A wooden block in the shape of a square prism with a base area of 16 square units and height of 3 units has all its surfaces painted. Then, this wooden block is cut to obtain 48 unit cubes.
Of the unit cubes obtained this way, how many have exactly two faces painted?
A) 10
B) 12
C) 14
D) 18
E) 20

A decoration as shown in dark color has been made on a floor covered with tiles in the shape of regular hexagons.
Given that the area of each hexagon is 1 square unit, what is the area covered by this decoration in square units?
A) 8
B) 9
C) 10
D) 11
E) 12

According to the given information, what is the area of the shaded region in $\mathbf { cm } ^ { \mathbf { 2 } }$?
A) $4 ( 3 \pi + 4 \sqrt { 3 } )$
B) $6 ( \pi + 4 \sqrt { 3 } )$
C) $6 ( 2 \pi + 3 \sqrt { 3 } )$
D) $12 ( \pi + 2 \sqrt { 3 } )$
E) $12 ( 2 \pi + \sqrt { 3 } )$

In the coordinate plane, the following regular hexagon ABCDEF with center at point O is given.
This hexagon is rotated $120 ^ { \circ }$ around its center in the direction of the arrow. After the rotation, the symmetry of the resulting hexagon with respect to the y-axis is taken.
According to this, which point arrives at the position where point F was located initially?
A) A
B) B
C) C
D) D
E) E

$$\begin{array} { r } A B D \\ - \quad B B C \\ \hline 294 \end{array} \quad \begin{array} { r } A C \\ - B D \\ \hline ? \end{array}$$
According to the subtraction operation given on the left, what is the result of the subtraction operation on the right?
A) 44
B) 36
C) 34
D) 26
E) 24

$\mathrm { p } : \sqrt { 3 } + \sqrt { 5 } = \sqrt { 8 }$ q: $\sqrt { 5 } - \sqrt { 3 } = \sqrt { 2 }$ r: $\sqrt { 3 } \cdot \sqrt { 5 } = \sqrt { 15 }$ The following propositions are given. Accordingly, which of the following compound propositions is true?
A) $p \wedge ( r \vee q )$
B) $( p \vee q ) \wedge r$
C) $r \Rightarrow ( p \wedge q )$
D) $p \vee ( r \Rightarrow q )$
E) $p \Rightarrow ( q \wedge r )$

When the distinct positive integers $a , 2 , b , 9$ and 6 are arranged from smallest to largest, the middle number is a.
Accordingly, which of the following cannot $b$ be?
A) 1
B) 3
C) 5
D) 8
E) 10

Let $d$ be the greatest common divisor of positive integers $a$ and $b$. I. The number $d ^ { 2 }$ divides the number $a ^ { 2 }$. II. The number $d ^ { 2 }$ divides the number $a ^ { 2 } + b$. III. The number $\mathrm { d } ^ { 2 }$ divides the number $\mathrm { a } ^ { 2 } + \mathrm { b } ^ { 2 }$. Which of the following statements are always true?
A) Only I
B) Only II
C) I and III
D) II and III
E) I, II and III

Let $A = \{ 1,2,3,4,5,6 \}$ and $f : A \rightarrow A$ is a one-to-one function.
Accordingly, $$f ( 1 ) + f ( 2 ) + f ( 3 ) + f ( 4 )$$
What is the difference between the maximum and minimum values that this sum can take?
A) 6
B) 7
C) 8
D) 9
E) 10

The table of an operation $\Delta$ defined on the set $A = \{ 1,2,3,4,5 \}$ is given below.

$\Delta$	1	2	3	4	5
1	5	1	3	2	4
2	3	2	1	4	5
3	2	3	4	5	1
4	5	4	1	3	2
5	1	5	4	2	3

Also, for $\mathrm { a } \in \mathrm { A }$, the set $\mathrm { M } ( \mathrm { a } ) = \{ \mathrm { b } \in \mathrm { A } \mid \mathrm { a } \Delta \mathrm { b } = \mathrm { b } \Delta \mathrm { a } \}$ is defined.
Accordingly, which of the following is the set $\mathbf { M } ( \mathbf { 4 } )$?
A) $\{ 1,2,4 \}$
B) $\{ 1,3,5 \}$
C) $\{ 2,3,4 \}$
D) $\{ 2,4,5 \}$
E) $\{ 3,4,5 \}$

Let x and y be two-digit natural numbers such that
$$x - y = 65$$
How many x numbers satisfy this equation?
A) 20
B) 25
C) 30
D) 35
E) 40

Let p be a prime number. If the number $\mathrm { p } + 2$ is prime or if the number $\mathrm { p } + 2$ can be written as the product of two prime numbers, then p is called a Chen prime.
Accordingly, which of the following is not a Chen prime?
A) 37
B) 59
C) 67
D) 73
E) 83

The average of the profits obtained by a company in 2009, 2010 and 2011 is 4 million TL. In 2012, the company obtained 25\% more profit than in 2011, and the average profit obtained in these four years became 4.5 million TL.
Accordingly, how much profit did the company obtain in 2011?
A) 4.8
B) 5
C) 5.2
D) 5.4
E) 5.6

In the calendar of an ancient civilization,
1 month has 36 days
1 year has 10 months exist. In this civilization, dates given in the order day-month-year in the form AB-CD-ABCD are called ``symmetric days.''
According to this calendar, how many days after the date 20-08-2008 will the next symmetric day occur?
A) 360
B) 396
C) 480
D) 720
E) 756

A teacher conducted the following activity in class with four of her students named Ali, Banu, Can, and Do\u011fa.

• These students each think of a number. Let these numbers be $\mathrm { A } , \mathrm { B } , \mathrm { C }$ and D respectively.
• Each student writes their own number on a piece of paper and gives it to the teacher.
• The teacher calculates the result of the following addition operations written on the board and fills in the right side of the equations.

$$\begin{aligned} & A + B = \\ & B + D = \\ & A + B + C = \end{aligned}$$
Based on what is written on the board, which students alone have sufficient information to find all four numbers A, B, C, and D?
A) Ali, Banu, and Do\u011fa
B) Ali, Can, and Do\u011fa
C) Ali and Banu
D) Banu and Can
E) Can and Do\u011fa

Below is an abacus consisting of five sufficiently long rods. On the abacus; 1 bead is placed on the 1st rod, 2 beads on the 2nd rod, and similarly, as many beads as its number are placed on the other rods. Thus the first round is completed as shown in the figure.
Then we start over and 6 beads are placed on the 1st rod, 7 beads on the 2nd rod, and similarly, one more bead than was placed on the previous rod is placed on the other rods. After each round, the number of beads on the 5th rod plus one is placed on the 1st rod, and the rounds continue.
Accordingly, on which rod will the 220th bead to be placed be located?
A) I.
B) II.
C) III.
D) IV.
E) V.

ABCD is a trapezoid $\mathrm { DC } / / \mathrm { AB }$ DE//CB DE is an angle bisector $\mathrm { m } ( \widehat { \mathrm { DAE } } ) = 70 ^ { \circ }$ $\mathrm { m } ( \widehat { \mathrm { BCD } } ) = \mathrm { x }$ According to the given information above, what is x in degrees?
A) 105
B) 110
C) 115
D) 120
E) 125

A square with side length a units is divided into a total of eight squares, seven of which are congruent, and the resulting large square is called $\mathrm { K } _ { 1 }$ (Figure 1). Then the square $\mathrm { K } _ { 1 }$ is similarly divided to obtain square $\mathrm { K } _ { 2 }$ (Figure 2). When square $\mathrm { K } _ { 2 }$ is similarly divided, the resulting square $\mathrm { K } _ { 3 }$ has a side length of 27 units.
Accordingly, what is a?
A) 36
B) 49
C) 64
D) 81
E) 100

Two tanks in the shape of right circular cylinders with equal heights and base radii of 2 meters and 3 meters respectively are initially empty. Two separate faucets that discharge the same amount of water per unit time are used; the faucet for the small tank is opened 5 minutes after the faucet for the large tank is opened. When the faucet for the small tank is opened, the height of water in the large tank is 2 meters.
Accordingly, how many minutes after water starts being supplied to the small tank will the water heights in the tanks be equal?
A) 2
B) 3
C) 4
D) 5
E) 6

$$\left( 1 - \frac { 3 } { 5 } \right) \left( 1 - \frac { 3 } { 8 } \right) \left( 1 - \frac { 5 } { 13 } \right)$$
What is the result of this operation?
A) $\frac { 1 } { 3 }$
B) $\frac { 2 } { 5 }$
C) $\frac { 5 } { 8 }$
D) $\frac { 2 } { 13 }$
E) $\frac { 8 } { 13 }$

$$0,75 - \frac { 0,2 } { 0,3 + \frac { 0,1 } { 0,5 } }$$
What is the result of this operation?
A) 0.25
B) 0.35
C) 0.45
D) 0.5
E) 0.6

For every positive integer $n$, the number $n$ is defined as
$$n = ( n ) ( n + 2 ) ( n + 4 ) ( n + 6 )$$
Given this, what is the value of the expression $\frac { 12 - 10 } { 8 }$?
A) $\frac { 3 } { 2 }$
B) $\frac { 5 } { 2 }$
C) $\frac { 7 } { 3 }$
D) $\frac { 1 } { 4 }$
E) $\frac { 8 } { 5 }$

$a , b , c , d$ are distinct real numbers and
$$\begin{aligned} & b + c = d \\ & a \cdot b \cdot c = 0 \end{aligned}$$
Which of the following is true?
A) $a = 0$
B) $b = 0$
C) $c = 0$
D) $a+c=0$
E) $a + d = 0$

When the two-digit natural numbers AB and BA are divided by 17, the sum of the remainders obtained is 17.
Given this, what is the value of $| A - B |$?
A) 1
B) 2
C) 3
D) 4
E) 5

$a$ is a positive integer and
$$\operatorname { LCM } ( 5 , a ) = \operatorname { GCD } ( 20 , a )$$
Given this, what is the sum of the values that $a$ can take?
A) 25
B) 30
C) 35
D) 40
E) 45