly the power is off, and it is all black in the room. At least how many clothes should Olivia pick in order to guarantee that she gets $8$ clothes in the same color?


Jack mixed $20$ grams of sugar with $30$ grams of water. What is the percent concentration of the sugar solution? Then Jack added $50$ grams of water. What is the percent concentration the sugar solution?

$$40 \textbackslash\% $$; $$20\textbackslash\% $$.

$$40 \textbackslash\% $$; $$25 \textbackslash\% $$.

$$50 \textbackslash\% $$; $$20 \textbackslash\% $$.

$$50 \textbackslash\% $$;~$$25 \textbackslash\% $$.

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


Colin has $$70$$ stamps. He has $$7$$ times as many stamps as Ben. How many more stamps does Colin have than Ben?

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


In a certain year, June $$24$$\textsuperscript{th}~is Thursday. What day is August $$27$$\textsuperscript{th~}in this year?  $\textasciitilde$

Monday

Tuesday

Thursday

Friday

Saturday

Counting from June $$24$$\textsuperscript{th}, after $30-24=6$ days it is June $$30$$\textsuperscript{st}. After $58$ days it is August $$27$$\textsuperscript{th}. In total, there are $6+58=64$ days. $64\div 7 =9R1$, which means August $$27$$\textsuperscript{th~}is Friday.


A tank filled with 200 litres of water weighs 350kg. The same tank filled with 150 litres of water weighs 315kg. What is the weight of the empty tank?

None of the above

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


Esther made $$8$$ paper stars.  Faiza made $$4$$ times as many paper stars as Esther did.  Gurmit made $$5$$ times as many paper stars as Esther did,  How many paper stars did the three boys make altogether?


Debbie bought a loaf of bread for $$$4$$.  She paid for the bread with a $$$10$$ note.  How much change did Debbie receive? ．

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


Six rectangles each with a common base width of $2$ have lengths of $1,4,9,16,25$, and 36 . What is the sum of the areas of the six rectangles? (2014 AMC 8, Question \#6)

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

The sum of the areas is equal to $2 \cdot 1+2 \cdot 4+2 \cdot 9+2 \cdot 16+2 \cdot 25+2 \cdot 36$. This is equal to $2(1+4+9+16+25+36)$, which is equal to $2 \cdot 91$. This is equal to our final answer of (D) 182 .


My old printer printed $$13$$ pages in $$3$$ seconds. My new printer prints $$21$$ pages in $$2$$ seconds. In $$6$$ seconds my new printer printsmore pages than my old one could have.

My old printer printed $$13$$ pages in $$3$$ seconds or $$26$$ pages in $$6$$ seconds. My new printer prints $$21$$ pages in $$2$$ seconds or $$63$$ pages in $$6$$ seconds. The difference is $$63 - 26=37$$.


March $$12$$th, $$2012$$ was a Monday. What day was May $$1$$st, $$2015$$?

Tuesday

Wednesday

Thursday

Friday

March $$12$$th, $$2013$$: Tuesday  March $$12$$th, $$2014$$: Wednesday  March $$12$$th, $$2014$$: Thursday  $(31-12)+30+1=50$, $50\div 7=7\textbackslash{} \rm r \textasciitilde1$, so it was Friday.


SASMO 2014 P2 Q10  Tim is 8 years old and Sally is 4 years old. How old will Sally be when Tim is 14 years old?

None of the above

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


Pip is 10 years and 2 months old. Bud is 124 months old. Bob has been alive for 3660 days. Who is the oldest?

Pip

Bud

Bob


There are some ducks and chickens in a farm. The number of chickens is $10$ more than ducks.The number of ducks is half the number of chicken. How many ducks and chickens are there in the farm?  ~


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


There were some cupcakes in a bakery. First, Jade ate half of the cupcakes. Then, Neil ate half of the remaining cupcakes. Finally, Terry ate $6$ and there were $$2$$ cupcakes left. At beginning, how many cupcakes were there in the bakery?


If today is Tuesday, what day was it $$76$$ days ago?

$$$$Monday

$$$$Tuesday

$$$$Wednesday

$$$$Thursday

Today is Tues. $$77$$ days ago was Tues. $$76$$ days ago was Wed.


There is a piece of wire. First, half of the piece is used. Then, half of the remaining piece is used. Next, $$16$$ meters are used. Finally, $$9$$ meters are left. The original piece of the wire is~\uline{~~~~~~~~~~}~meters long.


Karl is now $10$ years old, and Ala is $3$ years old. How many years from now will Karl be twice as old as Ala?

The age difference is equal to $10-3=7$. When the age of Karl is twice the age of Ala, the age of Ala will be equal to the age difference which is $7$. Thus, it will pass $7-3 = 4$ years.


In a certain year, March $$27$$\textsuperscript{th}~is Friday. What day is April $$24$$\textsuperscript{th~}in this year?  $\textasciitilde$

Monday

Tuesday

Thursday

Friday

Saturday

Counting from March $$27$$\textsuperscript{th}, after $31-27=4$ days it is March $$31$$\textsuperscript{st}. After $24$ days it is April $$24$$\textsuperscript{th}. In total, there are $4+24=28$ days. $28\div 7 =4$, which means April $$24$$\textsuperscript{th~}is Friday.


How many digits have to be written in order to write down every number from $$1$$ to $$100$$ inclusive? ($$2007$$ Math Kangaroo Problem, Level $$3-4$$, Question \#$$23$$)

Overseas Competition->Knowledge Point->Word Problem Modules->Page Number Problem->Correspondence between Numbers and Page Numbers->Applying the Total Number of Numbers

$1$-digit numbers: $9\times1=9$ digits.  $2$-digit numbers: $90\times2=180$ digits.  $3$-digit numbers: $1\times3=3$ digits.  Total: $9+180+3=192$.


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

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

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 $$91$$.


The triplets Adam, Jan and Stas and their sister Marysia who is four years older than them were $24$ years old together three years ago. How old is Marysia today? (2001 Math Kangaroo Problem, Level 5-6, Question \#18)

Adam, Jan and Stas were $(24-4)\div4=5$ years old three years ago. Marysia was $5+4=9$ years old. Thus, Marysia is $9+3=12$ years old.


A mother cut a cake into $$12$$ equal slices. Her four children had a slice each and she had one too. Later, a neighbour ate four slices. What percentage of the cake was left at the end of the day?

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


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 $$1$$ metre 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.