Assume the number of bulls he bought was X, the number of cows he bought was Y, and the number of calves he bought was Z. Thus, we have 2 equations:1). X + Y + Z = 1002). 10X + 5Y + 0.5Z = 100From equation 1, we can have Z = 100 - X – Y. If we substitute Z in equation 2, then we can come up with the equation: 19X + 9Y = 100.Since X and Y must be whole numbers, when X = 1 (minimum), Y will be the maximum (9). When Y = 1, X will be the maximum(4). We can easily figure out X = 1 and Y = 9. From equation 1, we can figure out Z = 90.The answer is: 1 Bull + 9 Cows + 90 Calves.
The canvas must be 10 inches wide and 20 inches high. The picture itself must be 6 inches in width and 12 inches in height.
Mathematics high school level quiz - Part I
Mathematics Quiz Ideas
The Quiz format (5 minutes)
Quiz will have two parts
The buzzing part
The doing part
Doing part – At the beginning of the quiz, each
group is handed cards with problems to be
solved. All groups have the same problems. The
team that solves announces the solution.
This round is also open to the teachers!!! You may
pick up the cards and try your hand at the quiz as
Each Q = 1 minute
Total time = 6 minutes
Warm –up!! Question # 1
In a triangle the centroid is the meeting
point of the
Warm –up!! Question #4
Use five 5s to get a target number 26
Can you plug in either addition(+),
subtraction(-), multiplication(x), division(/) and
parenthesis among five number 5s to make a
target result number 26?
(5 x 5 x 5) + 5) / 5 = 26
(5 / 5 / 5 + 5) x 5 = 26
Warm-up !! Question #5
Fill in numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9
into boxes to make the equation work.
Warm –up!! Question #6
There is a number whose double is
greater than its half by 45. Can you find
30 (its double 60 is 45 more than half of it
Real Math!! Round : 2
Each Q = 2 minutes
Total time = 12 minutes
Real Math!! Question #1
A shopkeeper marks the list price of an
article at 400% above its cost. He gives a
discount of 80% on the list price. He
a profit of 320%
no profit no loss
loss of 10%
loss of 20%.
Real Math!! Question #2
Next door to me live four brothers. Their
average height is 74 inches and the
difference in height among the first three
men is 2 inches. The difference between
the third and the fourth man is 6 inches.
What are their heights?
Flex your brain cells!! Round: 3
Each Q = 3 minutes
Total time = 18 minutes
Logic!! Question #1
An artist wanted to paint a picture on a
canvas which would allow for a margin of
4 inches on top and bottom and two
inches on each side. He wanted the
picture itself to occupy 72 square inches.
What would be the smallest dimensions,
the canvas should possess?
The canvas must be 10 inches wide and
20 inches high. The picture itself must be
6 inches in width and 12 inches in height.
Logic!! Question #2
Eight eggs look identical except one is
lighter. How can you weigh only 2 times on a
balance scale to find out which one is
If we give a number for each egg, said form 1 to 8.
We put egg 1, 2, and 3 on the left and egg 4, 5 and 6
on the right and weight them.
If they are balanced then we know egg 1 to 6 are OK.
We just need to put egg 7 on one side and egg 8 on
the other side and weight them.
Otherwise, one side will be lighter. We just assume
the left side is lighter we can just put egg 1 on the
left, egg 2 on the right, weight them one more time. If
they are balanced then egg 3 is lighter. Otherwise if
left side is lighter, ball 1 is lighter. If right side is
lighter, ball 2 is lighter.
Logic !! Question #3
Use the given relationships between the figures and
words to find two solutions:
= L A G
= L E B
= _ _ _
= R A B
= R E G
R E B R A G = ??
= L E G
R E B R A G =
Notice that horizontal figures both contain an L, the two vertical
figures contain an R.
The equation with two figures both contain a B and the equation with
three figures both have a G. The circles have an A and the
diamonds an E. Therefore,
L = horizontal R= vertical G = 3 B =2 A =
Logic!! Question #4
We paint each face of the 4 feet cube with
the color red, then cut the cube into 64 one
foot small cubes. How many small cubes
will have no red color on any side of the
cube? How many small cubes have 1 face with red
color? How many small cubes have 3 faces with red
If you cut out 2 feet from each side (one foot
from each end), the remaining cubes will
have 2 x 2 x2 = 8. Only 8 cubes have no
color. For each side, the middle 4 cubes have
one face with color.
There are 6 sides for a cube. Therefore there
are 4 x 6 = 24 cubes with one red face. Only
corner cube will have 3 red face.
Since there are 8 corners, 8 cubes have 3 red
Logic !! Question #5
I have a horse. Do you know what color it is?
A said, "I guess it is not black".
B said, "It is either brown, or gray". C said "I
know it is gray".
I said, "At least one of you is right and at least
one of you is wrong." What is the color of my
horse if the color is one of the above?
If the horse is brown. then every one is
right. This is not the answer.
If the horse is black, then every one is
wrong. This is not the answer either.
Therefore, the horse is gray. To verify
A was right, B was right, but C was
Logic !! Question #6
Solve the following:
ABCD x 4= DCBA
ON x 4 = GO
Problem solving Round :4
Each Q = 4 minutes
Total time = 24 minutes
Problem solving #1
A, B and C can walk at the rate of 3, 4 and 5
km per hour respectively. They start from the
same place at 07.00 AM, 08.00 AM and
09.00 AM respectively. When B catches up
with A, B sends back A with a message to C.
At what time does C get the message?
Problem solving #3
The sum of the infinite series ½ + ¼ +
1/8 + 1/16 ..........= 1. Then what is the
sum of the infinite series ¼ + 1/16 +
1/64 + 1/256..........?
1/3 (the diff between the denominator
and numerator of the first fraction is 3)
Problem solving #4
78% of all people are gum chewers and
35 % of all people are under the age of
fifteen. Given that a person has been
selected at random , what is the
probability that the person is not a gum
chewer and above age 15?
22% x 65% = 14.3% are not gum
chewers or above the age of fifteen.
Problem solving #5
The units digit of the number
( 1 + 9 + 92 + 93 + ………+ 92010 ) is:
Problem solving #6
One cement block balances evenly on the
scales with three quarters of a pound and three
quarters of a block. What is the weight of the
The block weighs 3 pounds
x = ¾ x + ¾ lb
Math Model Making!! Round :5
15 minutes for demo
Elvis the Elf decided to create a landing of
marble tiles on a rectangular area 13 x 5
sq.ft. He determined he needed 65 tiles,
measuring 1 sq. foot. He purchased 65
tiles but discovered that one was
damaged. He needed to cover the area
using only 64 tiles. How did he do this?
Model 1: Answer
Draw a 8 x 8 square and a 13 x 5
rectangle. Divide the square into 2
congruent triangles and 2 congruent
trapezia. And put these pieces together in
Model # 2
Verify the following identity
(a+b)2 = a2 + b2 + 2ab
Verify the following identity
(a+b+c)2 = a2 + b2 + c2 + 2ab + 2bc + 2cd
Model #2 : Answer
With 1 square of a2 units, 1 square of b2
units and 2 rectangles of area ab units.
Take a square of 18 units x 18 units and
divide into sections of 10 units, 6 units and
2 units. And demonstrate.
Proof of Pythagoras theorem
Using two squares of 17 units and 4 right
triangles of 5, 12 and 13 units
(a+b)3 = a3 + b3 + 3a2b + 3ab2
How do you form a cone from a sector of
Model #4 : Answer
Take cubes of dimension a units and b
units and 3 cuboids, using the above
dimensions. Place them together to show
Draw a circle and cut out a sector of
degree measure 120°.
Determine the area of a circle using the
area formula for a rectangle.
Determine the area of a trapezium.
Model #5: Answer
Draw a circle. Cut it into sectors. And
arrange the sectors to form a rectangle.
Using the formula for area of a rectangle,
arrive at the area of a circle.
Draw two congruent trapezia. Place them
in such a way as to get a parallelogram.
Now get the area of the trapezium.
This is a cube. Put it together and
determine what algebraic identity it
Written work!! Round :6
Answer discussion time: 10
Long time ago, a rancher spent $100.00 and
bought 100 animals. There were 3 kind of
animals he bought: each Bull cost him $10.00,
each Cow cost him $5.00 and each Calf cost
him $0.50. How many he bought for each kind of
1 Bull + 9 Cows + 90 Calves.
(Assume the number of bulls he bought was X, the number of
cows he bought was Y, and the number of calves he bought
was Z. Thus, we have 2 equations:
1). X + Y + Z = 100
2). 10X + 5Y + 0.5Z = 100
From equation 1, we can have Z = 100 - X – Y. If we substitute Z
in equation 2, then we can come up with the equation:
19X + 9Y = 100.
Since X and Y must be whole numbers, when X = 1 (minimum),
Y will be the maximum (9). When Y = 1, X will be the
maximum(4). We can easily figure out X = 1 and Y = 9. From
equation 1, we can figure out Z = 90.)
Solve the cryptarithm :
Four married couples played a tennis
tournament of “mixed doubles”. A man
and a woman always played against a
man and a woman. However, no person
ever played with or against any other
person more than once. They all played
together in two courts on three successive
days. Can you show how they could have
Two women were selling marbles in the market place –
one at three for a paisa and the other at two for a paisa.
One day both of them were obliged to return home when
they each had thirty marbles unsold. They put together
the two lots of marbles and handing them over to a friend
asked her to sell them at five for 2 paise. According to
them, 3 for one paisa and 2 for 1 paisa was the same as
5 for 2 paisa.
Now they were expecting to get 25 paise for the marbles,
as they would have got, had they sold separately. But
much to their surprise, they got only 24 paise for the
entire lot. Now where did the one paisa go? Can you
explain the mystery?
All the nine digits are arranged here
so as to form four square numbers. – 9,
81, 324, 576.
How would you put them together so as
to form a single smallest possible
square number and a single largest
possible square number?
Question # 6
Cubes and squares can be one and the
same. But if this so happens, they need
a new name. Squbes sounds ok, but can
you now tell where the next one is at?
64 729 4096 15625
The next one is 46656.
Disregarding the number 1, these
are the four consecutive lowest
numbers that are both cubes and
64 = 82 or 43 729 = 272 or 93
4096= 642 or 163 15625 = 1252
or 253 and the fifth is
46656 = 2162 or 363