Let $a \in \{-6, -4, -2, 2, 4, 6\}$ be the leading coefficient of a real-coefficient cubic polynomial $f(x)$. If the graph of the function $y = f(x)$ intersects the $x$-axis at three points whose $x$-coordinates form an arithmetic sequence with first term $-7$ and common difference $a$, how many values of $a$ satisfy $f(0) > 0$? (1) 1 (2) 2 (3) 3 (4) 4 (5) 5
Sequence 1 is an arithmetic progression with first term 11 and common difference 3. Sequence 2 is an arithmetic progression with first term 2 and common difference 5. Some numbers that appear in Sequence 1 also appear in Sequence 2. Let $N$ be the 20th such number. What is the remainder when $N$ is divided by 7 ?
A selection, $S$, of $n$ terms is taken from the arithmetic sequence $1,4,7,10 , \ldots , 70$. Consider the following statement: (*) There are two distinct terms in $S$ whose sum is 74 . What is the smallest value of $n$ for which (*) is necessarily true? A 12 B 13 C 14 D 21 E 22 F 23
For integers $\mathrm { x } , \mathrm { y }$ and z $$2 x = 3 y = 5 z$$ Given this, which of the possible values of the sum $x + y + z$ is closest to 100? A) 93 B) 96 C) 98 D) 103 E) 105
A school principal sends an electronic mail on Monday to some students of the school containing the note, ``Every student who receives this message should send it to two students the next day.'' The students who receive the message follow what is written in that note. By the end of Friday of the same week, this message reaches all students in the school and each student receives this message only once. Given that the number of students in the school is 930, how many students was this message initially sent to? A) 6 B) 10 C) 15 D) 21 E) 30
On a circular playground, five players named Ali, Büşra, Cem, Deniz, and Ekin are playing with a ball in positions shown in the figure. In each turn of this game; the player holding the ball passes it to the third player after them in the direction of the arrow. Initially, the ball is in Ali's hands and the game starts when Ali passes the ball to Deniz. Deniz received the ball on the 1st turn, Büşra on the 2nd turn, and the game continued in this way. Accordingly, who received the ball on the 99th turn? A) Ali B) Büşra C) Cem D) Deniz E) Ekin
When all of the numbers 1, 2, 3, 4, 5, 6, and 7 are placed in 7 boxes with addition or subtraction symbols between them, with one number in each box, the result of the operation obtained is 4. $$\square + \square + \square + \square + \square - \mathrm { A } - \mathrm { B } = 4$$ Accordingly, what is the product A · B? A) 15 B) 24 C) 28 D) 30 E) 35