A positive number A is shown on the number line as in the figure. Then, on this number line; numbers whose distance from 0 is equal to half the distance of number A from 0 are marked. If the distance from one of the marked numbers to number A is 6 units, what is the sum of the possible values of number A? A) 15 B) 16 C) 18 D) 20 E) 21
Let $a$ and $b$ be real numbers. The functions f and g are defined on the set of real numbers as $$\begin{aligned}
& f(x) = ax - b \\
& g(x) = bx - 2
\end{aligned}$$ Given that $$\begin{aligned}
& (f + g)(1) = f(1) \\
& (f + g)(2) = g(2)
\end{aligned}$$ what is the product $\mathbf{a} \cdot \mathbf{b}$? A) 2 B) 4 C) 6 D) 8 E) 10
In the rectangular coordinate plane, the graphs of functions $\mathrm{f}(\mathrm{x})$ and $\mathrm{g}(\mathrm{x})$ defined on the interval $[0,3]$ are given in the figure. For a number $\mathrm{a} \in (0,1)$, $$\begin{aligned}
& \mathrm{b} = (f \circ g)(a) \\
& c = (g \circ f)(a)
\end{aligned}$$ are determined. Accordingly, which of the following is the correct ordering of the numbers a, b, and c? A) a $<$ b $<$ c B) a $<$ c $<$ b C) b $<$ a $<$ c D) b $<$ c $<$ a E) c $<$ a $<$ b
An airline has a total of 8 cabin crew members with different work experience for one morning and one evening flight to be performed. Each of these employees will be on only one team, and two four-person flight teams will be formed from these employees such that the three most experienced employees are not on the same team. Accordingly, in how many different ways can the morning and evening flight teams be formed? A) 48 B) 54 C) 56 D) 60 E) 64
Below are four cards with the numbers 6, 8, 10, and 12 written on them. Seeing these cards, Yiğit makes the claim: ``If I randomly select two of the cards and add the numbers written on them, the probability that I find my age is $\frac{1}{3}$.'' Given that this claim is correct, what is Yiğit's age? A) 14 B) 16 C) 18 D) 20 E) 22
Emre marks a point on the x-axis of the Cartesian coordinate plane in a mathematics class activity. Then, by decreasing the x-coordinate of this marked point by 1 unit and increasing the y-coordinate by 3 units, he obtains a second point, and when he applies the same operation to the second point, he obtains a third point on the y-axis. What is the sum of the coordinates of the fourth point that Emre will obtain by applying the same operation to the third point? A) 4 B) 5 C) 6 D) 7 E) 8