A survey shows that $73 \%$ of the persons working in an office like coffee, whereas $65 \%$ like tea. If $x$ denotes the percentage of them, who like both coffee and tea, then $x$ cannot be:
(1) 63
(2) 36
(3) 54
(4) 38

Let $x$ and $y$ be distinct integers where $1 \leq x \leq 25$ and $1 \leq y \leq 25$. Then, the number of ways of choosing $x$ and $y$, such that $x + y$ is divisible by 5 , is $\_\_\_\_$ .

An integer is chosen at random from the integers $1,2,3 , \ldots , 50$. The probability that the chosen integer is a multiple of atleast one of 4, 6 and 7 is
(1) $\frac { 8 } { 25 }$
(2) $\frac { 21 } { 50 }$

A tour company has organized tours to three different museums. The following is known about those who participated in these tours.

• 30 people participated in each tour.
• 10 people participated in all three tours.
• 33 people participated in at least two tours.

Accordingly, how many people participated in only one of the tours?
A) 10
B) 11
C) 12
D) 13
E) 14

In the Venn diagram below

• Set A of names starting with the letter A,
• Set N of names ending with the letter N,
• Set B of 5-letter names

are shown.
Accordingly, $$\mathrm{K} = \{\mathrm{AÇELYA}, \mathrm{AHMET}, \mathrm{AYSUN}, \mathrm{BEREN}, \mathrm{KENAN}, \mathrm{NERMIN}\}$$
how many elements of the set are elements of the set represented by the shaded regions in the figure?
A) 1
B) 2
C) 3
D) 4
E) 5

For each of the 25 guests attending an opening, one glass each of mandarin juice, pomegranate juice, and orange juice was prepared and served to the guests. The following are known about these beverages served.

• All guests took at least one type of beverage.
• No guest took more than one glass of the same type of beverage.
• No guest took exactly two types of beverages.

At the end of the opening, it was determined that 7 glasses of mandarin juice, 8 glasses of pomegranate juice, and 9 glasses of orange juice were not taken.
Accordingly, how many guests at this opening took all three types of beverages?
A) 7
B) 9
C) 11
D) 13
E) 15

In the Venn diagram below

• Set A represents integers divisible by 2 without remainder,
• Set B represents integers divisible by 3 without remainder,
• Set C represents integers divisible by 12 without remainder.

Accordingly,
I. 18
II. 24
III. 42
Which of these numbers is an element of the set represented by the shaded region?
A) Only I
B) Only II
C) I and II

In a friend group consisting of two girls and three boys, the girls' names are AYLIN and BENSU, and two of the boys' names are AKIN and KENAN.
The set of letters in the girls' names is set X, and the set of letters in the boys' names is set Y.
Given that $\mathbf{X} \cap \mathbf{Y} = \{\mathbf{A}, \mathbf{B}, \mathbf{E}, \mathbf{N}, \mathbf{U}\}$, which of the following could be the name of the other boy in the friend group?
A) BARIŞ B) BILAL C) BURAY D) BULUT E) BURAK