Problem solving

2011 Calendar
Problem
Solving

LORETO MORALES

MARIELLA ALEXES ROMBAOA

MECHILLE LACUESTA

DIAN MENESES

CAROLYN GRANDE

Free Powerpoint Templates JOYCE ESTEBAN
MYRELL

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Batman has been imprisoned by the
Riddler. To escape he must find the
quickest way to move the tower of
plutonium disks from one post to another
so that the disks have the same
arrangement as on the original post. He
may move only one disk at a time. What is
the minimum number of moves he must
make in order to move the ten disk tower
and have it appear the same?

Hint and answer

Hints:
1) Batman can put all disks on one post and then switch to
the second post in 20 moves. How would he reduce his task?
Answer:
The quickest way is to move each disk
onto the first post
except for the last disk -> which is 9
moves.
Then move the last disk to the second
post which is one
move.
Then move each of the disks on the first
post to the second
post which is an additional 9 moves.
9 + 9 + 1 = 19 moves

BACK

Seth and Bob each began reading a Hardy
Boys book today. If Seth reads 8 pages each
day and Bob reads 5 pages each day, what
page will Bob be reading when Seth is
reading page 56? (Hint: Complete the table.)
Day Seth's Page Bob's Page
1 8 5
2 16 10
3 24 15

Hint and answer

Day Seth's Page Bob's Page

1 8 5

2 16 10
3 24 15
4 32 20
5 40 25
6 48 30
7 56 35

BACK

How many different
cubes can you make if
each face of a given
cube has a line
connecting the center
points of two opposite
edges?

Hint and answer

Hint:
1) There are three sets of opposing faces that will be split into four.

BACK
23 = 8 cubes

Find the number of faces, edges and vertices on the figure shown.

•What would this figure be called?
•What would the two figures contained in it be called? Hint and answer

Hints:
NONE!
Answer:
17 edges 9 faces 10 vertices

Pentagonal Prism contains a rectangular prism
and a right trianglular prism.

BACK

Scientists have just discovered people on Neptune. There are 3
villages, 2 cities and 1 super city on Neptune. These are the
populations in 1994 and 1996.
1994 1996

Eilosa 129 204
Vertu 308 292
Pridi 90 50
Dedrun 500 600
Antran 700 693
Maran 1200 1500
List the places in order of increasing size in 1994 and 1996.
In which year was the population of the planet greater?

Hint and answer

Hints:
Sum each column!
Solution and Answer:
1994 1996
Eilosa 129 204
Vertu 308 292
Pridi 90 50
Dedrun 500 600
Antran 700 693
Maran 1200 1500
-----------------
2927 3339
3339 - 2927 = 412 therefore the population in '96 is greater

BACK

Can you find all
of the spokes? A
digit on a hub
denotes the
number of
spokes that meet
there. Spokes
never cross and
in the end
everything will
be connected.

Answer

A farmer grows 252 kilograms of
apples. He sells them to a grocer
who divides them into 5 kilogram
and 2 kilogram bags. If the grocer
uses the same number of 5 kg bags
as 2kg bags, then how many bags
did he use in all?

Need A Hint? And Answer

Hints:
1) Let x = total number of bags

Answer:
Let x = total number of bags

5(1/2 x) + 2 (1/2 x) = 252
2.5x + 1x = 252
3.5x=252
x = 72 bags.
BACK

This is a turtle graphics problem.
A bug is walking across the doorstep of a house. When he
starts out he is facing the house at the opposite side of the
doorstep. If he goes 3 units left, 1 unit right, 2 units left, 8
units left, what will the bug have to do to get back where
he started as quickly as possible without retracing his
steps?

Hint and answer

Hints:
1) Remember, you face the direction you go!
2) Draw a diagram.

HOUSE

Answer:
1 unit left and 3 units left.

BACK

Three ducks and two ducklings
weigh 32 kg. Four ducks and three
ducklings weigh 44kg. All ducks
weigh the same and all ducklings
weigh the same. What is the weight
of two ducks and one duckling?

Hint and answer

Hints:
1) Set up two equations

Answer:
Let D = the weight of one duck
d = the weight of one duckling
Solve:
(3D + 2d = 32)*3 ------> 9D + 6d = 96
(4D + 3d = 44)*2 ------> 8D + 6d = 88
______________
1D + 0d = 8 -----> D = 8
Substitute to solve for d:
4D + 3d = 44
4(8) + 3d = 44
32 + 3d = 44
3d = 12
d=4
Thus,
2D + d = 2(8) + 4 = 20 kgs.
BACK

It takes one man one day to dig a 2m x 2m x
2m hole. How long does it take 3 men
working at the same rate to dig a 4m x 4m x
4m hole?
If you can finish
these problem,
you'll be
smarter than I
am.

Hint and answer

Hints:
1) Find rate of one man
Answer:
Let x = rate of one man = 23 m3/ 1 day = 8m3/day
3x = rate of three men = 3(8m3/day) = 24m3/day

Volume to be shoveled = 64m3
Therefore, it would take three men
64m3/(24m3/day) = 2 2/3 days

BACK

Hints:
1) Try putting addition signs between the
different numbers.
2) Try this example:
ANSWER:
1) 9+8+7+65+4+3+2+1 = 99 -> 7 addition signs.
2) 9+8+7+6+5+43+21 = 99 -> 6 addition signs.

BACK

A 800 seat multiplex is divided into
3 theatres. There are 270 seats in
Theatre 1, and there are 150 more
seats in Theatre 2 than in Theatre
3. How many seats are in Theatre
2?

Hint and answer

Hints:
1) Let x = seats in Theatre 3. Then number of seats in Theatre 2
= x + 150 seats.
Answer:
Let x = number of seats in Theatre 3
T1 = Theatre 1 = 270 seats
T2 = Theatre 2 = 150 + x

T1 + T2 + T3 = 800 seats
270 + (150 + x) + x = 800
420 + 2x = 800
x = 190
If there are x = 190 seats in theatre 3,
then Theatre 2 has

150 + 190 = 340 seats
BACK

HINT:
1) Draw a diagram -> use least common multiples.
x = Frog 1
o = Frog 2

ANSWER:
• How many numbers between 1 and 18 are multiples
of 2 and 3?
• 6, 12, 18
[ ][o][x][o][ ][x/o][ ][o][x][o][ ][x/o][ ][o][x][o][ ][x/o]
• 1 2 3
• There will only be 3 lily pads that both frogs jump on
• - Number 6, 12 and 18.

BACK

ANSWER:
 (3/10)*? = 24 and 24/(3/10) =
80.

 Aunt Helen is 80 years old.

BACK

Question:

It takes one man one day to dig a
2m x 2m x 2m hole. How long does it
take 3 men working at the same rate
to dig a 4m x 4m x 4m hole?

Hint and answer

Hint: Find rate of one man
Answer:
Let
x = rate of one man = 23 m3/1day = 8m3/day
3x = rate of three men = 3(8m3/day) = 24m3/day

Volume to be shoveled = 64m3

Therefore, it would take three
men
64m3/(24m3/day) = 2 2/3 days
BACK

Hint: To find the answers, multiples of 2.

Answer: To find the multiples of a
number, multiply that number by 0, 1, 2, 3,
4, 5……
2 (0) = 0
2 (1) = 2
2(2) = 4
2 (4) = 8
2 (5) = 10
The next 3 garbage bins are placed near
the 6th, 8th, and 10th houses.
BACK

Question:
A farmer grows 252 kilograms of
apples. He sells them to a grocer who
divides them into 5 kilogram and 2
kilogram bags. If the grocer uses the
same number of 5 kg bags as 2kg bags,
then how many bags did he use in all?

Hint and answer

Hint: Let x = total number of
bags
Answer: Let x = total number of bags

5(1/2 x) + 2 (1/2 x) =
252
2.5x + 1x =
252
3.5x =
252
x = 72 bags.

BACK

Question:

A 800 seat multiplex is divided into 3
theatres. There are 270 seats in Theatre
1, and there are 150 more seats in
Theatre 2 than in Theatre 3. How many
seats are in Theatre 2?

Hint and answer

Hint :Let x = seats in Theatre 3. Then number of seats in
Theatre 2 = x + 150 seats .
Answer:
Let x = no. of seats in Theatre 3
T1 = Theatre 1 = 270 seats

t2 = Theatre 2 = 150 + x
T1 + T2 + T3 = 800 seats
270 + (150 + x) + x = 800
420 + 2x = 800
x = 190
If there are x = 190 seats in theatre 3, then
Theatre 2 has
150 + 190 = 340 seats
BACK

Question:
In 1969 the price of 5 kilograms
of flour was P0.75. In 1970 the price
was increased 15 percent. In 1971, the
1970 price was decreased by 5 percent.
What was the price of 5 kilograms of
flour in 1971?

Hint and answer

Hint: Let 1970 cost = (P0.75)*1.15

Answer: If the price of 5 Kg of flour in
1969 = P0.75, then
1970 = P0.75 x 1.15 = P0.8625
1971 = (PO0.75 x 1.15) x .95 = P0.82

BACK

Question:
A rectangular sheet
of wood has four small
squares removed. It is
then cut to make a box
that is 5cm by 4cm with
a volume of 60cm3.
(Four pieces of size A4
are removed.) Find the
original area of the
sheet of wood.

Hint and answer

Hint: Open top box
Answer: l x h x w = 60
h(5)(4) = 60
h=3
A(1) = 4 x 5 = 20
2A(2) = 2(3)(5) = 30
2A(3) = 2(3)(4) = 24
4A(4) = 4(3)(3) = 36

Total A = A(1) + 2A(2) + 2A(3) + 4A(4)
= 20 + 30 + 24 + 36
= 110cm2

BACK

Question:
Mary has $50.00. She goes to
the mall and buys lipstick and then she
buys shampoo, which is half the price of
the lipstick. She then spends half of
what she has left on a purse, leaving her
with $15.00.
How much did the shampoo cost?
How much did the lipstick cost?

Hint and answer

Hint: Purse cost $15.00
Answer: Let x = price of lipstick
1/2 x = price of shampoo
Cost of lipstick AND shampoo,combined = x +
1/2x
Money spent on lipstick and shampoo
combined:
$50.00 - ($15.00)*2 = $20.00
Therefore,
x + 1/2 x = $20.00
1.5x = $20.00
x = $13.33
Lipstick cost: x = $13.33
Shampoo cost: 1/2 x = 1/2 * $13.33 = $6.67
BACK

Question:
Stephanie had P40.00 savings. Her mother
gave her another P30.00 and her grandmother
gave her P10.00 to buy a pair of cleats. The pair
of cleats Stephanie wants costs P54.99.
If Stephanie buys the cleats at a no TAX sale,
write an equation using a variable to describe
the amount of money that Stephanie will have to
contribute from her savings.
Solve for the variable.

Hint and answer

Hint :Stephanie spends all of money from her
mother and grandmother

Answer:
Let x = Stephanie‘s contribution.

P30.00 + P10.00 = P40.00
P40.00 + x = P54.99
x = P14.99

BACK

Question:
Given a rectangular
prism. If the sides of
the rectangle A have
the same ratio to
each other as the
sides of rectangle B,
then what is
(a) The surface area of
the prism?
(b) The volume of the
prism?

Hint and answer

Hint: 1.Find length of x first
2.Find area of A and area of B

Answer: Dimensions B:
5/8 = 8/x
64 = 5x
12.8 = x
(a) Surface Area = 2 * Area A + 2 * Area B + Area
(top) + Area (bottom)
= 2(8*5) + 2(8*12.8) + 2(5*12.8)
= 412.8
(b) Volume = l x w x h
= (12.8)(5)(8)
= 512
BACK

Question:
The trails in a park
resemble the following
diagram. Find the total
length of the trails,
given that all the circles
have the same area
and circle 2 is tangent
to the midpoint of L.

Hint and answer

Hint: W = diameter = 2r

Answer:
2r + 3L + 3w + 3pi*a = 2(10) + 3(100) +
3(20)+3pi(20)
= 568.50m
(2r+L) + 2L + 3W + 3piW = (2(10)+40) +
2(40) + 3(20) 3pi(20)
= 388.50 m

BACK

Question:
The rent-a-stall horse barn has stalls for
1000 horses. Forty percent of the stalls
are for ponies. On Tuesday, there were
200 ponies and a bunch of quarter
horses at the horse barn. The horse
barn was 75 percent full.
How many quarter horses were in the
stalls?

Hint and answer

Hint: Find total number of stalls filled

Answer:
75% full = 75% * 1000 horses
= 750 horses
If there are 200 ponies, there must be
(750 - 200) = 550 quarter horses

BACK

Question:
A rectangular chalk board is 3 times as
long as it is wide. If it were 3 meters
shorter and 3 meters wider, it would be
square. What are the dimensions of the
chalk board?

Hint and answer

Hint: Sides of square are equal

Answer:
Let x= width of chalkboard
Therefore,
3x = length of chalkboard
Since sides of square are equal,
3x - 3 = x + 3
2x = 6
x=3
Dimensions of chalkboard:
width = x = 3 meters wide
length = 3x = 9 meters long

BACK

Question:
Three people share a car for a period of one
year and the mean number of kilometers
traveled by each person is 152 per month.
How many kilometers will be traveled in one
year?

Hint and answer

Find total number of kilometers
Hint:
traveled per month
Answer:

3 x 152km/month x 12 months/year
= 5472 km/year

BACK

Question:
A car dealer claims that by buying a new car
Mike will pay 1/5 less for gas then he pays for
the car he currently drives. If the car Mike
currently drives costs 1/6 less to gas up than
Dave's car, and Dave pays $700.00 per year,
what will it cost Mike to put gas in a new car
for one year (assuming all cars will be
traveling the same distance)?

Hint and answer

Hint: 1/6 less than 700 = 5/6(700)

Answer:

(700.00)(5/6)(4/5) = $466.67

BACK

Question:
A side of the equilateral
triangle A is twice the length
of a side of triangle B.
How many triangle B will fit
into triangle A?

Hint and answer

Hint: Draw triangle A and fit triangle Bs into it 2) How many
times will the area of B divide the area of A?

Answer:

4
triangles

BACK

Question:
A storage facility has space for 225 -
8 liter boxes and 515 - 27 liter boxes.
What is the volume of the facility? What
percent of the total volume is filled by
150 of the 8 liter boxes and 5 of the 27
liter boxes?

Hint and answer

Hint: Total volume = 8 * 225 + 27 *
515
Answer:

a) 225*8litres+515*27liters=TotalVol
15705 litres = 15.705
kilolitres
b) [(150*8 + 5*27) / 15705] x 100 percent
= 8.500 percent.

BACK

Question:
Marvin's Taxi Service charges $0.30 for
the first kilometer and $0.05 for each
additional km. If the cab fare was $3.20,
how far did the Taxi go?

Hint and answer

Hints:
Total volume = 8 * 225 + 27 * 515

Answer:
Cost of first kilometer = $0.30
Total cost of additional kilometers
= (3.20 - 0.30)
= 2.90
Total number of kilometers
= 1 +($2.90/$0.05)
= 1 + 58
= 59 km

BACK

Question:
What fraction of this square is shaded?

Hint and answer

Hints:
Use table to calculate total amount of gas used by each
person

Answer:
Total area of square = (1/4 + 3/4)*(2/3 +
1/3)
=1*1
=1
Shaded area = (2/3 * 3/4) = 0.5
Fraction of Total area shaded
=0.5/1
= 50%
BACK

Question:
The number of hours left in a day on Mars
was 1/4 of the number of hours that had
already passed. How many hours were
left in the day?
Day on Mars 40 hours.

Hint and answer

Hints:
Total area of square = (1/4 + 3/4) * (2/3 + 1/3) = 1
*1=1
Answer:
Let x = the number of hours that had already
passed
1/4 x = the number of hours remaining
IF total number of hours in a day = 40,
THEN
x + 1/4x = 40
5/4x = 40
160x = 5
x = 160/5
x = 32
Hours remaining = 1/4 x
= 1/4(32)
=8
BACK

Question:
A cereal company decided to
increase the height of its boxes
by 30 percent and reduce the
width in order to maintain the
same volume. If initially,
length 20cm
height 40cm
width = 30cm
What will the new height and
width be if length stays the
same?

Hint and answer

Hints:
An increase in the height h by 30% is (1+0.3)h=1.3h.

Answer:
Volume = l * w * h
= (20)(30)(40)cm3
= 24000cm3
New height = initial h + 0.3h
= 1.3h
= 1.3 * 40cm
= 52 cm
IF height = 52 cm, solve for w:
Volume = l * w * h
24000 cm3 = (20cm)(w)(52cm)
24000 cm3 = 1040(w)cm2
w = 23.08 cm

BACK

Question: of times a dog barks depends on the
The number
number of cars passing.
How many cars have passed when a dog barks 22
times? How many barks for 5 cars?
Cars Barks
------+-------
6 | 4
7 | 7
8 | 10
9 | 13
10 | 16

Hint and answer

Hint: Look for a pattern: Begin at the bottom of the column - subtract
the first number from the next number and compare to the difference of the

corresponding two numbers in the other column.

Answer:
Pattern:
6 - 13 = 3
10 - 7 = 3
0-9=1
8-7=1
3 barks for 1 car
Therefore, 22 barks for 12 cars.
BACK

Hints:
 Divide the face of the clock into three
parts with two lines so that the sum of
the numbers in the three parts are
equal.
 1) Divide the clock into three parts with
two lines. Add up the numbers in each
section. Are they equal? If not try again.

Answer:
 26+26+26 = 78

BACK

PROBLEM

 According to experts the first 4
moves in a chess game can be played
in 197299 totally different ways. If it
takes 30 seconds to make one move,
how long would it take one player to
try every possible set of 4 moves?

Hint and answer

Hints:
 1) 197299 sets of four moves
 2) Each of the 4 moves takes 30
seconds.

Answer:
 30 seconds * 4 * 197299 =
23675880 seconds.

BACK

PROBLEM
 A man has to be at work by 9:00 a.m.
and it takes him 15 minutes to get
dressed, 20 minutes to eat and 35
minutes to walk to work. What time
should he get up?

Hint and answer

Hints:
 1) Add up time required
 2) Subtract this time from the time he has
to be at work. Eg. 9:00 - 20 min= 8:40

Answer:
 9 hours - (15 + 20 + 35)
 9 hours - 70 minutes
 7 hours + 120 minutes - 70 minutes = 7
hours and 50 minutes = 7:50 AM

BACK

Question:
There are 360 degrees in a
circle. If the population of
various planets are
represented by a circle
graph, match the percentage
of the population of the solar
system that is found on each
planet with an area on the
graph.
Planet Percent
-----------+----------
Earth 27.78%
Mars 20.80
Venus 1 6.67
Jupiter 2.78
Mercury 2.78
Neptune 6.11
Pluto 1.67

Hint and answer

Hint: You will only find 99.98 percent
Answer:

BACK

Question:
A tire shop that sells only one size of tire,
.75 meters in diameter, decides to sell
tires for big rigs that are 1.5 meters in
diameter. If the cost of the .75 meter tires
is $100.00 for four, how much will it cost
for the 18 tires required for a big rig?
Prices increase proportionally with size.

Hint and answer

Hints:
1) Find the cost of a .75 m tire
2) Use to find cost of big rig tire
Answer:
Let x = price for each big rig tire
Size Price/tire
0.75m $100/4 = $25.00 each
1.5m x
Solve for x:
0.75m/$25.00 = 1.5/x
0.75x = 1.5 * $25.00
0.75x = $37.50
x = $50.00/tire
Therefore:
Price for 18 tires = 18($50.00) = $900.00

BACK

Question:
Four friends buy a pizza that costs $20.00. Each person
contributes a the following amount of money.
Jane $5.00
Mike 8.00
Mary 3.00
Joe 4.00
Each person will eat an amount of pizza proportional to
the amount of money they paid.
1)Draw a circle graph that represents the amount each
eat.
2)Draw the circle graph if Mike only eats half of his
pizza and gives half of what he has left to Mary.

Hint and answer

Hints: Find the proportion of money paid by each person
Answer:
Cost of
Pizza=$20.00

PROPORTIONS:
Jane:520=1/4 Jane: 5/20 =1/4
Mike:8/20=4/10=2/5
Mike: 8/20-4/20 = 4/20 = 1/ 5
Mary:3/20
Mary: 3/20 + 4/20 = 7/20
Joe: 4/20 = 15
Joe: 4/20 = 1/5

BACK

Question:
A boy ate 100 cookies in five days. Each
day he ate 6 more than the day
before. How many cookies did he eat
on the first day?

Hint and answer

Hint: Let x = the number of cookies eaten the first day

Answer:
Let x = the number of cookies eaten on the first day
Cookies Eaten
Day 1 x
2 x + 1(6)
3 x + 2(6)
4 x + 3(6)
5 x + 4(6)
TOTAL

5x + 10(6) = 100 cookies
Solve for x: 5x + 10(6) = 100
5x + 60 = 100
5x = 40
x=8

BACK

Question:
M and N are the
midpoints of the
sides of a square.
What is the ratio of
the area of triangle
AMN to the area of
the complete
square?

Hint and answer

Hints:
Triangle AMN: base = height = 1/2 s

Answer:
Since s = sides of square
Area square = s^2
Area triangle = (1/2)b*h
= (1/2)(1/2 s)(1/2 s)
= 1/8 s^2
Ratio = Area triangle/Area square = 1/8

BACK

Question:
There are 6 short
pieces of link chain,
each having 4 links.
It takes 10 seconds
to cut a link and 25
seconds to weld it
back together. What
is the shortest
possible time to
make the longest
chain?

Hint and answer

Hints:
Connecting 2 chains requires one cut and one
weld .
Answer:
Time to connect two chains = 1 cut + 1
weld
= 10s + 25s
To connect all chains together = 5
connections
=5(10+25)s
=5(35)
= 175

BACK

Question:
Magic Hexagon
Find the magic
constant and fill
in the numbers so
that every column
or diagonal has
the same sum.

Hint and answer

Hints:
Use the sum of the column of numbers given to
find the target total for each column or diagonal

Answer:

BACK

Question:
An artist draws a picture of a
house with a rose bush in front. In
his picture the rose bush is 1.5cm
high and the house is 7.5cm high. In
reality the rose bush is .75 meters
high. How tall is the house (in
meters)?

Hint and answer

Hints:
1) Convert meters to centimeters
2) Find the artist's scale, as indicated by the actual size of the rose
bush compared to the size of the artist's drawing
Answer:
Let x = artist's scale
1) Convert meters (m) to centimeters (cm)
In reality, rose bush = .75m*100 cm/m = 750
cm
2) Solve for x
1.5x = 750
x = 750/1.5
x = 500 cm
IF artist's scale = 1 cm:500cm THEN
In reality, house = 7.5cm * 500
cm
= 3750 cm
= 3.75 m

BACK

Question:
This picture shows a triangle in
which 3 lines are drawn to one
or the other of the opposing
sides from each of two vertices.
This divides the triangle into 16
no overlapping sections.
If 4 lines are drawn in the same
way, how many no overlapping
sections will the triangle have?

Hint and answer

Hint: The three lines divide the two sides in 4 pieces
each. Look at how many sections there would be if four
lines were extended from each vertex.

Answer: When 3 lines are extended from vertex, opposite
side is divided into four sections
When 3 lines are extended from two vertices:
Number of non over lapping sections formed = 42 = 16
If 4 lines are extended from vertex, opposite side is divided
into five sections
Therefore, when 4 lines are extended from two vertices:
Number of non over lapping sections formed = 52 = 25

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Question:
The sports commentator on the CFXU radio station
summarized the points scored by the St. F. X.
Basketball Team during this season as follows:
"The SMU scored a total of 1729 points in the last
season. This year St. F. X. scored of 1653 points. ST.
F.X. received 38 percent of the points for the total
season of all 4 teams. SMU finished in second place.
Acadia received only 14 percent of the points and
was beaten for third place by Dalhousie by 50
points."
If there were only 4 teams in the season, how many
points did each team receive?

Hint and answer

Hints:
ST. F.X. scored 1653 points, which was 38 percent of the
total points. Find total number of points for all 4 teams.

Answer: Let x = total number of points for the
season
1653 points were scored by ST. F.X., but ST. F.X. had only
38 percent of the total points for all four teams.
Solve for x:
x= 1653/0.38 = 4350 points
ACADIA:
14% * 4350 = 609
DALHOUSIE:
Acadia + 50 = 609 + 50 = 659
SMU:
4350 - (1653 + 609 + 659) = 1429

BACK

Question:
Rachel and Stephanie earn
$5.15/hour. Rachel works 13 hours
each week and Stephanie works 20
hours per week. Stephanie does not
get any paid vacation time. How long
a vacation would Stephanie have to
take to make the same amount of
money as Rachel in one year?

Hint and answer

Hints:
Look at Stephanie's weekly salary to determine how many weeks she
must work to make the same amount of money as Rachel makes in
one year

Answer:
Rachel:
WEEKLY: $5.15/hr * 13 hrs/wk = $66.95/wk
YEARLY: $66.95/wk * 52 weeks = $3481.40/yr
Stephanie:
WEEKLY: $5.15/hr * 20 hrs/wk = $103/wk
YEARLY: $103 * 52 weeks = $5356/yr
IF Stephanie and Rachel make the same amount of money in
one year, THEN Stephanie must only work:
($3481.40/yr)/($103/wk) = 33.8 weeks
Therefore, she must take
52 - 33.8 = 18.2 weeks/yr Unpaid Vacation Time

BACK

Question:
The Town of Antigonish has decided to put a paved
path around Columbus Field. The path will be
built so that the area of the park remains the
same. If the path is to be 3m wide...
a) What will be the perimeter of the path and the
park? The dimensions of the park are 210m x
460m.
b) What will be the area of the paved portion of
the park?

Hint and answer

Hints:
Draw a sketch
Answer:

p = 2(6 + 210) + 2(6+460) = 432 + 932

Area of paved
path = 2*3*466
+ 2*3*210 =
4056 m2
BACK

Question:
 Joe buys a cup of coffee that costs
$1.08. He pays with a two dollar coin.
 If the cashier gives him 8 coins for
his change, what could these coins
be?

Hint and answer

Hints:
There is more than one solution
Answer:
Amount of change Joe
receives:
$2.00 - $1.08 = $0.92
Two possible variations of coins
received:
(i) 3 quarters, 3 nickels, 2 pennies
3(.25) + 3(.05) + 2(.01) = .92
(ii) 2 quarters, 4 dimes, 2 pennies
2(.25) + 4(.10) + 2(0.01) = .92

BACK

Question:
Square ABCD has the
centers of 4 equal circles
as its vertices. Find the
shaded area. Shawn
bought a car for
$5600.00. He sold it to
Rachel for 5/6 the price
he paid for it. Rachel sold
it to Raelene for 1/5 less
than she paid. Raelene
sold it to Rick for 3/4
what she paid.
What did Rick pay for the
car?

Hint and answer

Hints:
Length of sides of square equal 2 * radius of circle (circles
are equal)
2) The square contains 4 quarters of equal circles
Answer:
Area of circle = pi * r2
Side of square = 2 * r = 2r
Area of square = (2r)2 = 4r2
Area of shaded region = Area of square 4 *
(1/4 area of each circle)
= 4r2 - 4 * 1/4(pi * r2)
= 4r2 - pi r2
= (4 - pi)r2

BACK

Question:
Points A and B on a map
are 12km apart if you
follow the path. A troop
of boy scouts leaves point
A at 11:00 a.m.. They are
all carrying packs and
travel 3km/hr until they
reach point C at 12:45. If
they want to reach point
B by 2:00, how fast will
they have to go

Hint and answer

Hints:
1) Distance = Rate * Time
2) Rate = Distance/Time

Answer:
 Travel time from A to C = 12:45 -11:00 = 1 hr 45 min = 1.75 hr

 Distance travelled:D = Rate * Time
= 3 km/hr * 1.75 hr
= 5.25 km
 Distance remaining (from point C to B):
= (12 - 5.25) km
= 6.75km
 Time remaining = 2:00 - 12:45 = 1 hr 15 min = 1.25 hr
 Rate at which distance must be travelled:
 Rate = Distance/Time
= 6.75 km / 1.25 hr
= 5.4 km/hr

BACK

Question:
Water conservation can be a big
problem in some parts of the world.
If a community's water pump drips 3
drops every second and each drop is
1 1/3ml, how much water will be
wasted in one year ?

Hint and answer

Hints:
1) Look at how much water drips every second
2) Calculate number of seconds in one year
Answer:
 Water lost per second:3 * (1 1/3 mL) = 4mL

 Number of seconds in one year: 60s/min x 60 min/hr x
24hr/day x 365d/y = 31 536 000 s

 Water lost in one year = 4mL/s * 31 536 000 s = 126 144 000 Ml

 Convert to Litres:126 144 000mL * 1L/1000 mL = 126 144 litres

BACK

Question:
 Shawn bought a car for P5600.00. He
sold it to Rachel for 5/6 the price he
paid for it. Rachel sold it to Raelene
for 1/5 less than she paid. Raelene
sold it to Rick for 3/4 what she paid.
 What did Rick pay for the car?

Hint and answer

Hints:
1) Calculate price each person paid for the car,
working from Rachel to Raelene, to Rick

Answer:
PURCHASE PRICE:
Rachel: 5/6 * P5600.00 = P4666.67

Raelene: 4/5 * P4666.67 = P3733.33

Rick: 3/4 * P3733.33 = P2800.00
OR you can take a shortcut:
Rick paid: P5600.00 (5/6)(4/5)(3/4) = P2800.00

BACK

 Elmer Fudd decided to grow a garden so he could
make salad. He wants to make it 10.1 m long and 4.2
m wide. However, in order to avoid Bugs Bunny from
entering his garden he must make a fence
surrounding the garden. He decides to make the
fence 11.2 m long and 5.0 m wide. What is the area
between the fence and the garden?

Hint and answer

Hints:
1) Find area for the garden.
2) Remember area equals length
multiplied by width.
3) Find the area of the space surrounded
by the fence.
Answer:
13.58 m2
BACK

 Jenny bought 7 t-shirts, one for each of
her seven brothers, for P9.95 each. The
cashier charged her an additional
P13.07 in sales tax. She left the store
with a measely P7.28. How much money
did Jenny start with?

Hint and answer

Hints:
1) What is the total amount the shirts
would cost without the sales tax?
2) If there is an additional P13.07 sales
tax how much did the cashier charge
her in total?
3) How much did Jenny start with?
Answer:
 P90.00
BACK

 a) What is the least fraction of a full turn you
could turn this geoboard for the shape to
look the same?
 b) Try making your own figure on the same
geoboard with the same turn symmetry.

Hint and answer

Hints:
1) How many times could you turn the
board and the shape still looks the
same?
2) Try labelling the figure and turning
your sheet of paper.
3)One full turn is when 1 returns to its
original position.
Answer:
1/4 turn.

BACK

 Jill was given 3 red candies, 2 blue
candies and 2 yellow candies. Use
several ratios to describe the candies
Jill has.

Hint and answer

Answer:
3 red : 2 blue
5 red and blue :
2 yellow
3 red : 7 candy.

BACK

A number line from 0 to 2 is divided into
seven equal segments. What fraction
names point A? What fraction names
point B?

Hint and answer

Hints:
• 1) What fraction, with denominator 7 reduces to
a value of 2?
• Example:
• 12/6 = 2 but we want ?/7 = 2
• (What is ?)
• 2) If the line is divided into 7 segments, what
would each point be labelled 0, 1/7, ... , ?/7=2 ?
• 3) Or should they be named 0, 2/7, 4/7, 6/7,
......14/7 ?
• 4) What is the fraction of A and B
Answer:

BACK

 a) If you saved P2.00 on January 1, P4.00 on
February 1, P6.00 on March 1, P8.00 on April
1, and so on, how much money would you
save in one year?
 b) If you saved P2.00 on January 1, P4.00 on
February 1, P8.00 on March 1, P16.00 on April
1, and so on. How much money would you
save in one year?

Hint and answer

Hints:
• 1) Make a chart to help you along with the problem.
January 2 February 4 March 6 April 8
May ? June ? July ? August ?
September ? October ? November ? December
?
2) How would you find the total amount of money you saved?
• 1) Do the same as in the last problem.
Answer:
• a) 2+4+6+8+10+12+14+14+18+20+22+24 = P156.00
• b) P8190.00

BACK

 What is the number you started with?

Hint and answer

Hints:
1) What are the factors of 12?
2) Can the other number be 3? Why or why
not? The numbers cannot be 3 because
the greatest common factor of both of the
numbers is 6. (3 cannot have a factor).
3) Can the other number be 6? Why or why
not?
Answer:
(462 * 3) / 0.1 = 13860 - 13860 / 308 = 45 ? =
45

BACK

A Drug Store parking lot has space for
1000 cars. 2/5 of the spaces are for
compact cars. On Tuesday, there were
200 compact cars and some standard
size cars in the parking lot. The parking
lot was 3/4 full.
 How many standard size cars were in
the parking lot?

Hint and answer

Hints:
1) The parking lot is 3/4 full, how many
cars are in the parking lot?
2) If 200 of these cars in the parking lot
are compact cars, how many are
standard sized cars?
Answer:
750 - 200 = 500 standard sized cars.

BACK

 How many triangles are in this figure?

Hint and answer

Hints:
1) Count all the triangles you can see. 2)
Some triangles are formed from smaller
triangles.
Answer:
 12+6+2+6+1+6+2+2 = 37

BACK

• Can you solve this magic square?
• Put the remaining numbers from 0 to 15 in the
16 small squares. The sum of the four numbers
in each row, column and two diagonals must
be 30.
• 15 | | | 12
----+----+----+----
| 10 | 9 |
----+----+----+----
| | |11
----+----+----+----
3| | | 0
Hint and answer

Hints:
1) Start with a block you know you can fill
then find the rest of the sums.
Answer:
15 | 1 | 2 | 12
----+----+----+----
4 | 10 | 9 | 7
----+----+----+----
8 | 6 | 5 | 11
----+----+----+----
3 | 13 | 14 | 0
BACK

• Mary and Jason were making propellers for their
wooden helicopters. Mary put a number on her
propellor and noticed that when she turned the
propellor she had the same number.

• Jason was trying to think of a number that he could
put on his that had the same rotational synmetry
(looks the same turned upside down). What is the
next larger number that has this property?

Hint and answer

Hints:
1) What other numbers have this same
property?
2) 0, 1, 6, and 8, 9, have this property?
3) What is be the next lower number?
Answer:
6009

BACK

 Farmer Tom put a square fence around
his vegetable garden to keep the deer
from eating his corn. One side was 10m
in length. If the posts were placed 2m
apart, how many posts did he use?

Hint and answer

Hints:
1) How many posts on one side of the square fence?
2) If there are 4 sides how many posts are there all
together?
3) Remember if you found your answer to be 20 that you
have counted the corner posts more than once.
Answer:

5 posts/10m 16

BACK

Ammie passed around a basket of strawberries to
the girls at her party. Before the party she ate 5
strawberries and gave a friend 3. Eight girls
arrived at the party. The first girl took a
strawberry, the second girl took 3 strawberries,
the third girl took 5 strawberries and so on. After
the last girl took her strawberries, the basket
was empty. How many strawberries were in the
basket at the beginning?

Hint and answer

Hints:
1) How many more strawberries did the second girl take then the first?
2) Make a chart and look for a pattern.
Girl | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
-------------+---+---+---+---+---+---+---+---
number of | | | | | | | |
strawberries |1|3|5| | | | |
taken | | | | | | | |
-------------+---+---+---+---+---+---+---+---
total number | | | | | | | |
taken |1|4|9| | | | |
| | | | | | | |
-------------+---+---+---+---+---+---+---+---
3) What was the TOTAL amount taken?
Answer:
72

BACK

A side of square B is four times the
length of a side of square A. How many
times greater is the area of square B
than the area of square A?

Hint and answer

Hints:
1) If the side of square A = 1cm, what is the length of side B?
2) What are the areas of square A and B?
3) How many times greater is the area of square B than the area of
square A?
Answer:
Let side of square A = 1 cm
Let the side of square B = 4cm
Area square A = 1 cm2
Area square B = 16 cm2
The area of square B is 16 times greater than the area of square
A.

BACK

 Shane the Snail started at the dot. What
side will he be on when he has crawled
13/20 of the distance around the regular
pentagon of equal sides?

Hint and answer

Hints:
 1) If side A has a length of 2cm, then what is the
perimeter of this pentagon?
 2) If he has crawled 13/20 of the total distance
(perimeter) then how far has he crawled? And what
side would this have to be?
Answer:
 Let one side of a pentagon = 2 cm
Therefore, perimeter = 10cm*(13/20) = 6.5cm
SIDE D

BACK

 The number of hours that were left in
the day was one-third of the number of
hours already passed. How many hours
were left in the day?

Hint and answer

Hints:
1) If there were 9 hours left in the day, what was 1/3 of the number
of hours that had already passed? Are they equal?
2) If there were 8 hours left in the day, what was 1/3 of the hours
that already passed? Are they equal?
3) Try different numbers to find the number of hours left in a day
that equals one-third of the number of hours that had already
passed.
Answer:
9 hours left = 1/3 (15) 6 hours left = 1/3 (18)
9 is not equal to 5 6 hours = 6 hours
6 hours were left in the day.

BACK

A rectangular kitchen table is three times
as long as it is wide. If it were 3m shorter
and 3 m wider it would be a square. What
are the dimensions of the rectangular
table?

Hint and answer

Hints:
1) If the length is 4m, what is the width of the rectangular table?
2) Is this table a square? Why or why not?
3) Make a table to help you.
Length of Width of Length of Width of Correct?
Rectangle Rectangle Square Square
Trial #1 3x4m=12m 4m 12m 3m=9m 4m+3m=7m NO

Trial #2 3x2m=6m 2m 6m-3m=3m 2m+3m=5m
NO
Trial #3

Answer:
width: 3m ; length: 3*3 = 9
width + 3 = 6 = length - 3 => a square

BACK

What is the starting number (?) ?

Hint and answer

Hints:
1) When you square a number, you multiply the
number by itself.
ex: 2x2=4 = 2^2 3x3=9 = 3^2
2) Reverse your steps. (Work backwards
starting with the result of 50).
Answer:
42 is the starting number.

BACK

 Derek started his car (automatic shift) drove 9 km
and spent 3 minutes waiting at traffic lights. About
how much gasoline did Derek's car use?
 CHART GIVEN:
AUTOMOBILE FUEL USAGE
Starting .015 Liters
Idling for 1 minute .047Litres
Moving
Manual Shift 30km 3.0 Litres
Automatic Shift 27km 3.0 Litres

Hint and answer

Hints:
1) If he spent 3 minutes idling, how much fuel did he burn in this
amount of time?
2) If it takes him 3.0 liters to go 27 km, how many liters can he go
for 9km?
3.0L/27km x 9km = ??
3) What is the total amount of gasoline Derek's car used?

Answer:
Starting 0.015 + 3(0.047L) + (3.0L/27km * 9km) = 1.156
Liters of fuel

BACK

Here's a question for you!!!
 One of these things does not belong
here, one of these things is not the
same. Can you tell which cube?

Hint and answer

Hints:
1) Look at the patters on the cubes
carefully.
2) If it helps, try making paper cubes with
these symbols.
Answer:
The third cube from left.

BACK

 Two carpenters decided to design desks
for students at the Junior High. The
dimensions of the desk are as shown.
How much wood would they need for 30
desks? (in cm2).

Hint and answer

Hints:
1) What is the area of one desk?
2) Find the area of each part and add all the areas to find the total
area.
3) If there are 30 desks, how much wood in square centimetres do
they need?

Answer:
Area of rectangle = 70cm x 30cm = 2100cm2
Triangles 2*(1/2 20cm x 30cm) = 600cm2
2100cm2 + 600cm2 = 2700cm2
30*(2700cm2) = 81000cm2 of wood

BACK

 Chatterbox made the following figures
with a piece of wood, 12 nails and an
elastic band. What is the area of the figure
(in units2)? Explain your method:

Hint and answer

Hints:
1) You can do this in many different ways. You can divide the
figure into different shapes to actually find the area of the
figure. Or you may want to try a different way.
Answer:
There are different methods a student may have in mind. But here
is one: Build a square around the shape. It has an area of 4
units.
Then substract the area of the two triangles.
Area = 2 ½

BACK

 Do these parallelograms have the same
area? How do you know?

Hint and answer

Hints:
1) How do you find the area of a
parallelogram?
Answer:
Yes, since you multiply the base and
height, it's really the same numbers,
so it doesn't matter which is the base
and which is the height.

BACK

PROBLEM
 Find the next 3 numbers in the following
sequence.
2, 5, 11, 23, ____, _____, ______.

Hint and answer

Solution and Answer
 1.Find the next 3 numbers in the following
sequence.
 2, 5, 11, 23, ____, _____, ______.
 Pattern : x 2 + 1
 47, 95, 191

BACK

 .If
this pattern was formed to make a cube,
what numbers would appear where the
question marks are?

Hint and answer

 2. If this pattern was formed to make a
cube, what numbers would appear where
the question marks are?

 ?=1
 ?=4
 ?=2

BACK

 The number of line segments joining a set
of points increases as the number of points
increases. Find how many line segments
there will be when there are 8 points; 10
points.

Hint and answer

 .Thenumber of line segments joining a set
of points increases as the number of points
increases. Find how many line segments
there will be when there are 8 points; 10
points.
1
Points 2 3 4 5 ...... 8 9
n
0
4
Lines 1 3 6 10 ...... 28 36 n(n-1) 2
5
+ + + + + + +
......
2 3 4 5 7 8 9

BACK

 For the hexagon with 42 dots, how many
dots are there on each side?

Hint and answer

 Forthe hexagon with 42 dots, how many
dots are there on each side?

No. of dots 6 12 18 ...... 42 n

(n 6)+
Dots per side 2 3 4 ...... 8
1

BACK

 Look for a common element in each of the
following.
This is a RUMDA. This is a not RUMDA.

This is a RUMDA. Is this a RUMDA (A)?

This is a RUMDA. Is this a RUMDA (B)?

This is a not RUMDA.

Hint and answer

 Look for a common element in each of the
following.
This is a RUMDA. This is a not RUMDA.

This is a RUMDA. Is this a RUMDA (A)?YES

This is a RUMDA. Is this a RUMDA (B)?NO

This is a not RUMDA.

BACK

 If
the figure on the left is continued, how
many letters will be in the J row?
 Which row will contain 27 letters?
 A
BBB
CCCCC
DDDDDD

Hint and answer

Solution and Answer

Letter A B C D E ...... J K L M N General
Numeral
1 2 3 4 5 ...... 10 11 12 13 14 n
Order
Total No. 1 3 5 7 9 ...... 19 21 23 25 27 2n-1

BACK

 The Adams family was going to buy a car for
$5800. The car dealer offered the Adams
family two options for buying the car. They
could pay the full amount in cash, or they
could pay $1000.00 down and $230.00 a
month for 24 months on the installment plan.
How much more would they pay for the car
on the installment plan?

Hint and answer

 Hints:
 1) Try and calculate the amount of money
that they would have to pay for the
installment plan.
 2) Calculate the difference between the
installment plan and the initial amount if
they paid today.
 Answer:
 1000.00 + 230.00 * 24 = $6520.00
 6250.00 - 5800.00 = $720.00 more for the
installment plan.
BACK

 Lisa Lilly was the best runner in the eighth
grade. One day she ran 100m in 40 seconds,
200m in 1 minute and 10 seconds, and 200m
over low hurdles in one and a half minutes.
How many more seconds did it take her to
run the 200m over low hurdles then it did to
run the 200m dash?

Hint and answer

 Hints:
 1) What information is important in this
question?
 2) How long did it take her to run 200m in
seconds?
 Answer:
To run the 200m: 1 min = 60s + 10s =
70s
 To run 200m with hurdles: 60s + 30s =
90s

 90s - 70s = 20s longer.
BACK

 Three students have to write a make up test. Mark
scored 24/60 on his first test and 32/40 on his make up
test. Jake scored 35/70 on his first test and 54/60 on his
makeup test. Marilyn scored 27/90 on her first test and
45/50 on her second test.
 A) Which student improved the most and by what
percentage?
 B) If the teacher gives each student a final grade using
70% of the makeup test mark and 30% of the first test
mark, what mark would each student receive? Who did
the best overall?

Hint and answer

Hints:
1) Make a chart of the percentages scored on each test for each student. As the following:
PERCENTAGE FOR FIRST TEST PERCENTAGE FOR SECOND TEST DIFFERENCE
MARK
JAKE
MARILYN
2) If you forget how to do percent, heres a hint: divide the denominator into the numerator and multiply by 100%
Part B
Hint:
1) Try making another chart with percentages of each test. Like the following:
30% of first test 70% of second test SumFinal Mark
MARK
JAKE
MARILYN
Answer: A)
| PERCENTAGE PERCENTAGE
| FOR FIRST TEST FOR SECOND TEST DIFFERENCE
---------------+--------------------------------------------------------
MARK | 40% 80% 40%
JAKE | 50% 90% 40%
MARILYN | 30% 90% 60%
B)
| 30% of 70% of Sum Final
| first test second test Mark
---------------+--------------------------------------------------------
MARK | 12% 56% 68%
JAKE | 15% 63% 78%
MARILYN | 9% 63% 72%
Jake did the best overall.

BACK

 George, Sam, Andrew and Brandon each had four dates
to four different Parish Center Dances with four
different girls, named Cher, Connie, Melissa and
Kendra. On the second date, George dated Connie and
Brandan dated Kendra. On the third date Andrew went
out with Melissa and Sam went out with Connie.
Melissa went out with George and Cher went out with
Sam on the fourth date. What couples went out together
on the first date if no pairs went out more than once?

Hint and answer

Hints:
 1) Make a chart to help you use logical
reasoning

Answer:
 Cher dated George.
 Brandan dated Melissa
 Connie dated Andrew
 Sam dated Kendra
BACK

 A large piece of construction paper is .01mm thick. It
is cut in half and one piece is placed on the other to
make a pile. These are cut in half and all four pieces
are placed in a pile. These four are cut in half and
placed in a pile, and the process is continued. After
the pieces have been cut and piled for the tenth time,
what is the height of the pile in cm.

Hint and answer

Solution and Answer
 Hints:
1) Try to draw a sketch of how many sheets are piled as the pile is cut
each time.
2) Now try to find a pattern in the numbers.

3) How many sheets will you have after the sheets are cut and piled 10
times.
4) How many cm high is this pile. Don't forget to change your mm to cm.
 Answer:
1 cut ---> 2 sheets
2 cuts---> 4 sheets
3 cuts---> 8 sheets
4 cuts---> 16 sheets
...
10 cuts--> 210 sheets
1024 (.01) = 10.24mm = 1.024 cm

BACK

 What is the sum of all the digits in the
sequence 1, 2, 3, 4, 5, 6, 7,...99, 100?
 NOTE: (Sum of the digits, not the
numbers!)

Hint and answer

Hints:
1) When all else fails, make a chart or a table. Start by writing the
numbers in columns and rows.
ex. 0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
| | | | | | | | | |
| | | | | | | | | |
2) Now examine the digits in the rows (horizontal). What do you
notice about digits? Try and find a pattern in the ones place.
3) Carry on to find a pattern in the ten's place.
4) Don't forget about the number 100!!
Answer:
10 (45) + 10 (45) + 1 = 901
1 + 10 * (the sum of the digits 1 to 9) + 10 * (the sum of the digits
1 to 9) = 901

BACK

 Silver's Cleaners decided to raise the price of
dry cleaning a sports coat from $4.00 to
$5.00. The same percentage increase was
applied to dry cleaning a jacket. The old cost
of dry cleaning a jacket was $10.00. What is
the new cost of dry cleaning a jacket?

Hint and answer

 Hints:
 1) To find the percentage increase in the dry
cleaning of a sports coat, set up an algebraic
equation.
 4 * x = 5.00
 2) Now what is the price of the new cost of dry
cleaning a jacket?
 Answer:
 Let x = percent increase
 4.00 * x = 5.00
 x = 5.00/4.00 * 100% = 125%
 10.00 * 125% = $12.50 is the new cost of cleaning
a jacket

BACK

A Christmas gift is tied with ribbon as
shown. The bow requires 47cm of
ribbon. What is the total length of the
ribbon in metres?

Hint and answer

 Hints:
 1) How many faces / sides are on a cube. How long is the piece
of ribbon on each side? Find the total length of the ribbon on
the sides.
 2) Now the top and the bottom look like:

 What is the total length of the ribbon for the top and bottom?
 3) Find the total length of all the ribbon in meters.
 Answer:
 On 4 sides 20cm of ribbon each = 80cm on the top and
bottom.
 .5 * 10cm = 25cm
 2 * 25cm = 50cm

 Total amount of ribbon 47cm + 50 cm + 80cm = 177cm =
1.77m

BACK

 Fourstrips of paneling 40 cm long and
4cm wide are arranged to form a
square. What is the area of the inner
square in cm2?

Hint and answer

 Hints:
 1) Draw and label the diagram with the
dimensions given.
 2) Now find the inner dimensions of the
paneling and find the area.

 Answer:


 362 = 1296 cm2
BACK

 In the following diagram of the front
view of the Great Pyramid, the measure
of the angle PRQ is 120 degrees, and
the measure of the angle PST is 110
degrees. What is the measure of the
angle RPS in degrees?

Hint and answer

 Hints:
 1) Do you remember how many degrees there are in a triangle or a
straight line?
 2) There are 180 degrees in a triangle. That is the sum of the angles in a
triangle is 180 degrees. A straight line is 180 degrees.

 3) Say your diagram was as the following:


 ? = 180 degrees - 150 degrees
 ? = 30 degrees
 4) Solve the problem!!!
 Answer:

 180 degrees - 120 degrees = 60 degrees
 60 degrees + 70 degrees = 130 degrees

BACK

 Mr. MacDonald recorded the test marks
for his eighth grade class of 25
students. He used the marks recorded
to calculate the average to be 72.
Sandra's mark of 86 was incorrectly
marked as 36. What was the correct
average for the test?

Hint and answer

 Hints:
1) What does Mr. MacDonald have to do to find the average
mark of his class?
2) Average means the sum of the test marks divided by the
number of students. So, what was the sum of all the
tests?
3) After you have the sum of all the tests you can find the
correct average by correcting Mr. MacDonald's sum and
finding the correct average.
 Answer:
x / 25 = 72
x = 1800 = the sum of all the grades
1800 - 36 + 86 = 1850
1800 / 25 = 74%

BACK

 Chip said to Dale "If you give me one acorn, then we
will have an equal number of acorns." Dale replied
with delight "If you give me one acorn, then I will
have double the number you have!" What was the
total number of acorns they had in their tree? How
many did Chip have and how many did Dale have?

Hint and answer

 Hints:
1) Try different numbers that will satisfy the
conditions given in the number.
2) The sum of the numbers of acorns is
twice six. Find out the how many Chip had
and Dale had.
 Answer:
Let C = # of acorns Chip had and D = #
acorns Dale had.
Then C + 1 = D - 1 ; D=! = 2(C-1).
Solve to get C = 5 and D = 7.
BACK

 Bart Simpson decided to make a graph
of his weekly earning of $120.00 from
his paper route. To make the size of
each sector proportional to the amount
distributed what does the angle x in
degrees have to be?

Hint and answer

 Hints:
1) One way to overcome this problem is to think of
percentages. What is the percent of $15 out of the
total $120 earnings?
2) Now we know what percent of his total earnings
is. How many degrees are in a circle?
3) The percent of money he spends on music is how
many degrees in the circle?
 Answer:
45 degrees
Percentages:
$15/$120 *100% = 12.5%
360 degrees * 12.5% = 45 degrees
BACK

 Jane was walking the long way home from school.
She started walking East. She walked 3 km East
when she met a dog. She ran back to the school and
decided to take the alternative route. So she walked
North 4 km to her home. If she had walked straight
home from where she met the dog, how far would it
have been to her home?

Hint and answer

 Hints:
1) Show diagram.
2) Do you remember how to find the missing side of a right triangle?
3) The Pythagorean theorem says, the hypotenuse, which is the longest
side opposite the right angle, is equal to the square root of the sums of
the squares of the other two sides.
Z 2 = X2 + Y2
4) How many additional meters would she have to walk?

 Answer:

42 + 33 = ?2
25 = ?2
5km = ? 3km + 5km = 8km
She would have to walk an additional 4 kilometers to get home from
where she met the dog.

BACK

 The Gillis's house has a pool with the
shape as shown. They want to make a
cover for it for the harsh winter. How
much to the nearest cent are they going
to have to spend on material if it costs
$5.00/m2.

Hint and answer

1) You must find the total area of the pool.
2) The pool can be divided into 3 different shapes.
3) The area of a circle is A = Pi * r2
4) Find the total amount of money given that it costs $5.00 per meter
squared.

Answer:
Areas: semi circle: area = Pi * radius squared
= 1/2 Pi * r2
= 1/2 Pi (2m)2
= 1/2 Pi (4m,sup>2)
= 2Pi m 2
triangle : area = 1/2 base * height
= 1/2 (3m)(4m)
= 6 m2
rectangle : area = (4m)(6m)
= 24 m2
Total area = 24 + 2Pi + 6 = 36.28 m2.
 Cost = $5.00/m * 36.28 m,sup>2 = $181.42
BACK

 Batman must solve the following
problem to escape the Riddler. The mid-
points of the sides of a square are
joined as shown. A fraction of the
original square is shaded. What is the
fraction? Can you help him?

Hint and answer

 Hints:
1) Divide the square into 4 equal parts.
Can you see the answer?
 Answer:
1/4

BACK

 Matthew is at a zoo. He takes a picture
of a one-metre snake beside a brick
wall. When he developed his pictures,
the one-metre snake is 2cm long and
the wall is 4.5cm high. What was the
actual height of the brick wall in cm.

Hint and answer

Hints:
1) If the snake is one meter long in real life and 2cm long in
the picture, how high is the building if it is 4.5cm long in
the picture.
2) The easiest way to do this is to set up a ratio like:
100 x
---- = ---
2cm 4.5cm
Solve for x, which is the height of the building.
Answer:
The snake is one meter long.
100/2 = x/4.5
x = 450/2 = 225cm high

BACK

 Joe's rich uncle gave him a looney on
his first birthday. On each birthday after
that he doubled his previous gift. By the
day after Joe's eight birthday, what was
the total amount that his uncle had
given him?

Hint and answer

Hints:
1) Make a chart
-> 1st birthday $1
2nd birthday $2
3rd birthday $4
|
|
2) How much did he get in total?
Answer:
1st birthday -> $1
2nd birthday -> $2
3rd birthday -> $4
$8
$16
$32
$64
$128
------
$255
BACK

 Ms. Smith, Ms. Gracia, and Ms. O'Leary all teach
at St. Andrew Junior High School. One of the
women is a mathematics teacher, one an art
teacher and one science teacher. The art teacher
, an only child, has taught the least number of
years. Ms. Garcia, who married Ms. Smith's
brother, has taught more years than the
mathematics teacher. Name the subject each
woman teaches.

Hint and answer

Hints:
1) Try to limit the amount of possibilities for each
teacher.
Example: Ms. Garcia can't teach art because she
has taught more years than the mathematics
teacher, and the art teacher has taught the
least number of years.
Answer:
Mathematics Science Art
| | |
Ms. Smith Ms. Gracia Ms. O'Leary

BACK

 Jim has three times as many comic
books as Charles. Charles has two-
thirds as many comic books as Bob.
Bob has 27 comic books. How many
comic books does Jim have.

Hint and answer

Hints:
1) The best way to approach this problem is to work
backwards. Try starting with statements: If Bob has 27
comic books and Charles has 2/3 as many, how many
does Charles have?
2) Jim has 3 times as many as Charles. So how many comic
books does Jim have?
3) If you need help in setting up equations, here's a start:
2/3 * # of Bob's comics = # of Charles comics
=>Now do the same thing for Jim:
3 * # of Charles comics = # of Jim's comics
Answer:
2/3 * 27 = # of Charle's comics = 18
Jim has 3 * 18 = 54 comic books

BACK

 Friendly'sClothing Store bought
handkerchiefs, six for $10, and sold
them 4 for $10. They made $60 profit.
How many handkerchiefs did they sell?

Hint and answer

Hints:
1) First try and calculate how much Friendly's paid for each handkerchief when they bought them and
how much a customer paid for each handkerchief. You can set up algebraic expressions to help
you.
6p = $10 and 4s = $10
p = price of hamdkerchiefs and s = selling price of handkerchief
-> Find p and s
2) Now how can we tackle how many handkerchiefs they sold if the store made $60.00? One way to
start is to set up an algebraic expressions that will solve for the number of handkerchiefs. If the
store pays $10/6 for a handkerchief and sells it for $2.50 then how many should it sell make
$60.00?
(s-p)*x = $60.00
-> Solve this algebraic equation for x, where x is the number of handkerchiefs.

Answer:
6 for $10 4 for $10.00
1 for $10/6
1 for $2.50
x$2.50 - x$10/6 = $60.00
.83x = $60.00
x = 72 handkerchiefs.

BACK

 You, in your new red Porsche, decide to
make a 160km trip to Carolina Beach,
travelling at 80km/hr. You make the
return trip travelling at a rate of
48km/hr. What was your average speed
for the entire trip?

Hint and answer

Hints:
1) In order to find the average speed, you must find the
tthe total time it took you to travel to and from
Carolina beach.
2) Remember: Rate = distance/time
3) The average speed is the total distance divided by
the total time.
Answer:
How many hours in total does it take you?
160km/80km/hr = 2hr 160km/48km/hr = 3.33hr
Average speed = (160 + 16)0/(2 + 3.33) = 60km/hr

BACK

 Who am I???
 The names of my mother, my father, my
brother, my sister and me in no
particular order are Sandy, Sharon, Pat,
Jennifer and Connie
 Pat is younger than I am.
 I am older than Connie.
 Sharon is younger than Jennifer.

Hint and answer

Hints:
1) This is a reasoning problem. Use the
clues to figure out the problem.
Answer:
· -You must be a girl,
· -Your brother Pat is younger than you,
· -Connie is a younger sister,
· -Jennifer must be the mother,
· -You are Sharon.
BACK

 The points A, B, C, D, and E are located
on a straight line in order.
 The distance from A to E is 20cm.
 The distance from A to D is 15cm.
 The distance from B to E is 10cm.
 C is halfway between B and D.
 What is the distance from B to C?

Hint and answer

Hints:
1) What is the distance from D to E?
2) What is the distance from B to D?
3) What is the distance from D to C?
Answer:
DE = 5cm
BE = 10cm
BC = 2.5cm
BACK

 Bob is reading a 445 page book. He has
already read 157 pages. If he reads 24
pages a day, how long will it take him to
finish the book?
 b) Bob read 157 pages of a 445 page
book. He finished the rest in 9 days.
How many pages did he average each
day while completing the book?

Hint and answer

Hints:
1) How many pages are in the book?
2) How many pages has Bob read?
3) How fast does he read?
4) How many page does Bob have left to read?
5) If Bob had 48 pages left to read, how many days would it take?
6) How should you determine the number of days it will take to read 288
pages?
b)
Hints:
1) Try using what you learned in part a to solve b.
Answer:
a)
445 - 157 = 288 pages left
288/24 = 12
It will take twelve days to finish the book.
b)
288/9 = 32 pages a day

BACK

 Pioneer Video is giving away a free movie to anyone
who can solve this puzzle. Place the numbers one to
nine in the squares so that none of the rows,
columns or diagonals have the same sum.
 | |
 ---+---+---
 | |
 ---+---+---
 | |
 Olivia won a free movie, what was her solution?

Solution and answer

Solution and Answer
 Hints:
1) This is a trial and error problem. You must first try one set and then add up the
rows, columns, and diagonals. If it works you've found an answer.
 Answer:
2|7|3
-----------
4|6|9
-----------
1|8|5

6|1|2
-----------
4|5|7
-----------
3|9|8

1|3|5
-----------
2|4|6
-----------
7|8|9

BACK

 Homer Simpson entered a pie eating
contest at the country fair. Homer was
determined to win and went into
training for 6 days. Each day he ate 4
more pies than the day before. Homer
ate 150 pies while in training. How
many pies did he eat each day?

Solution and answer

Solution and Answer
Hints:
1) Make a guess then check your guess!
2) If Homer ate one pie the first day how many would he eat the second
day?
3) If he ate 10 pies on the first day, how many would he have eaten all
together at the end of the 6 days?
4) Would guessing that Homer ate 20 pies on the first day be a good
guess?
5) Try another number!
Answer:
1st -> 15
2nd -> 19
3rd -> 23
4th -> 27
5th -> 31
6th -> 35
-----------
150 pies

BACK

 Belgium Cheese costs $1.70 for 1/2
kilograms. How much will 2 and 1/2
kilograms of cheese cost?

Solution and answer

Hints:
1) Set up a proportional equation
2) $1.70/ 1/2 kilogram = x/2.5 kilograms
Solve for x
Answer:
$1.70/.5 = x/ 2.5
.5x = 4.25/.5
x = $8.50
BACK

 The Canadian record for the most
consecutive sit-ups is 17,000 in 7 hours
and 27 minutes.
 At a rate of 40 sit-ups per minute, how
many hours and minutes would it take
to tie the record. Is this rate better than
the Canadian record?

Solution and answer

Hints:
1) How many sit-ups would you have to do to tie the record?
2) If you can do 40 sit-ups per minute, how many minutes does it
take to do 17,000?
3) To answer the secnd part, what is the rate of sit-ups/minute of
the Canadian record?
Whose rate is better?
Answer:
17000/7*60 + 27 = 38.03 sit-ups/min -> Record

17000/40 = 425 minutes = 7 hours and 5 minutes
Your rate is better!!

BACK

 On an algebra test, I had seven times as
many correct answers as incorrect
ones. There were 120 items on the test,
how many did I get right?

Solution and answer

Solution and Answer

Hints:
1) One way to approach this problem is with algebraic
expressions. Let x = # of incorrect answers. What does the
number of correct answers equal in terms of x?
2) The number of items on the test equals the number of incorrect
answers + the number of incorrect answers.
Answers:
x = # of incorrect answers
7x = # of correct answers
120 = 8x
x = 15 incorrect
7*15 = 105 correct

BACK

 IfI pile grapefruit in a pyramid with 1
grapefruit in the first layer, 4 in the
second layer (from the top), 9 in the
third layer, and 16 in the fourth layer,
how many grapefruit will I need to make
a pile with 10 layers?

Solution and answer

Solution and Answer
Hints:
1) Is there a pattern in piling the grapefruit?
2) Make a chart and find the sum.
1st 1
2nd 4
3rd 9
| |
| |
37)
Answer:
1 -> 4
2 -> 9
3 -> 16
4 -> 25
5 -> 36
6 -> 49
7 -> 64
8 -> 81
9 -> 100
----------------
385 grapefruit

BACK

 Big-Bird wants to make a picture frame for his picture of Elmo.
He is given the piece of plywood shown. He wants to make it in
a shape (the shaded area). In order to do so, he must connect
all the mid-points of the sides of a rectangle. What is the area of
the piece of wood he will be using for the picture frame? What
is the perimeter of the inside of frame?

Solution and answer

Hints:
1) Try to decide how you could break up the figure and find the area.
2) How would you find the perimeter? You must know the length of the
sides.
3) HINT!!! Divide the figure by connecting the midpoints of each side by a
line. Now do you
Answer:
x squared = 22 + 1.52 Perimeter = 4(2.5) = 10cm
x = 2.5

Area of a triangle = 1/2*bh
= .5 * 2 * 1.5
= 1.5

Area = 4(1.5) = 6 cm2

BACK

 What's the number I'm thinking of? It is
greater than 44 squared and less than
45 squared. 5 squared is one of its
factors, and it is a multiple of 13.

Solution and answer

Hints:
1) This is a trial and error problem. Answering these questions will
help you:
· a) What is the value of 44 squared?
· b) What is the value of 45 squared
· c) What is a factor? d) What does a mulitple mean? <- CHECK!!!!
Answer:
2025 > x > 1936
1950 = 13 * 150

BACK

A book exhibition was held for four
days in a school. Number of tickets sold
on first, second, third and fourth day
were 1094, 1812, 2050 and 2751
respectively. Find the total number of
tickets sold for the exhibition

Solution and answer

 Number of tickets sold on the first day = 1094

 Number of tickets sold on the second day = 1812

 Number of tickets sold on the third day = 2050

 Number of tickets sold on the fourth day = 2751

 Total number of tickets sold = 1094 + 1812 + 2050 +
2751 = 7707

 Hence total number of tickets sold = 7707 Ans
BACK

 Solve: (-7) - 8 - (-25)

Solution and answer

 (-7)- 8 - (-25)
 = -7 - 8 + 25

Collecting & Solving like terms
 = -15 + 25
 = 10 Ans

BACK

 Find cost of fencing a rectangular park
whose length is 250 m, breadth = 175 m
at P12 per meter.

Solution and answer

Length of rectangular park = 250 m
Breadth of rectangular park = 175 m
Perimeter of park = 2 (l + b)
= 2 (250 m + 175 m)
= 2 (425 m)
Thus, perimeter of park = 850 m
Cost of fencing 1 m = P 12
Cost of fencing 850 m = P 12 x 850
= P 10200
Ans
BACK

 The cost of 4 dozen bananas is Rs. 60.
How many bananas can be purchased for
Rs. 12.50 ?

Solution and answer

 Number of bananas bought for Rs. 60 = 4
dozen = 4 x 12 = 48
 Number of bananas bought for Re. 1 =

 Number of bananas bought for
Rs.12.50
= x 12.50 = 10

So, number of bananas bought for Rs. 12.50 =
10 Ans
BACK

 Aneesh made 42 runs in 6 overs. Anoop
made 63 runs in 7 overs. Who made
more runs in 1 over ?

Solution and answer

Aneesh made 42 runs in 6 overs.
 So, number of runs made in 1 over = = 7
Anoop made 63 runs in 7 overs
 So, number of runs made in 1 over = = 9

So, Anoop made more runs in 1
over

BACK

 The Band Committee of 100 people wishes to
set up a telephone call system. The initial
contact person calls three other people, each
of whom call three others and so on, until all
the people in the Band Committee have been
contacted. What is the maximum number of
people they need to make the calls.

Solution and answer

Hints:
1) Try and draw a flow chart to explain how the telephone system works.

2) How many people have to do the calling in order for 100 people to be
called?

ANSWER:
27 + 27 + 6 + 6 = 66

BACK

 Mark and Fred had some money in the
ratio 6:1. Mark gave half of his money to
Fred. Find the ratio of the amount of
money Mark had left to the amount of
money Fred had in the end.

Hint and answer

After

The ratio of the amount of money Mark had left to the amount of money Fred had in
the end is 3:4.
BACK

• Carol puts some green and red unit cubes in a
box. The ratio of the number of green cubes to
the number of red cubes is 2:1. She adds 12
more red cubes in the box and the ratio becomes
4:5.
• a) How many green cubes are there in the box?
• b) How many red cubes does Carol have in the
end?

Hint and answer

After

From the model, we see that:
a) 3 units = 12 cubes
1 unit = 12 ÷3 = 4 cubes
4 units = 4 × 4 = 16 cubes
There are 16 green cubes in the
box.
b) 5 units = 5 × 4 = 20 cubes
Carol has 20 red cubes in the end.

BACK

 The weight of 25 bags of rice is 650 kg.
Find the weight of hundred bags of rice?

Hint and answer

 since
the weight of 25 bags of rice is 650kg.
Then the weight of 1 bag of rice is 650 ÷ 25=
26kg
Then weight of 100 bags of rice is
26 x 100= 2600 kg
ANSWER
2600 kg

BACK

 FindHCF of 136, 170 and 255 by division
method

Hint and answer

 First we find the HCF of 136 and 170
136)170(1
136
34
HCF of 136 and 170 = 34

 Now we find the HCF of 34 and 255
34)255(7
238
17)34(2
34
0
 HCF of 34 and 255 =17
 Hence HCF of 136,170 and 255 = 17
 Find the LCM of 20, 30 and 50 by division method:
2] 20, 30, 50
5] 10, 15, 25
2, 3, 5
 LCM = 2x 5x 2x 3x 5 = 300

BACK

 Ken wants to make a half circle with a
diameter of 5 cm, using a metal wire. How
long is the wire he needs? What is the
area of the half circle? Use pi = 3.14

Hint and answer

 Length of the wire = (5 x 3.14) ÷ 2 + 5 =
12.85 cm
Area = (5/2)2 x 3.14 ÷ 2 = 9.81 cm2
Answer
 9.81 cm2

BACK

A satellite orbits the earth at a height of
343 kilometers. If it makes 8 revolutions
around the earth, how many kilometers
does it travel? Earth's diameter is 6371
kilometers. Use pi = 3.14

Hint and answer

 The diameter of the circle that the satellite
travels is 6371 + 2 x 343 = 7057
kilometers; The answer is: 7057 x 3.14 x 8
= 177271.84 kilometers
 Answer
177271.84 kilometers

BACK

 Jane went to the store to buy some
clothes. There was one sweater with an
original price of $40. It was 15% off that
day. Jane bought that sweater. (a) What
was the cost of the sweater? If Jane pays
8% sales tax, how much did Jane pay for
the sweater including the sales tax?

Hint and answer

 40x 15% = $6, $40 -$6 = $34 is the cost of
the sweater.
Sales tax is $34 x 8% = $2.72;
Therefore Jane paid $34 + $2.72 = $36.72

Answer
a) $34, b) $36.72

BACK

 Charlie Joe Purple has been taking math
tests. The average score of his first 3 test
is 95 points. The average score of his next
2 test is 90 points. What is the Charlie's
average score of all 5 tests?

Hint and answer

(95 x 3 + 90 x 2) ÷ 5 = 93

Answer
93

BACK

 5thgrade classes at Franklin Elementary
completed a final science test. The
average score of the female students is
82, and the average score of the male
students is 79. There are 42 girls, and 38
boys in the 5th grade. What is the average
test score of the entire 5th grade?

Hint and answer

Find the total score from all the students:
82 x 42 + 79 x 38 = 6446
Divide the total score by the total number
of students: 42 + 38 = 80
(82 x 42 + 79 x 38) ÷ (42 + 38) = 6446 ÷ 80
= 80.6
 Answer
80.6
BACK

 ABCD and MNOP are squares. M, N, O,
and P are at mid point of the 4 sides of
square ABCD. If MN is 8 inches, what is
the area of square ABCD?

Hint and answer

 Draw lines PN and MO. You can see that
area of square MNOP is half of the area of
ABCD. The area of square MNOP is 8 x 8
= 64 square inches;
 Area of ABCD = 2 x 64 = 128 square
inches
 Answer
128 square inches

BACK

 Smart multiplications

a) 39 x 5 x 20
b) 25 x 125 x 32

Hint and answer

 (a)
Rearrange the numbers to 39 x (5 x 20) =
39 x 100 = 3900

(b) Rearrange the numbers to 25 x 125 x 4 x
8 = 25 x 4 x 125 x 8 = 100 x 1000 =
100000 Answer

BACK

 The area of the rectangle is 224 square
inches. The length of the rectangle is 14
inches. What is the perimeter of the
rectangle?

Hint and answer

The other side of the rectangle is 224 ÷ 14 =
16.
The perimeter = 14 x 2 + 16 x 2 = 60
inches
Answer
60 inches

BACK

 Smart multiplications
a) 125 x 88
b) 108 x 125

Hint and answer

a) Rearrange the numbers to 125 x (80 + 8)
= 10000 + 1000 = 11000
b) Rearrange the numbers to (100 + 8) x
125 = 100 x 125 + 8 x 125 = 12500 + 1000
= 1350
Answers
a) 11000, b) 13500

BACK

Calculate

a) 36.12 x 7.8
b) 42.3 x 3.5

Hint and answer

Answer
a) 281.736, b) 148.05

BACK

Jerry's train has 4 cars of different colors,
yellow, green, red and blue. How many
different ways can Jerry arrange his train
cars?

Hint and answer

4 x 3 x 2 = 24
Answer
24

BACK

A basket has 15 apples, 8 oranges and 27
plums mixed randomly. If you close your
eyes and grab a fruit from the basket, what
is the probability of you getting an orange?

Hint and answer

The total number of fruits is 50. So the
probability of picking an orange is 8/50 or
4/25.

Answer
8/50=4/25

BACK

 Nina has sweaters that are pink, blue, red,
and gray. She has pants that are: khaki,
black and blue. How many different
combinations of sweaters and pants can
she wear?

Hint and answer

4 x 3 = 12

Answer
12

BACK

Use the signs “+”, “-” , “x”
and/or ( ) to make the equation
work. Find 2

Hint and answer

1) 1 + 2 + 3 + 4 + 5 + 6 + 7 + (8 x 9) = 100

2) (1 + 2) x 3 + (4 x 5) + 6 + (7 x 8) + 9 =
100

Answer: 100

BACK

 What is the surface area of the following
structure made of 5 cubes glued together.
The side of each cube is 1 inch? Only
consider the surfaces that are exposed.

Hint and answer

Count the number of cube you can see
systematically.

Answer
22 square inches

BACK

• Method 1:
Looking from front: 4; back: 4, Left: 3, right: 3, Top: 4, Bottom: 4;
The number of cube surfaces are 4 x 2 + 3 x 2 + 4 x 2 = 22 square
inches
• Method 2:
Surfaces by cube: The four visible cubes have 5 surfaces each. The
cube in the back has 2 surfaces.
The number of cube surfaces are 5 + 5 + 5 + 5 + 2 = 22 square
inches
• what are all the factors of 124?

Hint and answer

Answer
1, 2, 31, 62, 124

BACK

 Since 124 is an even number, 2 is a factor.
124 ÷ 2 = 62 which is an even number,
therefore 4 is a factor. 62 ÷ 2 = 31,
therefore 31 is a factor. 31 is a prime
number.
 What three consecutive odd numbers have
a product of 15525?

Hint and answer

Answer
23 x 25 x 27 = 15525

BACK

Fill in the squares with single digits (1
to 9) so that the sum of the 4 numbers
equals to 120.

Hint and answer

Start with the ones place. The sum is 0. Therefore the the sum of
the 4 digits at the one's place needs to be 10 or 20.
1 + 2 + 3 + 4 = 10, or 1 + 3 + 7 + 9 = 20. The sum of the 3 digits on
the tens place plus the carry over needs to be 10 or 11. Try them
out and you will get the answers.

Answer
There are more answers. Here is one
example

BACK

 Today is Saturday. What day of the week is
it 200 days from today?

Hint and answer

There are 7 days in a week. 200 ÷ 7 = 28R4;
Therefore, 200 days from today is Wednesday

Answer
Wednesday

BACK

 A, B and C each represents a different
number between 1 and 9. What do A, B
and C represent in the following addition
problem?

Hint and answer

 What is the surface area of the following
structure made of 8 cubes glued together.
The side of each cube is 1 inch. Only
consider the surfaces that are exposed.

Hint and answer

Answer
32 square inches

BACK

Count the number of cube you can see
systematically.
Looking from front: 4; back: 4, Left: 7,
right: 7, Top: 5, Bottom: 5;
The number of cube surfaces are 4 x 2 + 7
x 2 + 5 x 2 = 32 square inches

you have a blue coin and a yellow coin.
Place them in the following squares so
that the blue one is always 1 row above
the yellow one. How many different ways
are there to place them in this manner?

Hint and answer

 Blue one in the first row: 3,
Blue one in the 2nd row: 3 x 5 = 15;
Total = 3 + 15 = 18
Answer
18

BACK

 Find the sequence and fill in the blanks
 (1 ,4, 8), (2, 8, 16), (3, 12, 24), (4, 16, 32),
...
The 10th group is (__, __, __)

Hint and answer

Leading number sequence is 1, 2, 3, 4, 5, 6,
7, 8, 9, 10
Middle number sequence is 4, 8, 12, 16,
20, 24, 28, 32, 36, 40
The ending number sequence is 8, 16, 24,
32, 40, 48, 56, 64, 72, 80

Answer
(10, 40, 80)
BACK

A farmer has 150 rabbits. There are 4
times as many female rabbits as male
rabbits. How many male and female
rabbits are there?

Hint and answer

• Solutions: You do not need algebra to solve this
problem. Instead, use a graph shown to help solve the
problem. Each line represents an unknown number of
rabbits.
• Male rabbits ___
Female rabbits ___ ___ ___ ___
• There are totally 5 lines, which is equivalent to 150
rabbits. Therefore, each line represents 150 ÷ 5 = 30
rabbits;
Male rabbits = 30
Female rabbits = 30 x 4 = 120
Answer
Male rabbits = 30
Female rabbits = 120
BACK

 Annie, Betty and Corina went to the farm
to pick apples. The total number of apples
they picked were 120. Annie picked twice
as many as Betty did, and Betty picked 3
times as many as Corina did. How many
apples did they each pick?

Hint and answer

 You do not need algebra to solve this problem. Instead, use a graph shown
to help solve the problem. Each yellow bar represents some number of
apples. For example, the number of apples Corina picked is represented by
1 bar. Since Betty picked 3 times as many as Corina did; 3 yellow bars
represents what she picked. The number Annie picked is represented by 6
yellow bars. There are totally 10 bars, which is equivalent to 120 apples.
Therefore, each yellow bar is equivalent to 120 ÷ 10 = 12 apples. Therefore
Annie picked 72 (= 12 x 6) apples, Betty picked 36 (= 12 x 3) apples, and
Corina picked 12 apples.

Answer
Annie = 72
Betty = 32
Corina = 12
BACK

What is in the ones place of the product
below?
3 x 3 x 3 x 3 x 3 x 3........... to a total of
thirty-four three

Hint and answer

SOLUTION
3
3x3=9
3 x 3 x 3 = 27
3 x 3 x 3 x 3 = 81
3 x 3 x 3 x 3 x 3 = AB3
...........................
Answer
9

BACK

 Ling has some chickens and
rabbits. There are 22 feet and 8 heads in
all.
How many chickens and rabbits does Ling
have?

Hint and answer

First assume Ling has only chickens and no rabbits.
8 chickens would have 16 feet. However, since there are
22 feet in all, there are 6 extra feet (22 - 16 = 6).
Each rabbit has 2 additional feet compared with a chicken.
Therefore, there has to be 3 (6 divided by 2) rabbits.
ANSWER
Ling has 3 rabbits and 5 chickens.

BACK

 Rochelle took her final tests of several
subjects. Her average score NOT including
English is 88. Her average score including
English is 90. Her English score is 98. How
many subject tests did she take?

Hint and answer

The difference between the English score
and the average of the other subject test
scores is 98 - 88 = 10;
The increase in average score when
English is include is 90 – 88 = 2; The
number of tests is (98 - 88) ÷ (90-88) = 10
÷ 2= 5
ANSWER
5 subjects
BACK

 The length of AE is 80 millimeters. B is the
midpoint of AD, C is the midpoint of BD,
and D is the midpoint of CE. How long is
line AB?

Hint and answer

Answer
40 millimeters

BACK

 The diameter of the circles is 2 cm.
Calculate the area that is purple

Hint and answer

The purple area is the area of the square
subtract the area of the 4 circles. The sides
of the square is 4 cm.
Therefore the purple area is 4 x 4 - 4 x (3.14
x 1 x 1) = 3.44 square cm
ANSWER
3.44 square cm

BACK

 How many triangles are there?

Hint and answer

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