The total amount of oranges and mandarins in a warehouse is 50 tons. 7\% of the oranges and 8\% of the mandarins have rotted. The total amount of rotted oranges and mandarins is 3.8 tons.
Accordingly, how many tons of sound oranges are in the warehouse?
A) 17.5 B) 17.6 C) 18 D) 17 E) 18.6

If 3 women board a bus, $\frac{2}{3}$ of the passengers are women. If 4 men got off the bus, $\frac{1}{4}$ of the passengers would be men.
Accordingly, how many passengers are on the bus?
A) 32 B) 24 C) 21 D) 28 E) 30

The share of kindergartens among all schools in a province was 10\% in 2000 and 15\% in 2010. Of the 50 schools opened in this province between 2000-2010, 20 are kindergartens.
Accordingly, how many kindergartens were there in this province in 2000?
A) 30 B) 40 C) 20 D) 25 E) 35

ABC is an isosceles triangle, [AD] is an angle bisector
$$\mathrm{m}(\widehat{\mathrm{ACB}}) = 40^{\circ}$$ $$\mathrm{m}(\widehat{\mathrm{ADC}}) = x$$
In the isosceles triangle ABC above where $|\mathrm{AC}| = |\mathrm{BC}|$, what is x in degrees?
A) 105 B) 110 C) 115 D) 120 E) 125

ABC is a triangle
$|\mathrm{AD}| = |\mathrm{DC}|$
$|\mathrm{BF}| = |\mathrm{FD}|$
According to the given information above, what is the ratio $\frac{|AF|}{|FE|}$?
A) $\frac{7}{2}$ B) $\frac{8}{3}$ C) 2 D) $\frac{5}{2}$ E) 3

ABCD is a rhombus, DAF is a triangle
$$|CE| = 4 \text{ cm}$$ $$|EB| = 6 \text{ cm}$$ $$|BF| = x$$
According to the given information above, what is $x$ in cm?
A) 10 B) 12 C) 14 D) 9 E) 15

The reflection of the right triangle ABC given in the rectangular coordinate plane with respect to the y-axis is taken, and the triangle $A'B'C'$ is obtained such that A is paired with $A'$, B with $B'$, and C with $C'$ as symmetric point pairs. This obtained triangle is then rotated $90^{\circ}$ clockwise around point $A'$.
As a result of this rotation, what are the coordinates of the B'' point corresponding to $\mathrm{B}'$?
A) $(0, 3)$ B) $(2, 4)$ C) $(3, 5)$ D) $(4, 6)$ E) $(5, 4)$

A rectangular piece of paper ABCD shown below is folded so that vertices B and D coincide. Let E be the folding point on side [AB] such that $|AE| = 1$ unit.
As a result of the folding, the overlapping parts of the paper form a dark-colored equilateral triangular region DEF.
Accordingly, what is the area of the paper in square units?
A) $6\sqrt{2}$ B) $2\sqrt{2}$ C) $4\sqrt{3}$ D) $3\sqrt{3}$ E) $4\sqrt{2}$

$$A = \left[ \begin{array} { l l } 1 & 1 \\ 0 & 1 \end{array} \right], \quad B = \left[ \begin{array} { l l } 1 & 0 \\ \cdots & \cdots \end{array} \right]$$

What is the representation in base 2 of the number $(15)_8$ given in base 8?
A) $(1001)_2$
B) $(1011)_2$
C) $(1101)_2$
D) $(1110)_2$
E) $(1111)_2$

$$\frac { 10,25 } { 0,5 } - \frac { 3,1 } { 0,2 }$$
What is the result of this operation?
A) 5
B) 5,5
C) 6
D) 6,5
E) 7

$$\begin{array} { r } ABC \\ \times \quad 42 \\ \hline \ldots \\ + 864 \\ \hline \ldots \ldots \end{array}$$
According to what is given above, what is the result of the multiplication operation?
A) 8974
B) 9072
C) 9164
D) 9254
E) 9382

$$\begin{aligned} & A = \left[ \frac { -3 } { 2 } , \sqrt { 5 } \right] \\ & B = \left[ \sqrt { 3 } , \frac { 16 } { 3 } \right] \end{aligned}$$
For the closed intervals, how many elements does the set $( A \cup B ) \cap Z$ have? (Z is the set of integers.)
A) 4
B) 5
C) 6
D) 7
E) 8

For positive integers $a , b$ and $c$
$$8! - 6 \cdot ( 6! ) = 2 ^ { a } \cdot 3 ^ { b } \cdot 5 ^ { c }$$
Given that, what is the sum $\mathrm { a } + \mathrm { b } + \mathrm { c }$?
A) 7
B) 8
C) 9
D) 10
E) 11

$$\frac { x } { 2 \cdot 3 \cdot 5 } - \frac { y } { 2 ^ { 2 } \cdot 3 } + \frac { z } { 3 ^ { 2 } \cdot 5 } = \frac { 1 } { 10 }$$
Given that, what is the value of the expression $\mathbf { 6x } - \mathbf { 15y } + \mathbf { 4z }$?
A) 9
B) 11
C) 12
D) 15
E) 18

There is a relationship between positive integers $a$ and $b$
$$a = \operatorname { GCD } ( 2012 , b )$$
Accordingly, I. If a is an odd number, then b is an even number. II. If $a$ is an even number, then $b$ is also an even number. III. If b is an even number, then a is also an even number. Which of the following statements are true?
A) Only I
B) Only III
C) I and II
D) II and III
E) I, II and III

For a three-digit number $ABC$ $ABC = A ^ { 3 } + B ^ { 3 } + C ^ { 3 }$ if this holds, this number is called an Armstrong number. For example, since $153 = 1 ^ { 3 } + 5 ^ { 3 } + 3 ^ { 3 }$, 153 is an Armstrong number.
If the number 3K1 is an Armstrong number, what is the digit K?
A) 5
B) 6
C) 7
D) 8
E) 9

A student made an error while proving the following claim that he thought was true.
Claim: For any sets $A$, $B$, $C$, we have $A \backslash ( B \cap C ) \subseteq ( A \backslash B ) \cap ( A \backslash C )$.
The student's proof:
If I show that every element of the set $A \backslash ( B \cap C )$ is in the set $( A \backslash B ) \cap ( A \backslash C )$, the proof is complete.
Now, let $x \in A \backslash ( B \cap C )$. (I) From this, $x \in A$ and $x \notin ( B \cap C )$. (II) From this, $x \in A$ and $( x \notin B$ and $x \notin C )$. (III) From this, $( x \in A$ and $x \notin B )$ and $( x \in A$ and $x \notin C )$. (IV) From this, $x \in A \backslash B$ and $x \in A \backslash C$. (V) From this, $x \in [ ( A \backslash B ) \cap ( A \backslash C ) ]$.
In which of the numbered steps did this student make an error?
A) I
B) II
C) III
D) IV
E) V

All 60 walnuts will be distributed to $n$ students according to the following conditions:

• Each student will receive an equal number of walnuts.
• Each student will receive at least 2 and at most 10 walnuts.

Accordingly, how many different values can n take?
A) 5
B) 6
C) 7
D) 8
E) 9

For every real number a
$$a = 1 - a$$
is defined in this way. Accordingly, what is the value of $x$ that satisfies the equality $x - 2 = 3 [ x - 1$?
A) $\frac { -1 } { 2 }$
B) $\frac { -2 } { 5 }$
C) $\frac { 3 } { 5 }$
D) $\frac { 5 } { 7 }$
E) $\frac { 2 } { 7 }$

An operation $\Delta$ on the set of real numbers is defined for every real number $\mathrm { a } , \mathrm { b }$ as
$$\mathrm { a } \Delta \mathrm {~b} = \left( \mathrm { a } ^ { 2 } \cdot \mathrm {~b} \right) - \mathrm { a } + \mathrm { b }$$
Given that $x \neq y$ and $x \Delta y = y \Delta x$, what is the product $x \cdot y$?
A) 2
B) 3
C) 4
D) $\frac { 2 } { 3 }$
E) $\frac { 3 } { 4 }$

Ahmet who went to a restaurant has 40 TL, Burak has 30 TL and Cenk has 20 TL.
If these three friends share the 63 TL bill in direct proportion to their money, how much does Ahmet pay?
A) 21
B) 24
C) 25
D) 27
E) 28

A tea factory mixed 15 tons of type A tea costing 12 TL per kilogram with 20 tons of type B tea costing 9 TL per kilogram and sold the resulting blended tea at 11 TL per kilogram.
Accordingly, by how much TL does the revenue from the sale of blended tea exceed the revenue that would be obtained from selling the teas separately?
A) 24000
B) 25000
C) 28000
D) 30000
E) 36000

A certain number of pens will be distributed to a group of students. If these pens were 6 more or 7 fewer, they could be distributed equally without any remainder.
Accordingly, given that this number of pens is more than 112, what is the minimum number of pens?
A) 115
B) 124
C) 126
D) 130
E) 137

In a store, soaps are sold in packs of three and packs of two. The unit price of soaps in the three-pack is 10\% cheaper than the unit price of soaps in the two-pack.
Since the selling price of the three-pack in this store is 3.5 TL more than the selling price of the two-pack, what is the selling price of the two-pack in TL?
A) 7
B) 8
C) 10
D) 12
E) 14