A bag of toffee is $7$ dollars, a bag of cotton candy is $6$ dollars, and a bag of orange candy is $15$ dollars. Now, the candy shop decides to mix $40$ bags of toffee, $50$ bags of cotton candy, and $10$ 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: $40\times 7+50\times 6+10\times 15=730$ dollars  A bag of assorted candy: $$730\div 100=7.3$$ dollars


A drawer contains $10$ yellow socks, $8$ blue socks and $4$ pink socks. Bella picks socks from the drawer without looking. What is the smallest number of socks she must pick to make sure she has at least one sock of each colour?

Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Questions Involving Average->Extreme Value of Average


Peter has some toy cars, and Paul has $$4$$ more toy cars than Peter. Altogether they have $$36$$ toy cars. How many toy cars does Paul 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

Paul has $$(36 + 4) \div 2 = 20$$ toy cars.


There is an equation with all integers in the upper squares, and the answer on the right side is only the approximation of $$\frac{\square }{3}+\frac{\square }{5}+\frac{\square }{7}\approx 1.16$$ after rounding off. The numbers in each of the three upper squares of the equation are~\uline{~~~~~~~~~~}~in order.

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


Nancy has $23$ donuts. She gives one donut to Sana, and then Nancy has $10$ more donuts than Sana. At beginning, how many donuts does Sana have?

Overseas Competition->Knowledge Point->Word Problem Modules


Joann\textquotesingle s birthday in $$2020$$ was May $$10$$\textsuperscript{th}, which was Sunday. Elizabeth\textquotesingle s birthday in $$2020$$ was June $$21$$\textsuperscript{st}. What day of the week is Elizabeth\textquotesingle s birthday on?

Thursday

Saturday

Sunday

Tuesday

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

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


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

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


Ellis\textquotesingle s Eel Emporium contains a large tank holding three different types of eel: electric eels, moray eels and freshwater eels. A notice on the tank reads as follows:  All the eels are electric eels except for $$12$$  All the eels are moray eels except for $$14$$  All the eels are freshwater eels except for $$16$$  How many eels are in the tank?

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

Let the number of electric eels be $$x$$, the number of moray eels be $$y $$ and the number of freshwater eels be $$z$$. The information on the notice tells us that $$y + z = 12$$, $$x + z = 14$$ and $$x + y = 16$$. When you add these three equations, you obtain $$2x + 2y + 2z = 42$$ and hence $$x + y + z = 21$$. Therefore the number of eels in the tank is $$21$$.


Tom and Ben played a quiz game. $$2$$ points for a correct answer. Tom got $$5$$ questions right, Ben got $$8$$ questions right. How many more points than Ben did Tom get?~(adapted from $$2021$$ Math kangaroo, Level $$1-2$$, Question \#$$14$$)

August got $$5\times2=10$$ points, and Ben got $$8\times2=16$$ points.  $$16-10=6$$


Farmer Baar has 36 sheep, some pink and the rest white. There are twice as many pink sheep as white sheep. How many of the sheep are pink?

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


John is 33 years old. His three sons are 5, 6 and 10 years old. In how many years will the three sons together be as old as their father?

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

Let x be the number of years needed for the ages of the three sons sum up to be equal to their dad\textquotesingle s age.  Their dad\textquotesingle s age is then 33+x, while the sum of the sons\textquotesingle{} age is  (5+x) x (6+x)+(10+x)=21+3x.  We have the following equation:  21+3x = 33+x  2x = 12  x = 6


In Grade $3$, Amy\textquotesingle s height was $136$ cm. When she was Grade $4$, the doctor said that her height was $15$cm taller than last year. What was her height in Grade $4$? (adapted from $$2019$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$3$$)

$15$ cm

$137$ cm

$151$ cm

$161$ cm

$167$ cm

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


Blii and Elsa went to see a movie together and sat in the same row. Ela was in the sixth row counting from the front of the room and Elsa was seated in the fourteenth counting from the end. How many rows in their room? (Adapted from 2001 Math Kangaroo Problem, Level 3-4, Question \#13)

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


Several people buy a boardgame together. If each person pays $60$ dollars, $60$ more dollars are needed for the payment. If each person pays $70$ dollars, $10$ dollars are remaining. How much is the boardgame in dollars?

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


Farmer Dunphy has $$100$$ metres of fencing.  He wants to make a closed rectangular pen.  He uses a long wall for one of the sides.  Each side of the pen is a whole number in metres.  What is the largest area that the pen can be?

Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems Combined with Geometry->Tile Word Problems

$a+2b=100$, when $$a=2b=50$$, the largest area is $$50\times (50\div 2)=1250$$ m\textsuperscript{2}.


How many fingers are there on a dozen pairs of gloves if each glove has $$5$$ fingers?

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

There are $$2\times5 =10$$ fingers on a pair of gloves. $$\text{A}$$ dozen pairs have $$12 \times 10 = 120$$.


Kevin got $$80\textbackslash\%$$ of the problems correct on a $$25-$$problem test, $$ 90\textbackslash\%$$ on a $$40-$$problem test, and $$70\textbackslash\%$$ on a $$10-$$problem test. What percent of all the problems did Kevin answer correctly? (2010 AMC8 Problem, Question \#9)

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

Ryan answered $$(0.8)(25)=20$$ problems correct on the first test, $$(0.9)(40)=36$$ on the second, and $$(0.7)(10)=7$$ on the third. This amounts to a total of $$ 20+36+7=63$$ problems correct. The, total number of problems is $$25+40+10=75$$.Therefore, the percendage is $$\frac {63}{75}\to(\rm D)84$$.


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

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

If $2-1=1$ fewer card is given to students, the situation would transfer from \textquotesingle a shortage of $12$ cards\textquotesingle~ to \textquotesingle all cards are just divided\textquotesingle.  So, there are in total $12$ students.


SASMO 2015 P2 Q5  Today, Wednesday, 8th of April 2015, is the day of the SASMO competition and your friend says tha the Singapore Math Kangaroo Contest was 14 days ago. On which day was the SMKC?

23rd of March, Monday

24th of March, Tuesday

25th of March, Wednesday

26th of March, Thursday

27th of March, Friday


Suppose $20 \textbackslash\%$ of $x$ equals $30 \textbackslash\%$ of $y$. What percentage of $y$ is $x$ ? (adapted from 2020 AMC 8, Question 15)

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

Since $20 \textbackslash\%=\frac{1}{5}$, multiplying the given condition by 5 shows that $x$ is $30 \cdot 5=(\mathbf{C}) 150$ percent of $y$.


A shop purchased some tennis rackets at ＄$$100$$ each, and then sold them at ＄$$150$$ each. How much did the shopkeeper earn for $$10$$ rackets?

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


Jack bought a batch of goods that he hoped to earn a $$50\textbackslash\%$$ profit after selling them. On the first day, he sold $$60\textbackslash\%$$ of his goods at a profit of $$50\textbackslash\%$$. On the second day, he sold all remaining goods for a discount. If the total profit is $$76\textbackslash\%$$ of the planned profit, what was the discount rate?

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

Let the cost for the batch of goods be $$m$$ dollars.  Jack finally earned: $$m\times 50\textbackslash\%\times 92\textbackslash\%=0.38m$$.  On the first day he earned: $$m\times 60\textbackslash\%\times 50\textbackslash\%=0.30m$$.  Profit for the second day: $$0.38m-0.30m=0.08m$$.  Profit rate for the second day: $$\frac{0.08m}{\left( m-0.6m \right)}=20\textbackslash\%$$.  Percentage discount: $$1-\frac{\left( 1+20\textbackslash\% \right)}{\left( 1+50\textbackslash\% \right)}=20\textbackslash\%$$.


Paul has $13$ books, and Jenny has $6$ more books than Paul. How many books do Paul and Jenny have together?

Jenny has $$13 + 6 = 19$$ books. So, there are $13 + 19 = 32$ books in total.


In the land of Seuss, a plate of green eggs costs twice as much as a plate of ham. If a plate of ham costs $$5$$￠, how much would $$1$$ pay for $$2$$ plates of green eggs and $$3$$ plates of ham?

Since a plate of green eggs costs twice as much as a plate of ham, a plate of the eggs costs $$10$$￠. The cost of $$2$$ plates of eggs and $$3$$ plates of ham is $$2\times 10$$￠$$+3\times 5$$￠$$=20$$￠$$+15$$￠$$=35$$￠.


The sum of $$2$$ positive whole numbers is $$3$$ times their difference. When the larger is divided by the smaller, the quotient is．

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

The sum must be a multiple of $$3$$. There are many examples, e.g., $$2\And 1$$, $$4\And 2$$, $$10\And 5$$, etc. The quotient is always $$2$$.


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


At the 2018 Tompkins County Fair a vendor is offering a "fair special" on shoes. If you buy one pair of shoes at the regular price of $\textbackslash$ 80$, you get a second pair at a $34\textbackslash\%$ discount, and a third pair at half the regular price. James took advantage of the "fair special" to buy three pairs. What percentage of the $\textbackslash$ 240$ 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 $=\textbackslash$ 240$. Then, find the amount of money using the discount: $80+0.66\times 80+\frac{1}{2} \times 80=\textbackslash$ 172.8$. Finding the percentage yields $\frac{172.8}{240}=72\textbackslash\%$ To find the percent saved, we have $100 \textbackslash\%-72\textbackslash\%= 28\textbackslash\%$


I had $$3$$ dozen socks in my drawer, but I lost $$2$$ pairs. How many socks do I now have in my drawer?

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

I had $$3$$ dozen socks in my drawer, which is $$36$$ socks. When I lost $$2$$ pairs, I lost $$4$$ socks, so I had $$32$$ socks left.


Mike and Jack compete in the long jump. Mike jumps twice as far as Jack once. Mike jumps three times. How many times can jack jump the distance equal to Mike？(adapted from $$2008$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$6$$)

We can imagine the distance of Jack\textquotesingle s long jump as $1$, and the distance of Mike\textquotesingle s long jump as $2$. The distance that Mike jumps three times is $2$$\times$$3$=$6$.  ~Jack needs to jump $6$$\div$$1=$$6$ times.


NBA playoffs are held annually. The $62$\textsuperscript{nd~}NBA playoffs were held in $2008$. When Cindy was $7$ years old, the $66$\textsuperscript{th}~NBA playoffs were held. How old is Cindy in $2022$?

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


Rina bought a handbag for＄$$60$$ at a discount of $$20\textbackslash\%$$. Ana paid＄$$67.5$$ for the same handbag. What was the discount rate given to Ana?

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

Original price: $$60\div \left( 1-20\textbackslash\% \right)=75$$.  Discount for Ana: $$\left( 75-67.5 \right)\div 75=10\textbackslash\%$$.


SASMO 2014 P2 Q5  What number between 37 and 47 is exactly divisible by both 2 and 3?

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


If each fork costs ＄$$6$$, each spoon costs ＄$$7$$, and each knife costs ＄$$8$$, what is the total cost of $$3$$ forks, $$4$$ spoons, and $$5$$ knives?


A given month has $$31$$ days, and it has four Mondays and four Thursdays. What day of the week is the $$20^{\rm th}$$ of this month?

$$$$Wednesday$$$$.

Thursday

Friday

Sunday

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

It implies that there are four Mondays, four Tuesdays, four Wednesdays, and four Thursdays. Similarly, there are five Fridays, five Saturdays, and five Sundays. The first day of the month therefore must be a Friday. $$20\div7=2\text{ R }6$$. The $$20^{\rm th}$$ day of this month is a Wednesday, which is the $$6^{\rm th}$$ day after Friday, inclusive.


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?

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.


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? (Math kangaroo Problem, Level $$5-6$$)

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 $30\times2=60$.


If $$2$$ watermelons can serve $$15$$ people, I need  watermelons for $$60$$ people.

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

If $$2$$ melons can serve $$15$$ people, I need $$4\times2=8$$ melons for $$4\times15=60$$ people.


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

$$ 52 $$

$$ 63 $$

$$ 74$$

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

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 $$24$$th birthday, so Allen\textquotesingle s age at that time was $$52 +11 =63$$.


A glass contains $$240$$ $$\rm ml$$ of water. The water takes up $$\frac 23$$ of the volume of the glass. What is the volume of the glass, in milliliters?

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


At the pumpkin festival, Mike brought a $10$ pounds pumpkin. Mary\textquotesingle s pumpkin weighed $5$ pounds more than Mike\textquotesingle s. How many pounds is Mary\textquotesingle s pumpkin？(adapted from $$2009$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$6$$)

Mary\textquotesingle s pumpkin weighs $5$ pounds more than Mike\textquotesingle s, so it\textquotesingle s $10 + 5 = 15$ pounds.


Water makes up $$84\textbackslash\%$$ of the weight of Kubus the Camel when he is thirsty. After he drinks, Kubus weighs $$800$$ kg and water makes up $$85\textbackslash\%$$ of his weight. What is the weight of Kubus the Camel when he is thirsty? ($$2001$$ Math Kangaroo Problem, Level $$9-10$$, Question \#$$16$$)

$$672$$ kg

$$680$$ kg

$$715$$ kg

$$720$$ kg

$$750$$ kg

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

The ratio between the thirsty Kubus and the water he drank: $$(100-85):(85-84)=15:1$$.  So, the weight of the thirsty Kubus is: $$800 \times \frac{15}{15+1}=750$$ kg.


Arthur decided to lose weight. On the first month, he lost $2$ kg. He decided that each month he would be losing twice as much kilograms as the month before. How many kilograms did Arthur lose in total in the first three monthes?

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


How many tens must be added to $$215$$ to make $$985$$?~\uline{~~~~~~~~~~}~tens

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

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


Determine whether 2008 is a common year or a leap year.

a common year

a leap year

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


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

$$90$$ grams

$$100$$ grams

$$120$$ grams

$$150$$ grams

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

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


If $$19^{}\text{th}$$March is Monday, what day of the week is $$1$$\textsuperscript{st~}March ?

Sunday

Monday

Wednesday

Thursday

Saturday

There are 19 days between $$19^{}\text{th}$$March and~ $$1$$\textsuperscript{st~}March.  Apart from $19$\textsuperscript{th} March itself, there are $18$ days,  18 days = 2 week and 4 days.  Therefore,~~$$1$$\textsuperscript{st~}March is Thursday.


Elsa started to raise some chicken in her farm in January. The number of chicken triples every month, while she goes to the market to sell $81$ chicken every month. On April when she came back from the market, she found she had no chicken left.  How many chicken did she raise in January?

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


Mariam had ＄$$4y$$. After buying some cloth at ＄$$7$$ per metre, she had ＄$$y$$ left. How many metres of cloth did she buy?

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

Amount of money she spent to buy the cloth  $$\rightarrow$$＄$$4y-$$＄$$y$$  $$=$$＄$$3y$$,  Length of cloth she bought  $$\rightarrow$$＄$$3y\div $$＄$$7/\text{m}$$  $$= \frac{3y}{7}\text{m}$$.


A pencil is one dollar, and a pencil box is two dollars more expensive than a pencil. Jimmy has seven dollars and bought a pencil box. How many pencils can Jimmy buy？(adapted from $$2009$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$6$$)

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

A pencil box costs two dollars more than a pencil, so it\textquotesingle s $1+2=3$ dollars. $7-3=4$. So~He can buy $4\div1=4$~pencils.


The February of a given year has five Fridays. What day of the week was January $$31$$\textsuperscript{th~}of that year?

Friday

Saturday

Wednesday

Thursday

There are seven days in a week. In order to have five Fridays, a month has at least $$4\times 7+1=29$$ days. Since February has at most $$29$$ days, the $$1$$\textsuperscript{st} and $$29$$\textsuperscript{th} days of this February must be Friday, which means that January $$31$$ is Thursday.


George takes 4 minutes to go from 1st floor to 3rd floor. He just realised that he forgot his water bottle on the 5th floor. He is now on the 2nd floor. How long would it take him to get his watter bottle?

4 minutes

5 minutes

6 minutes

8 minutes

None of the above.

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

2 gaps between 1st to 3rd floor. hence, 4/2=2 minutes per gap.  Moving from 2nd to 5th floor, 3 gaps -\textgreater{} 3 gaps x 2 minutes per gap = 6 minutes.


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

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

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


If $$15^{}\text{th}$$March is Monday, what day of the week is $$26$$\textsuperscript{th} March ?

Sunday

Monday

Wednesday

Friday

Saturday

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

There are 11 days between $$15^{}\text{th}$$March and~ $$26$$\textsuperscript{th} March.  11 days = 1 week and 4 days.  Therefore,~~$$26$$\textsuperscript{th} March is Friday.


Sarah is $$1.14\text{m}$$ tall. Benny is $$0.23\text{m}$$ taller than Sarah. What is the total height of the $$2$$ children? Round off your answer to $$1$$ decimal place.

Benny\textquotesingle s height $$=1.14+0.23=1.37\text{m}$$  Total heights of the $$2$$ children $$=1.14+1.37=2.51=2.5\text{m}$$ (rounded to $$1$$ d.p.)


There are~ $$30$$ students in Pat\textquotesingle s math class. If there are twice as many girls as boys in the class, how many boys are in the class?

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

There are $$30$$ students in Pat\textquotesingle s math class. With twice as many girls as boys, the class has $$20$$ girls and $$10$$ boys.


Lily\textquotesingle s family used $$21$$ tons of water in the first two months, and an average of $$31$$ tons of water on the remaining three tests. The average tons of water for the five months was~\uline{~~~~~~~~~~}~.

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

Total tons of water: $$21\times 2+31\times 3=135$$  Average tons of water: $$135\div 5=27$$


Mr.Smith wants to cut a wood into $5$ pieces. It takes him $2$ minutes to cut a piece. How many minutes will he use to cut?

Overseas Competition->Knowledge Point->Word Problem Modules

Mr.Smith needs to cut $5-1=4$ times, which means he needs to use $4 \times 2 = 8$ minutes to cut.


Paul had eight $$\textbackslash$5$$-notes at first. He exchanged all his money for $$\textbackslash$2$$-notes only. How many notes did he have in the end?

He has $=\textbackslash$5\times8=\textbackslash$40$  Number of $\textbackslash$2$-notes $=\textbackslash$40\div\textbackslash$2=20$


Farmer Dunphy has $$16$$ metres of fencing.  He wants to make a closed rectangular pen.  He uses a long wall for one of the sides.  Each side of the pen is a whole number in metres.  What is the largest area that the pen can be?

Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems Combined with Geometry->Tile Word Problems

$a+2b=16$, when $$a=2b=8$$, the largest area is $$8\times (8\div 2)=32$$ m\textsuperscript{2}.


In how many places do we need to break a wooden stick in order to get $$5$$ pieces? (1999 Math Kangaroo Problem, Level 3-4, Question \#3)

It depends on how long the stick is.

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


Tom starts a savings account with ＄$$4,000$$ at a bank. The interest rate is $$2\textbackslash\%$$ per year. How much interest will he earn in his savings account at the end of the second year?

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

$$4000\times \left( 1+2\textbackslash\% \right)\times \left( 1+2\textbackslash\% \right)-4000=161.6$$.


If there are $$8$$ pencils in each box, how many pencils are in $$80$$ boxes?

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

There are $$80 \times8 = 640$$ pencils in $$80$$ boxes.


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

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

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


Lisa is buying potatoes at a grocery store. She can either spend $10$ dollars on a $25\text{-lb}$ bag or $15$ dollars on a $35\text{-lb}$ bag. Whic is the cheaper one?

The $25\text{-lb}$ bag

The $35\text{-lb}$ bag

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

$$\frac{10}{25}\textasciitilde\textbackslash$ \text{/lb}=0.4\textasciitilde\textbackslash$ \text{/lb}$$  $$\frac{15}{35}\textasciitilde\textbackslash$ \text{/lb}=0.43\textasciitilde\textbackslash$ \text{/lb}$$  $$\frac{10}{25}\textless\frac{15}{35}$$  So, the answer is $$A$$.


Ali is arranging the books on his bookshelves. He puts half his books on the bottom shelf and two-thirds of what remains on the second shelf. Finally he splits the rest of his books over the other two shelves so that the third shelf contains four more books than the top shelf. There are three books on the top shelf. How many books are on the bottom shelf？

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

Since Ali places half his books on the bottom shelf and $$\frac{2}{3}$$ of the remainder on the second shelf, he places $$\frac{2}{3}\times\frac{1}{2}=\frac{1}{3}$$ of his books on the second shelf, leaving $$\left(1-\frac{1}{2}-\frac{1}{3}\right) =\frac{1}{6}$$~ of his books for the top two shelves. There are three books on the top shelf and four more, so seven books, on the third shelf. Therefore these $$10$$ books represent $$\frac{1}{6}$$ of the total number of books on the bookshelves. Hence there are $$60$$ books on the bookshelves and half of these, or $$30$$ books, on the bottom shelf.


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 $29$\textsuperscript{th}. $27\div7=3R6$, which means May $29$\textsuperscript{th}~is Wednesday.


Given that August $$15$$th of a given year is a Friday, What day is June $$10$$th of the same year?

Monday

Tuesday

Friday

Sunday


The selling price of a television is＄$$4800$$ and its profit percentage is $$20\textbackslash\%$$. If the cost of the television is not changed, how much should it be sold for if the profit percentage has to be $$75\textbackslash\%$$?

$$6000$$ dollars

$$6500$$ dollars

$$7000$$ dollars

$$8000$$ dollars

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

$$\frac{4800}{\left( 1+20\textbackslash\% \right)}=4000$$ dollars,  $$4000\times \left( 1+75\textbackslash\% \right)=7000$$ dollars.


The upper shelf of a bookshelf has $$143$$ books. The lower shelf has $$39$$ books. How many books should be taken from the upper shelf to the lower shelf so that both shelves will have the same number of books?

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


If Pip was 18 years old 5 years ago, how old will he be 7 years from now?

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


My dad, Burly Ird, says he has to moan at me two school mornings in every three to get me out of bed.  In a twelve-week term, with five schooldays each week, on how many mornings will he moan at me?

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

The number of moaning mornings is $$\frac{2}{3}\times 12 \times 5 = 40$$.


In one year, there were 5 Sundays in February. What day of the week was 3\textsuperscript{rd~}Feb ?

Saturday

Monday

Tuesday

Wednesday

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

Normally, there are 28 days in February, which has 4 Sundays at most. Therefore, it could be the leap year with 29 days in February. If there are 5 Sundays, the first day in Februray should be Sunday, so Feb 3rd is Tuesday.


The cost of a computer is $3500$ dollars and the profit percentage is $12\textbackslash\%$ for each computer. Find the price of the computer.

$$3850$$ dollars

$$3920$$ dollars

$$4200$$ dollars

$$4550$$ dollars

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

The price of the computer is: $3500\times(1+12\textbackslash\%)=3920$ dollars.


Given that March $$26$$\textsuperscript{th}, $$2021$$ was Friday, what day was April $$20$$\textsuperscript{th}, $$2021$$?  $\textasciitilde$

Monday

Tuesday

Thursday

Wednesday

Friday

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

Counting from March $$26$$\textsuperscript{th}, $$2021$$, after $31-26=5$ days it was March $$31$$\textsuperscript{st}, $$2021$$. After $20$ days it was April $$20$$\textsuperscript{th}, $$2021$$. In total, there were $5+20=25$ days. $25\div 7 =3R4$, which means April $$20$$\textsuperscript{th}, $$2021$$ was Tuesday.


Tom, Joanna and Jacky each come up with a number. The sum of the three numbers is $$360$$. Tom\textquotesingle s number is twice Joanna\textquotesingle s number, and Joanna\textquotesingle s number is three times Jacky\textquotesingle s number. What are these three numbers?

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

Jacky\textquotesingle s number is ``$$1$$'', so Joanna\textquotesingle s number is ``$$3$$'', and Tom\textquotesingle s number is ``$$6$$''.  Jacky\textquotesingle s number: $$360 \div (6 +3+1) =36$$. Joanna\textquotesingle s number: $$36 \times 3=108$$. Tom\textquotesingle s number: $$36 \times 6 =216$$.


( $$2004$$ AMC $$8$$ Problem, Question \#$$12$$)  Niki usually leaves her cell phone on. If her cell phone is on but she is not actually using it, the battery will last for $$24$$ hours. If she is using it constantly, the battery will last for only $$3$$ hours. Since the last recharge, her phone has been on $$9$$ hours, and during that time she has used it for $$60$$ minutes. If she doesn\textquotesingle t use it any more but leaves the phone on, how many more hours will the battery last?

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

When not being used, the cell phone uses up $$\dfrac{1}{24}$$ of its battery per hour. When being used, the cell phone uses up $$\dfrac{1}{3}$$ of its battery per hour. Since Niki\textquotesingle s phone has been on for $$9$$ hours, of those $$8$$ simply on and~~being used to talk, $$8\left(\dfrac{1}{24}\right)+1\left(\dfrac{1}{3}\right)=\dfrac{2}{3}$$ of its battery has been used up. To drain the remaining $$\dfrac{1}{3}$$ the phone can last for $$\dfrac{\dfrac{1}{3}}{\dfrac{1}{24}}=\boxed{(\text{B})8}$$ more hours without being used.


Mike bought five ice creams. He had three brothers and he gave each brother an ice cream. How many ice creams was left?~(adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$3$$)

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

Each brother gets one ice cream, and three brothers need three ice cream, so Mike has $5-3=2$~ice cream left.


Elmp visits the Sesame Street Park every Wednesday. If the 1st of January 2017 was Sunday and February has 28 days, what was the last date in March 2017 in which Elmo visited Sesame Street Park?

28th March

29th March

30th March

31st March

None of the above.


A construction team is going to build a road of $50$ miles. The plan is that it finishes $30$\% of the road in the first month, $40$\% of the road in the second month and $30$\% of the road in the third month. How many miles can be built after two months?

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


Kate bought $$2$$ apple pies and Lucy bought $$4$$ cupcakes. They each paid the same amount of money and together they paid $$16$$ dollars. How many dollars does $$1$$ cupcake cost?

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

$4$ cupcakes cost $16\div2=8$ dollars, so one cupcake cost $8\div4=2$ dollars.


Esther made $$18$$ paper stars and she made $$3$$ times as many paper stars as Amy. How many paper stars did Amy make?

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


In a class of pupils, $80\textbackslash\%$ participated in basketball, $85\textbackslash\%$ participated in football, $74\textbackslash\%$ participated in softball and $68\textbackslash\%$ participated in squash. Find the minimum percentage of pupils who participated in all the four sports events.

None of the above

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

Least percentage of pupils who participated in both basketball and football  $=80\textbackslash\%+ 85\textbackslash\%-100\textbackslash\% =65\textbackslash\%$,  Least percentage of pupils who participated in basketball, football and softball  $=65\textbackslash\%+74\textbackslash\%-100\textbackslash\% =39\textbackslash\%$,  Least percentage of pupils who participated in basketball, football, softball and squash  $=39\textbackslash\%+ 68\textbackslash\%-100\textbackslash\% = 7\textbackslash\%$.


Simon has two identical aquariums. There are $$26$$ quarts of water in one, and $$42$$ quarts of water in the other. How many quarts of water does Simon need to pour from the second aquarium into the first in order to have the same amount of water in both?

Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Giving and Receiving

Difference: $42-26=16$  Move: Half of $16=8$


In $$20$$ years, Li will be $$3$$ times as old as he is now. How old will he be in $$10$$ years?

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

In $$20$$ years, Li will be $$3$$ times his age now, so $$20$$ must be twice his age now. Thus, Li is $$10$$ now and will be $$20$$ in $$10$$ years.


When Paul is $$4$$ years old, his brother Peter is $$7$$ years old. How old is Paul when Peter is $$10$$ years old?  Paul is~\uline{~~~~~~~~~~}~years old.

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

We can find their age difference is $$7-4=3$$. It will never change. So when Peter is $$10$$ years old, Paul is $$10-3=7$$ years old.


If Paul gives $$6$$ candies to Billy, they will have the same number of candies. At beginning, Paul has $$17$$ candies. How many candies does Billy have, originally?

Overseas Competition->Knowledge Point->Word Problem Modules


Su Li has the same number of ten-cent and fifty-cent coins. The total value is ＄$$6$$. How many coins does she have in all?

None of the above


Andy is $18$ years old and his mother is $$54$$ years old now. In how many years\textquotesingle{} time will the sum of their ages be $$90$$?


Together, Mom Kangaroo and her son Jumper weigh $60$ kilograms. Mom Kangaroo alone weighs $52$ kilograms. How much does Jumper weigh? ($$2019$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$3$$)

2 kilograms

4 kilograms

8 kilograms

30 kilograms

46 kilograms

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

Jumper\textquotesingle s weight is Mom Kangaroo and Jumper\textquotesingle s weight minus the mom\textquotesingle s weight.


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

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 $


Alex had $76.  He spent some of it in a shop.  Then he gave half of what he had left to Charlie.  Charlie spent a quarter of what Alex gave him on lunch.  Charlie spent $9 on lunch.  How much did Alex spend in the shop?

Charlie\textquotesingle s 1/4 is 9, so Charlie gets 4\times 9=36 dollars, and Alex is left with 36+36=72 dollars, so he spends 76-72=4 dollars


Min Ho deposited ＄$$20 000$$ into a bank at the beginning of the year. The annual interest for depositing money into the bank was $$5\textbackslash\%$$. How much did Min Ho have in the bank at the end of the year if he did not take out any money from the bank?．

$$\textbackslash$19 000$$

$$\textbackslash$21 000$$

$$\textbackslash$31 000$$

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

He has $20000 \times 1.05 = \textbackslash$21000$ at the end of the year.


The pages of a book are numbered 1, 2, 3 $\cdots$ . In total, it takes 852 digits to number all the pages of the book. What is the number of the last page?

Overseas Competition->Knowledge Point->Word Problem Modules->Page Number Problem


Eddie and Frank can complete a job together in $$15$$ days. Eddie can do it alone in $$20$$ days. Frank can do it alone indays.

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


There are $$600$$ pupils in Pip\textquotesingle s school, with $$30$$ more girls than boys. How many girls are at Pip\textquotesingle s school?

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

Let there be $$g$$ girls in Pip\textquotesingle s school. Then there are $$(g-30)$$ boys at the school. So $$g+g-30=600$$. Therefore $$2g=630$$, that is $$g=315$$.


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

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


Half a loaf of bread costs $$6$$ pence more than one quarter of a loaf of bread. How many pence does a whole loaf of bread cost?

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

One quarter of a loaf of bread is ``$$1$$.'' Half a loaf of bread is ``$$2$$.''  One quarter of a loaf of bread: $$6 \div (2-1) =6$$. A whole loaf of bread: $$6 \times 4 =24$$.


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

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


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


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

$$ 10 $$

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


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? ($$2012$$ AMC $$8$$ problem, Question \#$$19$$)

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


After Anna spends $\dfrac{1}{3}$~of her money and loses $\dfrac{1}{2}$~of the remainder, she then has~$\textbackslash$10$ left. She started with．

After Anna spends $\dfrac{1}{3}$~of her money, she has $\dfrac{2}{3}$~left. If she loses $\dfrac{1}{2}$~of this, she has $\dfrac{1}{3}$~left. Since$\dfrac{1}{3}=$$\textbackslash$10$,~$\dfrac{3}{3}=3\times$$\textbackslash$10=$$\textbackslash$30$.


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

Sunday

Monday

Tuesday

Wednesday

The cycle includes seven days, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday. There are in total $$7+30+1=38$$ days from March $$25$$ to May $$1$$. Since $$38\div7=5 \text{ R }3$$，$$$$May$$$$ $$1$$ is the $$3^{\rm rd}$$ day in the cycle, it is a Wednesday.


In an arts and crafts class, the students cut out some triangles, quadrilaterals and pentagons. All the shapes combined have $$394$$ sides. Among them, there are $$2$$ pentagons and the number of quadrilaterals is $$82$$ more than that of triangles. How many quadrilaterals are there?

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

Let $$x$$ represent the number of quadrilaterals, thus the number of triangles can be represented as $$(x-82)$$.  So we have $$2\times5+4x +3(x-82)=394$$. implying that $$x =90$$. Therefore there are $$90$$ quadrilaterals.


Sam wants to use two kinds of sugar water with concentrations of $$5\textbackslash\%$$ and $$20\textbackslash\%$$ to make a sugar water of $$300$$g with a concentration of $$15\textbackslash\%$$. He correctly calculated the required ratio of the two solutions, but reversed the two bottles of sugar water when preparing them. The actual concentration of the wrongly mixed sugar water is~\uline{~~~~~~~~~~}~$$\textbackslash\%$$.

None of the above

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


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

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.


Eddie spends $12$ minutes to climb from the first floor to the third floor at a constant speed. At this speed, how many minutes does Eddie need to climb from the first floor to the sixth floor?

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


The number of months in a year minus the number of days in a week equals．

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

The number of months in a year minus the number of days in a week is $$12-7 = 5$$.


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)

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

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 $100 \textbackslash\%-70\textbackslash\%= 30\textbackslash\%$


Find the average of these numbers: $7,9,5,3,6$

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


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 $6$ cupcakes and there were $$2$$ cupcakes left. At beginning, how many cupcakes were there in the bakery?

Overseas Competition->Knowledge Point->Word Problem Modules


In a zoo, there are three monkeys. The monkeys are all younger than $$5$$ years old. None of them has the same age, and all their ages are whole numbers. The product of their ages is $$8$$. What is the sum of their ages?

The whole numbers smaller than $$5$$ are: $$1, 2, 3, 4$$ (age cannot be $$0$$)  The product of three numbers is $$8$$.  $$1\times2\times4=8$$  Their sum: $$1+2+4=7$$


After every $$3$$ steps that Pip takes forward, he takes $$2$$ steps backwards. Each step is $$1 $$$$\text{m}$$. Pip starts at one end of a $$100$$ $$\text{m}$$ hall. Pip will first reach the other end after~\uline{~~~~~~~~~~}~steps.

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


Susan is $6$ years old. Her sister is one year younger and her brother is one year older. What is the sum of the ages of the three siblings?

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

Susan\textquotesingle s sister is $6-1=5$ years old and her brother is $6+1=7$ years old. The sum of the ages of the three siblings is $5+6+7=18$.


Peter has $$20$$ grams of a $$20\textbackslash\%$$ salt solution. How many grams of salt should he add to make it a $$25\textbackslash\%$$ solution?

$1$ grams

$$\dfrac{4}{3}$$ grams

$4$ grams

$5$ grams

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

Method $$1$$:  Suppose $$x$$ ounces of salt should be added to the solution:  $$\dfrac{20\times20\textbackslash\%+x}{20+x}=25\textbackslash\%$$  $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde x=\dfrac{4}{3}$$.  Method $$2$$:  $$20\times(1-20\textbackslash\%)\div(1-25\textbackslash\%)-20=\dfrac{4}{3}$$.


Bridget bakes $48$ loaves of bread for her bakery. She sells half of them in the morning for ＄$2.50$ each. In the afternoon she sells two thirds of what she has left, and because they are not fresh, she charges only half price. In the late afternoon she sells the remaining loaves at a dollar each. Each loaf costs ＄$0.75$ for her to make. In dollars, what is her profit for the day?($$2014$$ AMC $$10$$A Problem, Question \#$$3$$)

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

She first sells one-half of her $48$ loaves, or $$\frac{48}{2}=24$$ loaves. Each loaf sells for＄$2.50$, so her total earnings in the morning is equal to$24\times $＄$2.50=$＄$60$. This leaves $24$ loaves left, and Bridget will sell $\frac{2}{3}\times24=16$ of them for a price of＄$\frac{2.50}{2}=$＄$1.25$. Thus, her total earnings for the afternoon is$16\times~ $＄$1.25=$＄$20$. Finally, Bridget will sell the remaining $24-16=8$ loaves for a dollar each. This is a total of＄$1\times~ 8=$＄$8$. The total amount of money she makes is equal to $60+20+8=$＄$88$. However, since Bridget spends＄$0.75$ making each loaf of bread, the total cost to make the bread is equal to＄$0.75\times 48=$＄$36$. Her total profit is the amount of money she spent subtracted from the amount of money she made, which is $88-36=52\Rightarrow \left(\text{E}\right)52$.


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

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


Tom, Jim and Peter earned £$620$ together for painting a wall.  The ratio of Tom\textquotesingle s reward to Jim\textquotesingle s reward is $3:4$.  The ratio of Jim\textquotesingle s reward to Peter\textquotesingle s reward is $6:5$.  How much money did Tom earn?

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


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

Sunday

Monday

Tuesday

Thursday

Saturday

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


John bought some cupcakes, and each of them cost $4$ dollars. He gave the salesperson $20$ dollars and got $4$ dollars as change. How many cupcakes did John buy? (Adapted from 2005 Math Kangaroo Problem, Level 3-4, Question \#3)

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


There are two bookshelves, A and B. Shelf A has $$1100$$ books, and shelf B has books $$300$$. We need to take  books from shelf A to shelf B, so that books in shelf B is three times more than self A.

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


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? (adapted from 2007 AMC 8, Question \#17 )

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 .


Twice my house number, plus $$4$$, is $$18$$. What\textquotesingle s my house number?

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

Twice $$7$$, plus $$4$$ is $$18$$, so $$7$$ is my house number


Alex is $8$ years older than her two sisters who are twins. The sum of the ages of all three girls is $32$ years old. How old is Alex? ($2007$ Math Kangaroo Problem, Level $5$-$6$, Question \#$9$)

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

The age of each sister is $(32-8) \div 3 =8$ years old. Thus, Alex is $8 +8 =16$ years old.


Jacob and Zain take pencils from a box of $$21$$ pencils without replacing them. On Monday Jacob takes $$\frac{2}{3}$$ of the number of pencils that Zain takes. On Tuesday Jacob takes $$\frac{1}{2}$$ of the number of pencils that Zain takes. On Wednesday morning the box is empty. How many pencils does Jacob take?

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

Let the number of pencils Zain takes on Monday and Tuesday be $$x$$ and $$y $$ respectively. Therefore $$x+\frac{2}{3}x+y+\frac{1}{2}y=21$$. Hence, when we multiply the equation through by $$6$$ to eliminate the fractions and simplify, we obtain $$10x+9y =126$$. Since $$x$$ and $$y$$ are both positive integers and since the units digit of $$10x$$ is $$0$$, the units digit of $$9y$$ is $$6$$ and hence $$y=4$$. Therefore $$x=9$$ and hence the number of pencils Zain takes is $$9+4=13$$. Therefore the number of pencils Jacob takes is $$21-13= 8$$.


The fruit store sold a total of $$33$$ boxes of apples in the first three days of last week, and an average of $$18$$ boxes of apples per day in the last four days. How many boxes of apples did this fruit store sell on average each day last week?


The length of Amy\textquotesingle s string is $$12$$ cm. The length of David\textquotesingle s string is $$24$$ cm. What is the total length of their strings?

$$16$$ cm

$$26$$ cm

$$36$$ cm

$$46$$ cm


If a construction company can construct a $$1000-$$meter highway in $$5$$ days, how many days does it take to construct a $$2600-$$meter highway at the same rate?

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

It can construct $$1000\div5=200$$ meters per day.  To construct $$2600$$ meters: $$2600\div200=13$$ days.


A school bought $$12$$ volleyballs and basketballs in total for ＄$$340$$. Each basketball costs ＄$$30$$. Each volleyball costs ＄$$25$$.  How many basketballs did the school buy?

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


Mariam had ＄$$4y$$. After buying some cloth at ＄$$7$$ per metre, she had ＄$$y$$ left. How many metres of cloth did she buy?

Amount of money she spent to buy the cloth  $$\rightarrow$$＄$$4y-$$＄$$y$$  $$=$$＄$$3y$$,  Length of cloth she bought  $$\rightarrow$$＄$$3y\div $$＄$$7/\text{m}$$  $$= \frac{3y}{7}\text{m}$$.


26, 7

25, 8

26, 8

25, 7


Nate eats $12$ pizza slices every day. How many pizza slices will nate eat after a week?


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 . (2017 Math Kangaroo Problem, Level 3-4, Question \#13)

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.


There are roughly three million people who live in Wales. Nearly six hundred thousand of them speak Welsh. Approximately what percentage of people living in Wales speak Welsh?

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

The fraction of people living in Wales who speak Welsh is $$\frac{600000}{3000000}$$. This can be simplified to $$\frac{1}{5}$$, and so the percentage is $$20\textbackslash\%$$.


A slug called Glug eats $$2$$ tomatoes for every $$3$$ strawberries. Yesterday it had eaten $$35$$ tomatoes and strawberries altogether. How many tomatoes did it eat?

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


At dinner, Mom tells Alice to take knifes and forks out of the cupboard and put it on each plate. It is known that there are six plates, four forks, and six knives. How many forks or knives does Alice need to get out of the cupboard ?~ (adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$6$$)

a fork

a knife

two forks

two knives

None of the above

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

Each plate needs a knife and a fork. There are six plates here, so $6$$\times$1$=6$pairs of knives and forks are required, that is, six knives and six forks. But now there are only four forks. $6-4=2$ forks are required.


Linda was born on May $6$\textsuperscript{th}. Her brother was born $9$ days earlier than her. When her brother was born? (adapted from $$2008$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$4$$)

April $27$\textsuperscript{th}

May $15$\textsuperscript{th}

April $28$\textsuperscript{th}

April $26$\textsuperscript{th}

May $16$\textsuperscript{th}

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

Nine days before May $6$\textsuperscript{th} is April $27$\textsuperscript{th}


There are $$15$$ balls in a box: white balls, red balls and black balls. The number of white balls is $$7$$ times greater than the number of red balls. How many black balls are there in the box? ($$1998$$ Math Kangaroo Problem, Level $$3-4$$, Question \#$$16$$)

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

The numbers of white balls and red balls in total must be a multiple of $7+1=8$, so from $1$ to $15$, only $8$ itself can match the condition. Thus, there are $15-8=7$ black balls in the box.


\textbf{\hspace{0pt}If a business owner has a \textsuperscript{$}100,000 accounting profit and could have made exactly $60,000 in his next best business opportunity, he has earned}

\textbf{$160,000 in economic profits.}

\textbf{$100,000 in economic profits.}

\textbf{$40,000 in economic profits.}

\textbf{neither an economic profit or loss.}

\textbf{none of the above.}

Overseas Competition->Knowledge Point->Word Problem Modules

\textbf{Accounting profit = revenue minus explicit costs. Economic profit = revenue minus both explicit and implicit costs. Accounting profit is always greater than economic profit as there's always an opportunity cost. \textsuperscript{$}100,000 accounting profit minus the implicit cost of \textsuperscript{$}60,000 = $40,000 in economic profit.}


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?

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 $$7000\div 175 =40$$.


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

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

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

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

None of the above

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

Kevin\textquotesingle s speed $=\dfrac{70}{1\dfrac{1}{2}}=\dfrac{140}{3} \text{km/h}$  Let John\textquotesingle s speed be $x \text{km/h}$.  $$\left (x+ \frac{140}{3}\right ) \times 8=800 \Rightarrow x=100- \frac{140}{3}= \frac{160}{3}=53 \frac{1}{3}\text{km/h}$$.


February 8th, 2016 is Monday. What day is March $$30$$th, 2016?

Monday

Tuesday

Wednesday

Thursday

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

$29-8+30=51$, $51\div7=7\textbackslash{} \rm R\textasciitilde2$,~ it\textquotesingle s Wednesday


The largest possible sum of $$4$$ unequal even numbers, none greater than $$100$$, is．

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

The largest possible sum is $$100 +98+96 + 94 =388$$.


There were some pieces of candy in a bowl. Sally took half of the pieces of candy. Then Tom took half of the pieces left in the bowl. After that, Clara took half of the remaining pieces. In the end, there were $$6$$ pieces of candy left in the bowl. How many pieces of candy were in the bowl at the beginning?

Overseas Competition->Knowledge Point->Word Problem Modules->Inverse Operation Problems->Giving Half of a Whole


Peter has $$20$$ ounces of a $$20\textbackslash\%$$ salt solution. How many ounces of salt should he add to make it a $$25\textbackslash\%$$ solution?

$1$ ounces

$$\dfrac{4}{3}$$ ounces

$4$ ounces

$5$ ounces

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

Method $$1$$:  Suppose $$x$$ ounces of salt should be added to the solution:  $$\dfrac{20\times20\textbackslash\%+x}{20+x}=25\textbackslash\%$$  $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde x=\dfrac{4}{3}$$.  Method $$2$$:  $$20\times(1-20\textbackslash\%)\div(1-25\textbackslash\%)-20=\dfrac{4}{3}$$.


There were $$8$$ students in a class. Each student shook hands only once with the other $$7$$ students in the class. How many handshakes were there in total?

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


If $$1$$ out of $$6$$ lightbulbs is defective and there are $$2016$$ lightbulbs, how many of them are not defective?

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

$$5$$ out of $$6$$ of the $$2016$$ lightbulbs are not defective. Thus $$2016 \times \frac{5}{6} =1680$$ lightbulbs are not defective.


In a very popular Chinese restaurant, all seats were filled and there were still $$8$$ customers in line outside the door. After some time, $$11$$ customers finish eating and leave the restaurant, and then $$15$$ more customers join the waiting line. How many people are still in line outside the door?

The line at the door started with $$8$$ people and $$15$$ more came in, for a total of $$23$$ people. After leaving $$11$$ customers, $$11$$ seats were empty, so the number of people left in line was $$23-11=12$$.


Siti has $$198$$ bookmarks. If she were to give $$6$$ bookmarks to each of her classmates, she would need $$18$$ more bookmarks. How many classmates does Siti have?

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


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


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

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


Factory $$A$$ can assemble $$20$$ televisions per hour and Factory $$B$$ can assemble $$30$$ televisions per hour. With these constant rates, if $$A$$ assembles $$300$$ televisions in a period, how many televisions can $$B$$ assemble within the same period?

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

Time: $$300\div20=15$$ hours.  So, Factory $$B$$ can assemble $$15\times30=450$$ televisions.


Mike deposited ＄$$10000$$ in the bank. He earned an interest of＄$$2100$$ at the end of the second year. What is the interest rate per year of this bank?

Suppose the interest rate is $$m$$:  $$\begin{eqnarray}10000\times \left( 1+m \right)\times \left( 1+m \right)\&=\&10000+2100 \textbackslash\textbackslash{} m\&=\&0.1 \end{eqnarray}$$


Given that May $4$ of a given year is a Wednesday, what day is May $30$ of the same year?

Saturday

Wednesday

Thursday

Tuesday

Monday

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

$30-4=26$ days later, it will be May $30$\textsuperscript{th}. $26\div7=3R5$, which means May $30$\textsuperscript{th}~is Monday.~


There are two factories producing the same kind of car parts. There are $36$ workers in factory $A$, and every worker produces $81$ parts on average. Each worker produces $101$ parts on average in factory $B$. Each worker can produce $89$ parts on average in two factories together. How many workers are there in factory $B$?

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


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

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

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

None of the above


Alex and Bob love to fold cranes. For a bag of $N$ cranes, Alex will need $2$ hours to complete while Bob will need $3$ hours. One morning, Alex and Bob started to fold cranes at the same time. After $30$ minutes, Alex rested for $10$ minutes before continuing to fold cranes while Bob did not rest at all. When they finished a bag of $N$ cranes together, Alex folded $24$ more cranes than Bob. Find the value of $N$.

None of the above

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


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

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 $$12 + 6= 18$$.


Chole has $64$ crackers and she is distributing the crackers to her $8$ friends. How many crackers will each of them get?


Marko has $$9$$ pieces of candy and Tomo has $$17$$ pieces of candy. How many pieces of candy does Tomo need to give to Marko so that each boy has the same number of pieces of candy?

Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Giving and Receiving

Difference: $17-9=8$  Move: Half of $8=4$


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?

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


There are $10$ trees on one side of a road. Workers plan to set one rubbish bin bwtween every two adjacent trees. How many rubbish bins do they need to prepare?

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


Mary and Jimmy are eating ice cream of the same size. Jimmy eats ice cream twice as fast as Mary. Mary finishes in four minutes. How many minutes Jimmy need?~(adapted from $$2008$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$6$$)

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

Jimmy\textquotesingle s speed is twice as fast as Mary\textquotesingle s, and the ice cream they eat is the same size, so Jimmy\textquotesingle s time is only half as long as Mary\textquotesingle s, that is, $4$$\div$$2= $$2$ minutes.


If $$60\text{cm}$$ of snow falls each hour, how much falls in $$100$$ minutes?

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

$$60 \text{cm}/\text{hr} =1 \text{cm}/\min = 100 \text{cm}/100 \text{mins} = 1 \text{m}/100 \text{mins}$$.


There are $$9$$ numbers with an average of $$72$$. After eliminating a number, the average of the remaining numbers is $$78$$. What is the eliminated number?


James made a running plan for this week. He ran $4$ km on average for the three days, and ran an average of $6$ km for the next two dyas, and ran $18$ km in total for the remaining two days to complete his plan. How many kilometers are there in James\textquotesingle{} running plan?


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 $$30$$.


THere are 3 families in my neighbourhood with three children each; two of the families have twins. All twins are boys. At most how many girls are in these families?

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

There are 3 families with 3 children = 3 x 3=9.  If there are 2 twin boys, 2 x 2 = 4, 0-4=5.


Abigail is saving $$50$$p each week.  How many weeks will she take to save £$$20$$?


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.

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.


Tobby attended a Nasional Maths Olympaid (NMO). Tobby answered all $50$ questions. For each correct answer, Tobby will get $4$ marks. However, for each wrong answer, Tobby will deduct $1$ mark. If Tobby scored $110$ marks in total, how many questions did Tobby answer correctly?

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

Assume all questions were answered correctly,  Total score $=50\times4=200$  Difference in total score $=200-110=90$  Change in score $=4+1=5$  No. of incorrect answer $=90\div5=18$  Correct answers $=50-18=32$


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

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

$50 \textbackslash\% \cdot 10=5$ $30 \textbackslash\% \cdot 20=6$ $30 \textbackslash\% \cdot 30=9$ Adding them up gets $5+6+9=20$. The overall percentage correct would be $\frac{20}{60}=\frac{1}{3}=0 . \overline{3} \approx(\mathbf{A}) 33$.


The state income tax where Kristin lives is levied at the rate of $$p\textbackslash\%$$ of the first ＄$$28000$$ of annual income plus $$ \left( {p+2} \right) \textbackslash\%$$ of any amount above ＄$$28000$$. Kristin noticed that the state income tax she paid amounted to $$ \left( {p+0.25} \right) \textbackslash\%$$ of her annual income. What was her annual income?

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

method $$1$$：$$Let$$ the income amount be denoted by $$A$$.  We know that $$\frac{A\left( p+.25 \right)}{100}=\frac{28000p}{100}+\frac{\left( p+2 \right)\left( A-28000 \right)}{100}$$  We can now try to solve for $$A$$:  $$\left( p+.25 \right)A=28000p+Ap+2A-28000p-56000$$  $$.25A=2A-56000$$  $$A=32000$$  so the answer is $$\boxed{ \text {B}}$$.  method $$2$$：$$Let$$ $$A$$, $$T$$ be Kristin\textquotesingle s annual income and the income tax total, respectively.  Notice that　  $$T=p\textbackslash\%\cdot 28000+\left( p+2 \right)\textbackslash\%\cdot \left( A-28000 \right)$$  $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde$$$$=\left[ p\textbackslash\%\cdot 28000+p\textbackslash\%\cdot \left( A-28000 \right) \right]+2\textbackslash\%\cdot \left( A-28000 \right)$$  $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde$$$$=p\textbackslash\%\cdot A+2\textbackslash\%\cdot \left( A-28000 \right)$$  We are also given that  $$T=\left( p+0.25 \right)\textbackslash\%\cdot A=p\textbackslash\%\cdot A+0.25\textbackslash\%\cdot A$$  Thus, $$p\textbackslash\%\cdot A+2\textbackslash\%\cdot \left( A-28000 \right)=p\textbackslash\%\cdot A+0.25\textbackslash\%\cdot A$$  $$2\textbackslash\%\cdot \left( A-28000 \right)=0.25\textbackslash\%\cdot A$$  Solve for $$A$$ to obtain $$A=32000$$. $$\boxed{ \text {B}}$$


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

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


There are $$8$$ standing in a straight line. The first student is at the start of the line, and the last student is at the end of the line. The distance between each student is $$2$$ meters. How long is the line? (Ignore the thickness of the trees.)

$8$ meters

$$11$$ meters

$$14$$ meters

$15$ meters

$16$ meters

There are $7$ intervals between the first student and the last student. Thus, the line is $7 \times2 = 14$ meters long.


June $$1^{}\text{st}$$ $$2013$$ falls on a Saturday. On what day of the week will August $$21^{}\text{st}$$ $$2013$$ fall?

Monday

Wednesday

Friday

Saturday

Sunday

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


SASMO 2015 P2 Q3  The sum of two numbers is 300. One number is 5 times of the other number. What is the difference between the two numbers?

None of the above

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


Cathy is drawing flowers. The first one is red, the next one blue, the one after it yellow, the fourth one pink, and then again red, blue, yellow, pink, and so on, in the same order. What color will be the $19$\textsuperscript{th}~flower? (Adapted from 2003 Math Kangaroo Problem, Level 3-4, Question \#4)

$$$$Blue

$$$$Pink

$$$$Red

$$$$Black

$$$$Yellow

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

$19\div4=4R3$, so the $19$\textsuperscript{th} flower is yellow.


John drinks $x$ cups of boba everyday on weekdays and $2$ cups of boba everyday on the weekends. Which of the following equations represents how many cups of boba John drinks every week?

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

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: $$5x+4$$


Of $$60$$ flamingos, twice as many stood on $$2$$ legs as stood on $$1$$. All together, on how many legs did all of these flamingos stand?

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

Of $$60$$ flamingos, $$40$$ stood on $$2$$ legs and $$20$$ stood on $$1$$. All together, these flamingos stood on $$[(40\times2)+20]$$ legs $$=100$$ legs.


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

The $$6$$th day

The $$7$$th day

The $$8$$th day

The $$9$$th day

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


Peter has some toy cars, and Paul has $$4$$ more toy cars than Peter. Altogether they have $$28$$ toy cars. How many toy cars does Paul 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

Paul has $$(28 + 4) \div 2 = 16$$ toy cars.


The average age of all the teachers in Gotia School is $34$. There are $3$ male teachers in Gotia School with an average age of $27$. The average age of female teachers is $35$. How many female teachers are there?

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

Total age less than the average: $(34-27)\times3=21$.  Thus, there are $21\div(35-34)=21$ female teachers.


Cagney can frost a cupcake every $$20$$ seconds and Lacey can frost a cupcake every $$30$$ seconds. Working together, how many cupcakes can they frost in $$5$$ minutes? ($$2012$$ AMC $$10\rm A$$ Problem, Question \#$$11$$)

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

Method1: Cagney can frost one in $$20$$ seconds, and Lacey can frost one in $$30$$ seconds. Working together, they can frost one in $$\dfrac{20\cdot30}{20+30}=\dfrac{600}{50}=12$$ seconds. In $$300$$ seconds ( $$5$$ minutes), they can frost $$\boxed{(\text{D})25}$$ cupcakes.  Method2: In $$300$$ seconds ($$5$$ minutes), Cagney will frost $$\dfrac{300}{20}=15$$ cupcakes, and Lacey will frost $$\dfrac{300}{30}=10$$ ~cupcakes. Therefore, working together they will frost $$15+10=\boxed{(\text{D})25}$$ cupcakes.  Method3: Since Cagney frosts $$3$$ cupcakes a minute, and Lacey frosts $$2$$ cupcakes a minute, they together frost $$3+2=5$$ cupcakes a minute. Therefore, in $$5$$ minutes, they frost $$5\times5=25\Rightarrow\boxed{(\text{D})}$$.


Bill, Sarah and James each has $4$ candies. Bill gives James some candies and James gives Sarah some candies. How many candies are there in total?

Overseas Competition->Knowledge Point->Word Problem Modules

Giving candies to each other won\textquotesingle t affect the sum of their candies, so there are $$4+4+4=12$$~in total.


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

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


If an object is thrown straight upward with an initial speed of 8 m/s and takes 3 seconds to strike the ground, from what height was the object thrown?  $\textasciitilde$  $\textasciitilde$  $\textasciitilde$  $\textasciitilde$

Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems->Finding the Height in Snail Climbing out of Wall Problems (completed)

Key: object is thrown upward. When it reaches the highest point, the velocity is 0. The whole journey is divided into 2 parts: upward - highest point - downward to hit the ground. 2 parts have different displacement (and different time).


Amit, Bede, Cain, Devi, Emily and Frederick sit around a circular table in that order. Amit starts by saying "$$2015$$", Bede says "$$2016$$", Cain says~"$$2017$$" and so on round the table. Who will eventually say"$$5102$$"?

$$$$Amit

$$$$Bede

$$$$Cain

$$$$Devi

$$$$Emily

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

After Amit says "$$2015$$", there are $$5102-2015=3087$$ numbers remaining. Thus the counting goes round the table $$3087\div6= 514$$ times with a remainder of $$3$$, so the last to count is Devi.


The length of a rectangle is increased by $50\textbackslash\%$ and the width is decreased by $20\textbackslash\%$. What percent of the old area is the new area? (adapted from 2009 AMC 8, Question \#8)


$$2$$ apples and $$3$$ peaches cost $$$11$$.  $$2$$ apples and $$2$$ peaches cost $$$8$$.  What is the cost of an apple?

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


Jenny need to reach her teacher house by $$2.15 \rm{p.m}$$ for piano class. From her house to teacher\textquotesingle s house, she need to walk for $$20$$ minutes. She was late for $$10$$ minutes. What time did she leave her house?

$$2.05 \rm{a.m.}$$

$$2.05 \rm{p.m.}$$

$$1.55 \rm{a.m.}$$

$$1.55 \rm{p.m.}$$

$$2.25 \rm{p.m.}$$

She reached at $$2.25 \rm{p.m.}$$, thus, $$20$$ minutes before that is $$2.05 \rm{p.m.}$$


I am twice the age of each of my sons, Barry and Larry. Our three ages have a total of $$76$$. How old is Barry?

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

The three ages have a total of four times Barry\textquotesingle s age. So Barry is $$76\div4 = 19$$.


Mike has $$47$$ ounces of salt solution. Given that there are $$12$$ ounces of pure salt in the solution, how much water is there?

$$25$$ ounces

$$35$$ ounces

$$45$$ ounces

$$59$$ ounces


Orange peel is a type of orange color mixing red and yellow paint with a ratio of $1:2$. In the shop, red paint is selling at $5$ dollars per ounce and yellow paint is selling at $4$ dollars per ounce. If Richard wants to make $12$ ounces of orange peel, how much money does she need?

$48$ dollars

$52$ dollars

$56$ dollars

$60$ dollars

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


At the "Think Flea Market", a vendor is offering a "fair special" on plushies. If you buy one plushie at the regular price of $\textbackslash$ 50$, you get a second one at a $40 \textbackslash\%$ discount, and a third one at half the regular price. Owen takes advantage of the "fair special" to buy three plushies. What percentage of the $\textbackslash$ 150$ regular price will he save? (adapted from 2013 AMC 8, Question \#12)

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

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


In London 2012, the USA won the most medals: 46 Gold, 29 Silver and 29 Bronze. China was second with 38 Gold, 27 Silver and 23 Bronze. How many more medals did the USA win compared to China?

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

USA won - 104 medals in total\textquotesingle{} China won 88 medals. Difference = 16.


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.


Speedy Wiggins cycles to school, a journey that takes $$30$$ minutes at $$12$$mph.  How far does he travel to school?

Cycling at $$12$$ mph, Speedy would go $$12$$ miles in an hour. So in $$30$$ minutes he cycles $$12$$ miles $$\div2 = 6$$ miles.


Geraint always cycles to work, leaving at $$8$$am every morning. When he averages $$15{\text{km}}/{\text{h}}\textbackslash;$$,he arrives $$10$$ minutes late. However, when he averages $$30{\text{km}}/{\text{h}}\textbackslash;$$, he arrives $$10$$ minutes early. What speed should he average to arrive on time?

$$21{\text{km}}/{\text{h}}\textbackslash;$$

$$22.5{\text{km}}/{\text{h}}\textbackslash;$$

$$24{\text{km}}/{\text{h}}\textbackslash;$$

$$25{\text{km}}/{\text{h}}\textbackslash;$$

Let $$x\text{km}$$ be the distance Geraint cycles and let $$t $$ hours be the time his journey should take if he is to be on time. Since $$\frac{\text{distance}}{\text{speed}}\text{=time}$$, the information in the question tells us that  $$\frac{x}{15}=t+\frac{1}{6}$$ and that $$\frac{x}{30}=t-\frac{1}{6}$$. When we subtract the second equation from the first, we obtain  $$\frac{x}{30}=\frac{2}{6}$$ and so $$x = 10$$. Hence, from the second equation, $$\frac{10}{30}=t-\frac{1}{6}$$ and so $$t=\frac{1}{3}+\frac{1}{6}=\frac{1}{2}$$. Therefore, to arrive on time, Geraint needs to travel $$10\text{km}$$ in~ $$\frac{1}{2}$$ hour, which is an average speed of $$20{\text{km}}/{\text{h}}\textbackslash;$$.


Susie Starfish and her five sisters went to the cinema with Ollie Octopus and his four brothers.  They bought a box of popcorn for every arm they had.  How many boxes of popcorn did they buy?

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

There are $$6$$ starfish and $$5$$ octopuses. So the number of boxes $$=6 \times5+5\times8 =70$$.


A $$12-$$hour clock loses $$10$$ minutes each day. The clock will first return to the correct time in．

$$36$$ days

$$72$$ days

$$120$$ days

$$144$$ days

$60$ days

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

Clock shows the correct time after a $$12-$$hr loss. With a $$10-$$min. loss daily, it takes $$6$$ days to lose $$1$$ hr \& $$72$$ days to lose $$12$$ hr.


After a discount of $$30\textbackslash\%$$, the price of a bed is＄$$210$$. Besides, senior citizens are given a further discount of＄$$15$$. What is the percentage discount given to senior citizens for the bed?

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

Original price: $$\frac{210}{(1-30\textbackslash\%)}=300$$.  Selling price after discount: $$210-15=195$$.  Discount rate: $$1-\left( {\frac{195}{300}} \right)=1-65\textbackslash\%=35\textbackslash\%$$.


Alex had some trading cards. After giving $36$ trading cards to Ben, Alex received another $42$ trading cards from David. If Alex has $241$ trading cards now, how many trading cards does he have at first?

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


How many digits have to be written in order to write down every number from $$1$$ to $$110$$?

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

From $$1$$ to $$9$$ there are~$1\times9=9$~digits.  From $$10$$ to $$99$$ there are~$2\times90=180$~digits.  From $$100$$ to $$110$$ there are~$3\times11=33$~digits.  In total, there are$9+180+33=222$~digits


Daniel raises some ducks and dogs. All the ducks and dogs have $18$ legs and $5$ pairs of wings in total. If all the ducks and dogs each lifts one leg off the ground, they lift~\uline{~~~~~~~~~~}~legs in total.

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

$5$ 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 and they will lift $7$ legs.


Lewis drives from London to Brighton at an average speed of $$60\text{mph}$$. On the way back, he gets stuck in traffic and his average speed is only $$40\text{mph}$$. What is his average speed for the whole journey?

Impossible to determine

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

Let the distance from London to Brighton be $$d$$ miles. Since time $$=$$ distance $$\div$$ speed, the times Lewis spent on the two parts of his journey are $$\frac{d}{60}$$ hours and $$\frac{d}{40}$$ hours. Hence the total time in hours that he travelled is$$\frac{d}{60}+ \frac{d}{40}= \frac{2d+3d}{120}= \frac{5d}{120}= \frac{d}{24}$$.  Therefore his average speed for the whole journey is $$2d \div \left( \frac{d}{24}\right)\text{mph}=48 \text{mph}$$.


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

$$90$$ grams

$$100$$ grams

$$120$$ grams

$$150$$ grams

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

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


Judy needed to reach the $10$\textsuperscript{th} floor of a building. It took her $40$ seconds to walk from the $1$\textsuperscript{st} floor to the $5$\textsuperscript{th} floor. How many seconds will it take to go from the $3$\textsuperscript{rd}~to the $10$\textsuperscript{th} floor at the same speed?

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


Bill, Sarah and James each has $4$ cookies at beginning. Bill gives James some cookies and James gives Sarah $2$ cookies. How many cookies do they have in total now?

Overseas Competition->Knowledge Point->Word Problem Modules

Giving cookies to each other won\textquotesingle t affect the sum of their cookies, so there are $$4+4+4=12$$~in total.


In a class of $$18$$ students, $$6$$ are wearing jeans. What is the ratio of students wearing jeans to students \emph{not} wearing jeans?

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

If $$6$$ students are wearing jeans, then $$18-6=12$$ are not. The ratio of students wearing jeans to students \emph{not} wearing jeans is $$6:12=1:2$$.


On average, each student has $$14$$ balls. Each of the $$15$$ girls has $$24$$ balls on average. There are $$25$$ boys, and their average number of balls is~\uline{~~~~~~~~~~}~.

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


All the animals stand in rows in the magic forest. There is the same number of animals in each row. There are $3$ rows on the left of monkey and $2$ rows on the right of it. In its row, there are $6$ animals in front of it and $2$ animals behind it. How many animals are there in the forest?


Billy has twice as many basketballs as soccer balls.  Milly has four times as many soccer balls as basketballs.  They have a total of 18 balls.  How many of them are basketballs?

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

Let Billy have $$b$$ soccer balls and $$2b$$ basketballs. Let Milly have $$m$$ basketballs and $$4m$$ soccer balls.  Therefore, as they have $$17$$ balls in total, $$3b + 5m= 18$$. The only positive integer solution of this equation is $$b= 1$$, $$m= 3$$. So the number of basketballs is $$2b + m = 2 \times 1 + 3 = 5$$.


Kate sold some dresses and Tasha sold $30$ more dresses than Kate. If Tasha sold thrice as many dresses as Kate, how many dresses did Kate sell?


The hands of a circular clock form aangle at $$6:15$$ P.M.


White and White Jr. have $$50$$ apples in total, and White has $$10$$ more appled than junior, so White Jr has~\uline{~~~~~~~~~~}~apples．

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


February

April

August

November

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


There are $$50$$ students in your class. The ratio of boys to girls is $$2:3$$. How many boys and girls are there?

$$30$$ and $$20$$

$$20$$ and $$30$$

$$15$$ and $$20$$

$$20$$ and $$15$$

According to the ratio $$2:3$$, we could know the total is $$5$$. Then the number of boys is $$50\times\frac{2}{5}=20$$. The number of girls is $$50\times\frac{3}{5}=30$$.


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.


Tom has $$20$$ toys in total, and Tim has $$2$$ more toys than Tom. The number of Amanda\textquotesingle s toys is equal to the sum of that of Tom and Tim. How many toys does Amanda have~\uline{~~~~~~~~~~}~.

None of the above

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

We know that Tim has $$20+2=22$$ toys. The sum of Tom\textquotesingle s and Tim\textquotesingle s toys is $$20+22=42$$.


The upper shelf of a bookshelf has $$143$$ books. The lower shelf has $$39$$ books. How many books should be taken from the upper shelf to the lower shelf so that both shelves will have the same number of books?

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


The length of a rectangle is increased by $30\textbackslash\%$ and the width is decreased by $25\textbackslash\%$. What percent of the old area is the new area? (adapted from 2009 AMC 8, Question \#8)

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


What is the greatest number of days that can occur after the first of one month and before the first of the next month?

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

A month has at most $$31$$ days, Hence, the greatest number of days in that month, after the first, is $$31 -1=30$$. Then, the next day is another $$1\text{st}$$.


Water from the first faucet fills the swimming pool in $18$ 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 $\frac1{18}$ and that of the other two is $\frac29$.  Thus it takes $1\div (\frac1{18}+\frac29\times2)=2$ hours to fill the pool.


SASMO 2015 P2 Q4  Susan prepared a plate of cookies for her friends Ashley, Sam, Max and Olivia. Susan tried the first cookie before serving them to her friends. Ashley took 2 cookies and gave 1 to Sam. Max then took 3 cookies, and gave 1 to Olivia and 1 to Susan. If they each ate the cookies they ended up with, who ate the most cookies?

Susan

Ashley

Sam

Max

Olivia

Susan: +1+1  Ashley: +1  Sam: +1  Max: +1  Olivia: +1


The distance between Town A and Town B is $620\text{km}$. Eric drives from Town A to Town B at a speed of $$75\text{km/h}$$ while Chien drives from Town B to Town A at a speed of $$80\text{km/h}$$. How many hours will it take for them to meet each other?

As they are driving toward each other, the total speed is $$75+80=155$$ miles per hour. Then the time needed is $$620\div155=4$$ hours.


Elmp vists the Sesame Street Park every Wednesday. If the 1st of January 2017 was Sunday and February has 28 days, what was the last date in March 2017 in which Elmo visited Sesame Street Park?

28th March

29th March

30th March

31st March

None of the above.


Ashley had a basket of apples. Her family took half of the apples after dinner. Next morning, her family took half of the remaining apples. There were $$2$$ apples left in the basket. How many apples were in the basket at first?

Overseas Competition->Knowledge Point->Word Problem Modules->Inverse Operation Problems->Giving Half of a Whole