Set 6

:00

Given two lines $y = 2x + 3$ and $y = ax + b$ have an intersection point. Determine the intersection point!

Decide whether statements $(1)$ and $(2)$ below are sufficient to answer the question.

$a \neq 2$
$b = 3$

Statement $(1)$ ALONE is sufficient, but statement $(2)$ alone is not sufficient.

Statement $(2)$ ALONE is sufficient, but statement $(1)$ alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements $(1)$ and $(2)$ TOGETHER are NOT sufficient.

A piece of wood weighs $90$ grams. After being dried in the sun, it weighs $60$ grams. What is the percentage of water content in the wet wood?

A family has $3$ children. It is known that at least one of the children is a girl. The probability that the family has $2$ girls and $1$ boy is

From the data $4$ , $5$ , $5$ , $2$ , $3$ , $1$ , $6$ , which statements are true?

Median $= 4$ .
Range $= 6$ .
Range $-$ median $= 1$ .
Mean $= 4.5$ .

$(1)$ , $(2)$ , and $(3)$ ONLY are correct.

$(1)$ and $(3)$ ONLY are correct.

$(2)$ and $(4)$ ONLY are correct.

ONLY $(4)$ is correct.

ALL choices are correct.

If $x$ and $y$ are integers satisfying $x^2 + y^2 = 169$ , then the possible values for $x + y$ are

$\pm 7$
$\pm 10$
$\pm 13$
$\pm 14$

$(1)$ , $(2)$ , and $(3)$ ONLY are correct.

$(1)$ and $(3)$ ONLY are correct.

$(2)$ and $(4)$ ONLY are correct.

ONLY $(4)$ is correct.

ALL choices are correct.

Given functions $f(x) = 2x - 3$ and $(g \circ f)(x) = 4x^2 - 12x + 10$ . The value of $g(1)$ is ....

The value of $x$ that satisfies $\begin{vmatrix} 3x & x \\ 2 & x \end{vmatrix} = \begin{vmatrix} 3 & 1 \\ 1 & 2 \end{vmatrix}$ is ....

$5 \text{ and } -3$

$-5 \text{ and } 3$

$\frac{5}{3} \text{ and } -1$

$-\frac{5}{3} \text{ and } 1$

$5 \text{ and } -1$

If $W(P@Q\#R) = 2P^2 - Q + 3\sqrt{R}$ , then the value of $W(5@8\#4) =$ ....

Consider the following plane figures:

Isosceles right triangle.
Right trapezoid (not a rectangle).
Rectangle (not a square).
Rhombus (not a square).

How many figures have the number of rotational symmetries equal to the number of folding symmetries (lines of symmetry)?

Given $a_1 = 8$ , $a_2 = -5$ , and $a_{n+1} = a_{n+2} - 4a_n$ . The value of $a_3 + a_4$ is ....

The ratio of a miniature of an object to its actual size is as follows. Miniature size : actual size = $5 : 2500$ If there is a rectangular object with an area of $540\text{ m}^2$ and a length of $30\text{ m}$ , then the width of the miniature of the object is ... cm.

The value of $a$ in the figure below is ...

Triangle

Geometric illustration with labeled angles.

For $0 < x < 1$ . Which of the following relationships is correct between quantities $P$ and $Q$ based on the information provided?

$P$	$Q$
$\frac{1-x^4}{1-x^2}$	$2+x$

If $g(x) = 3x + 2$ and $2g^2(x) - g(x^2) - 5g(x) = 7$ are satisfied by $x_1$ and $x_2$ , then the value of $x_1 + x_2$ is ...

The average of three numbers is $24$ . If one of the numbers is replaced by the number $14$ , the average of the three numbers decreases by $3$ .

$P$	$Q$
The number being replaced	$42$

To complete the construction of a building, $15$ people are needed to work for $35$ days. However, the building owner wants the building to be finished in $3$ weeks. To finish exactly as desired by the building owner, ... additional workers are needed.

Given an integer $m$ , if $m$ is divided by $7$ the remainder is $3$ , and if $m$ is divided by $3$ the remainder is $2$ . Possible values for $m$ are

$52$
$59$
$42$
$38$

If $(1)$ , $(2)$ , and $(3)$ are correct.

If $(1)$ and $(3)$ are correct.

If $(2)$ and $(4)$ are correct.

If only $(4)$ is correct.

If all are correct.

In a district, a survey was conducted on $300$ teenagers. There are $135$ people who participate in sports activities, and $255$ people who participate in nature lover activities. If $A$ is the minimum number of teenagers who participate in both and $B$ is the maximum number of teenagers who participate in both. Then the difference between $B$ and $A$ is ... people.

Given the following graph:

Function Graph

Graph of linear and exponential functions.

point $A(0, -2)$
point $B(0, 6)$
point $C(-3, 0)$
point $D(-2, 2)$

The correct statements are

If $f(x) = 5 - 4x^2$ and $g(x) = \frac{3x - 5}{2}$ , then $(f \circ g)(x) =$ ...

$-9x^2 + 30x + 30$

$-9x^2 + 30x - 20$

$-9x^2 - 30x - 20$

$-9x^2 + 30$

$-9x^2 - 20$

Try Out 2026

Set 6

:00

Given two lines $y = 2x + 3$ and $y = ax + b$ have an intersection point. Determine the intersection point!

Decide whether statements $(1)$ and $(2)$ below are sufficient to answer the question.

$a \neq 2$
$b = 3$

Statement $(1)$ ALONE is sufficient, but statement $(2)$ alone is not sufficient.

Statement $(2)$ ALONE is sufficient, but statement $(1)$ alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements $(1)$ and $(2)$ TOGETHER are NOT sufficient.

A piece of wood weighs $90$ grams. After being dried in the sun, it weighs $60$ grams. What is the percentage of water content in the wet wood?

A family has $3$ children. It is known that at least one of the children is a girl. The probability that the family has $2$ girls and $1$ boy is

From the data $4$ , $5$ , $5$ , $2$ , $3$ , $1$ , $6$ , which statements are true?

Median $= 4$ .
Range $= 6$ .
Range $-$ median $= 1$ .
Mean $= 4.5$ .

$(1)$ , $(2)$ , and $(3)$ ONLY are correct.

$(1)$ and $(3)$ ONLY are correct.

$(2)$ and $(4)$ ONLY are correct.

ONLY $(4)$ is correct.

ALL choices are correct.

If $x$ and $y$ are integers satisfying $x^2 + y^2 = 169$ , then the possible values for $x + y$ are

$\pm 7$
$\pm 10$
$\pm 13$
$\pm 14$

$(1)$ , $(2)$ , and $(3)$ ONLY are correct.

$(1)$ and $(3)$ ONLY are correct.

$(2)$ and $(4)$ ONLY are correct.

ONLY $(4)$ is correct.

ALL choices are correct.

Given functions $f(x) = 2x - 3$ and $(g \circ f)(x) = 4x^2 - 12x + 10$ . The value of $g(1)$ is ....

The value of $x$ that satisfies $\begin{vmatrix} 3x & x \\ 2 & x \end{vmatrix} = \begin{vmatrix} 3 & 1 \\ 1 & 2 \end{vmatrix}$ is ....

$5 \text{ and } -3$

$-5 \text{ and } 3$

$\frac{5}{3} \text{ and } -1$

$-\frac{5}{3} \text{ and } 1$

$5 \text{ and } -1$

If $W(P@Q\#R) = 2P^2 - Q + 3\sqrt{R}$ , then the value of $W(5@8\#4) =$ ....

Consider the following plane figures:

Isosceles right triangle.
Right trapezoid (not a rectangle).
Rectangle (not a square).
Rhombus (not a square).

How many figures have the number of rotational symmetries equal to the number of folding symmetries (lines of symmetry)?

Given $a_1 = 8$ , $a_2 = -5$ , and $a_{n+1} = a_{n+2} - 4a_n$ . The value of $a_3 + a_4$ is ....

The value of $a$ in the figure below is ...

Triangle

Geometric illustration with labeled angles.

For $0 < x < 1$ . Which of the following relationships is correct between quantities $P$ and $Q$ based on the information provided?

$P$	$Q$
$\frac{1-x^4}{1-x^2}$	$2+x$

If $g(x) = 3x + 2$ and $2g^2(x) - g(x^2) - 5g(x) = 7$ are satisfied by $x_1$ and $x_2$ , then the value of $x_1 + x_2$ is ...

The average of three numbers is $24$ . If one of the numbers is replaced by the number $14$ , the average of the three numbers decreases by $3$ .

$P$	$Q$
The number being replaced	$42$

Given an integer $m$ , if $m$ is divided by $7$ the remainder is $3$ , and if $m$ is divided by $3$ the remainder is $2$ . Possible values for $m$ are

$52$
$59$
$42$
$38$

If $(1)$ , $(2)$ , and $(3)$ are correct.

If $(1)$ and $(3)$ are correct.

If $(2)$ and $(4)$ are correct.

If only $(4)$ is correct.

If all are correct.

Given the following graph:

Function Graph

Graph of linear and exponential functions.

point $A(0, -2)$
point $B(0, 6)$
point $C(-3, 0)$
point $D(-2, 2)$

The correct statements are

If $f(x) = 5 - 4x^2$ and $g(x) = \frac{3x - 5}{2}$ , then $(f \circ g)(x) =$ ...

$-9x^2 + 30x + 30$

$-9x^2 + 30x - 20$

$-9x^2 - 30x - 20$

$-9x^2 + 30$

$-9x^2 - 20$

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