Question 171
Uma pesquisa mostrou que, em um grupo de 200 pessoas, 120 gostam de futebol, 90 gostam de vôlei e 40 gostam de ambos os esportes. O número de pessoas que não gostam de nenhum dos dois esportes é
(A) 10 (B) 20 (C) 30 (D) 40 (E) 50

Em uma sala de aula com 30 alunos, 18 estudam Matemática, 15 estudam Física e 8 estudam ambas as disciplinas. O número de alunos que não estudam nenhuma das duas disciplinas é
(A) 3 (B) 5 (C) 7 (D) 10 (E) 12

In a class of 30 students, 18 study mathematics, 15 study physics, and 8 study both subjects. How many students study neither mathematics nor physics?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Each student in a small school has to be a member of at least one of THREE school clubs. It is known that each club has 35 members. It is not known how many students are members of two of the three clubs, but it is known that exactly 10 students are members of all three clubs. What is the largest possible total number of students in the school? What is the smallest possible total number of students in the school?

Let the universal set $U = \mathbb{R}$, set $M = \{ x \mid x < 1 \}$, $N = \{ x \mid - 1 < x < 2 \}$, then $\{ x \mid x \geqslant 2 \} =$
A. $C _ { U } ( M \cup N )$
B. $N \cup C _ { U } M$
C. $C _ { U } ( M \cap N )$
D. $M \cup C _ { U } N$

144. In a bag there are $7$ white beads, $5$ black beads, and $3$ green beads. We draw beads from the bag until we are sure we have at least $4$ white beads or $3$ black beads or $2$ green beads. What is the minimum number of beads drawn?
(1) $6$ (2) $7$ (3) $8$ (4) $9$

101. In a class of 39 students, 16 are in the sports group, 12 are in the newspaper group, and 9 are only in the sports group. How many of these students are in neither of these two groups?
(1) $15$ (2) $16$ (3) $17$ (4) $18$

144- In a group of 7 literature books, 2 art books, and 10 mathematics books. At least how many books must we take from this group so that we are certain that, with at least 4 books, both subjects are represented?
\[ (1)\quad 10 \qquad (2)\quad 9 \qquad (3)\quad 8 \qquad (4)\quad 7 \]

Find the number of positive integers less than or equal to 6300 which are not divisible by 3, 5 and 7.

In a class of 45 students, three students can write well using either hand. The number of students who can write well only with the right hand is 24 more than the number of those who write well only with the left hand. Then, the number of students who can write well with the right hand is:
(A) 33
(B) 36
(C) 39
(D) 41

Let $X$ be the set consisting of the first 2018 terms of the arithmetic progression $1,6,11 , \ldots$, and $Y$ be the set consisting of the first 2018 terms of the arithmetic progression $9,16,23 , \ldots$. Then, the number of elements in the set $X \cup Y$ is $\_\_\_\_$.

In a study about a pandemic, data of 900 persons was collected. It was found that
190 persons had symptom of fever, 220 persons had symptom of cough, 220 persons had symptom of breathing problem, 330 persons had symptom of fever or cough or both, 350 persons had symptom of cough or breathing problem or both, 340 persons had symptom of fever or breathing problem or both, 30 persons had all three symptoms (fever, cough and breathing problem). If a person is chosen randomly from these 900 persons, then the probability that the person has at most one symptom is $\_\_\_\_$.

In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is:
(1) 42
(2) 1
(3) 38
(4) 102

In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :
(1) $\frac { 1 } { 6 }$
(2) $\frac { 5 } { 6 }$
(3) $\frac { 1 } { 3 }$
(4) $\frac { 2 } { 3 }$

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

The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7 is $\_\_\_\_$.

Let $A = \{ n \in [ 100,700 ] \cap \mathbb { N } : n$ is neither a multiple of 3 nor a multiple of $4 \}$. Then the number of elements in $A$ is
(1) 290
(2) 280
(3) 300
(4) 310

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) $\frac { 21 } { 50 }$

Q63. Let $A = \{ n \in [ 100,700 ] \cap \mathbb { N } : n$ is neither a multiple of 3 nor a multiple of $4 \}$. Then the number of elements in $A$ is
(1) 290
(2) 280
(3) 300
(4) 310

$$\begin{aligned} & A = \left\{ n \in Z ^ { + } \mid n \leq 100 ; n \text{ is divisible by } 3 \right\} \\ & B = \left\{ n \in Z ^ { + } \mid n \leq 100 ; n \text{ is divisible by } 5 \right\} \end{aligned}$$
The sets are given. Accordingly, how many elements does the difference set $\mathrm { A } \backslash \mathrm { B }$ have?
A) 33
B) 32
C) 30
D) 28
E) 27

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

Let $a$ and $b$ be digits. Given the sets
$$\begin{aligned} & A = \{ 5,6,7,8,9 \} \\ & B = \{ 1,4,5,7 \} \\ & C = \{ a , b \} \end{aligned}$$
If the number of elements in the Cartesian product $(A \cup C) \times (B \cup C)$ is 28, what is the sum $a + b$?
A) 5
B) 6
C) 8
D) 9
E) 11