Let $\mathbf { x }$ and $\mathbf { y }$ be real numbers. $$2 ^ { x } - 2 ^ { -y } \left( 2 ^ { x+y } - 2 \right)$$ Which of the following is this expression equal to? A) $2 ^ { x+1 }$ B) $2 ^ { y-x }$ C) $2 ^ { -y+1 }$ D) $\frac { 2 } { 9 }$ E) $\frac { 4 } { 9 }$
For real numbers $x , y$ and $z$ $$\begin{aligned} & x \cdot y = 14 \\ & x \cdot z = 20 \\ & 3x + 2y + z = 24 \end{aligned}$$ Given that, what is x? A) $\frac { 8 } { 3 }$ B) $\frac { 14 } { 5 }$ C) 3
$$\begin{aligned} & x = \frac { a - b } { a + b } \\ & y = \frac { b - c } { b + c } \end{aligned}$$ Given that, which of the following is the equivalent of the expression $\frac { 1 + y } { 1 - x }$ in terms of $a , b$ and $c$? A) $\frac { b - c } { a - b }$ B) $\frac { b + c } { a - b }$ C) $\frac { a - b } { a + c }$ D) $\frac { a - c } { b - c }$ E) $\frac { a + b } { b + c }$
Let a be a real number. The distance of a from 1 on the number line is $a + 4$ units. Accordingly, what is $|a|$? A) $\frac { 3 } { 2 }$ B) $\frac { 5 } { 2 }$ C) $\frac { 7 } { 2 }$ D) $\frac { 7 } { 3 }$ E) $\frac { 8 } { 3 }$
In a foreign language course, the average age of students in classes $A , B$ and $C$ is 20, 26 and 29 respectively. The average age of students in classes A and B together is 23, and the average age of students in classes B and C together is 28. According to this, what is the average age of all students in these three classes? A) 25,5 B) 26 C) 26,5 D) 27 E) 27,5
Four students of different heights line up randomly in a row. According to this, what is the probability that the shortest and tallest students are at the ends? A) $\frac { 1 } { 2 }$ B) $\frac { 1 } { 3 }$ C) $\frac { 1 } { 4 }$ D) $\frac { 1 } { 6 }$ E) $\frac { 1 } { 12 }$
When 130 liters of milk in a dairy is used to make cheese, the graph of the linear relationship between the remaining milk and the amount of cheese produced is given. According to this, when 10 kg of cheese is produced in this dairy, how many liters of milk remain? A) 50 B) 60 C) 65 D) 75 E) 80
The figure below shows the construction used to obtain a square with an area equal to that of a given rectangle. ABCD is a rectangle, HDFG is a square, semicircle with center O $$A ( ABCD ) = A ( HDFG )$$ The F vertex of the square HDFG in the figure lies on the semicircle with center O. Given that the perimeter of rectangle ABCD is 36 cm, what is the diameter of the circle in cm? A) 12 B) 15 C) 18 D) 21 E) 24
Below is shown a structure made with two identical rectangular prisms with edge lengths of 2, 3, and 4 units. These prisms are placed adjacent to each other as shown in the figure. According to this, what is the length of the line segment AB connecting vertices A and B in units? A) $6 \sqrt { 2 }$ B) $8 \sqrt { 3 }$ C) $5 \sqrt { 5 }$ D) 7 E) 9