Department of Mathematics and Statistics
AUS MathFest 2016
Student Name:
School:
Competition for Students
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Instructions:
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Duration: 75 minutes
This competition consists of 15 multiple choice questions
 Each question has one correct answer
 Enter your answers in pencil on the sheet provided.
 3 points for a correct answer
 −1 point for an incorrect answer
Calculators are not allowed
No cell phones
No questions or communication between participants
It is very unlikely you will be able to solve all the questions in the given
time
The results announced by the judges are final
Good Luck!
Name:
School:
1. The closest prime number to 118 is
a) 113
b) 117
c) 119
d) 121
e) 127
2. If one and a half chickens lay one and a half eggs in one and a half days then how many
eggs does one chicken lay in one day?
a) 1�3
b) 2�3
c) 3�2
d) 1
e) 2
3. If a circle has an area of 9 square meters then the diameter is
a) 3�𝜋
b) 6�𝜋
c) 3�
√𝜋
d) 6�
√𝜋
e) none of these
4. Four children, Safet, Sezadine, Kareem, and Muhamed, were playing outside my Villa
when suddenly I heard a loud noise followed by much shouting. I rushed out to find that
my window was broken with the soccer ball. Safet and Sezadine spoke almost at the same
time:
Safet saying, “It wasn't me!”
Sezadine saying, “It was Muhamed!”
Kareem yelled, “No, it was Sezadine!”
Muhamed said, with a straight face, “Sezadine is a liar.”
Only one of them was telling the truth, so who broke my window?
a) Safet
b) Sezadine
c) Kareem
d) Muhamed
5. Which one of the following numbers is the largest
a) 2002000
b) 95120
14
c) 2( 2 )
d) (64000) ∗ (64001) ∗ (64002) ∗ (64003) ∗ (64004) ∗ … ∗ (65000)
AUS MathFest
Competition for students
6. Thirteen students are taking both Math and English class. This number represents 13% of
all students taking Math class and 21% of all students taking English class. How many
students are taking at least one of those two classes?
a) 34
b) 169
c) 273
d) 162
e) 149
7. Two friends decided to explore the desert. They can walk only one direction (in a straight
line) and they have to come back in the same direction. Each one of them can carry food
supplies for 12 days. They can walk for 20 km in any given day. If they are not required
to return at the same time, what is the farthest distance that can be explored? (both have
to return)
a) 160
b) 140
c) 120
d) 100
e) 110
8. Suppose AUS has 2500 lockers and 2500 students both labeled from 1 to 2500. They
tried the following experiment. All lockers are initially closed. Then student number 1
opens all the lockers. Student number 2 closes the even numbered lockers. Student
number 3 changes the status (i.e. open to closed or closed to open) of all lockers that are
multiples of 3. This continues with each student changing the status of all the lockers
which are numbered by multiples of his or her number. After 700 students experimented,
what is the status of the locker 625?
a)
Open
b) Closed
c) It can’t be determined because 700 ≠ 625.
9.
The picture is of a steel beam supported on rollers. Say the circumference of each roller is
1 meter. How far forward will the beam have moved when the rollers have made one
complete revolution? (There is no slipping.)
𝑎) 𝜋
b) 2 𝜋
c) 1
d) 2
e) None of these
AUS MathFest
Competition for students
10. The value of: three plus three times three minus three divided by three plus three cubed
is:
a) 3�10
b) 30
c) 32
d) 33
e) 38
11. One of the AUS math professors was flying from South America to Dubai. He had a
connecting flight in Frankfurt in Germany. The connecting flight was late. He was bored
and decided to do something fun. He was walking around and found the moving
walkways very interesting. He measured the time and found out that he needs 1 minute to
walk the length of the walkway, moving in its forward direction. Walking at the same
rate in the opposite direction he needed 3 minutes to complete the same walkway. He
wanted to press the red button to stop the walkway and measure how long it will take him
to cover the same distance when the walkway is in the resting position. However, there
were security guards and he did not do it. He computed the time mathematically and
found out that he needs exactly:
a) 75 sec.
b) 90 sec.
c) 105 sec.
d) 120 sec.
e) 135 sec.
12. How many squares are in the figure below?
a) 26
b) 27
c) 30
d) 31
e) 34
AUS MathFest
Competition for students
13. Let 𝑎 and 𝑏 be two unequal numbers. We will show that 𝑎 = 𝑏.
Let 2𝑐 = 𝑎 + 𝑏. Then
𝑎2 − 𝑏 2 = 2𝑎𝑎 − 2𝑏𝑏
(multiply by (𝑎 − 𝑏) )
(1)
2
2
2
2
𝑎 − 2𝑎𝑎 + 𝑐 = 𝑏 − 2𝑏𝑏 + 𝑐 (add 𝑏 2 − 2𝑎𝑎 + 𝑐 2 )
(2)
(𝑎 − 𝑐)2 = (𝑏 − 𝑐)2
(factor both sides)
(3)
(4)
𝑎−𝑐 =𝑏−𝑐
(take square root)
(5)
𝑎=𝑏
(add 𝑐 to both sides)
In which line is the error:
a) 1
b) 2
c) 3
d) 4
e) 5
14. Four people toss a coin 16, 17, 18, and 19 times respectively. Which one is least likely to
have tossed more heads than tails?
a) 16
b) 17
c) 18
d) 19
15. The line segment AB is 1cm long, and it is tangent to the inner circle. Both circles have
the same center. What is the area of the region between the two circles.
a) 𝜋�3
b) 𝜋�2
A
c) 𝜋
1
d) 2 𝜋
B
e) 3 𝜋