DSAT extra practice Ch1 Lv3

Every evening after dinner, Lindsey walks her dog named Pepper. Assuming Lindsey’s home, Lindsey, and Pepper coordinates are 0, [math]x[/math], and 18 respectively. If the distance between Lindsey and Pepper is three times the distance between the Pepper and her home minus 2 meters. Which absolute value equation expresses their positional relationship?

$$2|6-x|+10$$If [math]x<6[/math], which of the following expressions is equivalent to the expression above?

$$|x-2|+|2-x|$$Which of the following expressions is equivalent to the expression above?

When the reciprocal of a negative number [math]m[/math] is divided by 18, the result is equal to [math]2m[/math]. Which of the following numbers could be [math]m[/math]?

Gordon uses a scissor to cut a rope into two pieces. Twice the length of the longer piece is six less than four times the length of the shorter piece. If the initial rope is 72 m, what is the length, in meters, of the longer piece?

If [math]a^2=11(b+c)[/math] where [math]a\neq0[/math], what is the value of [math]a^4(b+c)^{-2}[/math]?

$$((xy)^2z^{-1})^2\cdot(x^{-3}(y^2z)^2)^{-3}$$If the expression above can be written as [math]x^py^qz^r[/math] where [math]p, q[/math], and [math]r[/math] are constants, what is the value of [math]|p+q+r|[/math]?

Wesley, Jackie, and Mir have [math]x[/math], [math]y[/math], and [math]z[/math] marbles respectively. The ratio of [math]y[/math] to [math]z[/math] is 2:3 and the ratio of [math]x[/math] to [math]z[/math] is 3:4. Since they play marbles during Mr. Fang’s class, Mr. Fang confiscated all their marbles. Suppose Mr. Fang confiscated 116 marbles, how many marbles did Jackie have?

Let [math]a, b,[/math] and [math]c[/math] be three numbers. Suppose [math]3a=2b[/math] and [math]4a=5c[/math]. What is the value of [math]\dfrac{b}{c}[/math]?

Pure silver has a density of 1.049 grams per cubic centimeter. Andy has a pure sliver chain. Its volume of the chain is 250 cubic millimeters. What how many grams does Andy’s silver chain weigh?

To prevent getting a fine for speeding, Mr. Monkey usually looks at his dashboard while driving a car. However, he accidentally pressed the button for converting units. Suppose the dashboard shows 15 meters per second. What is the speed, in kilometers per hour of Mr. Monkey?

If [math]1\leq x<7[/math] and [math]-6<y\leq3[/math], what is the range of [math]x+y[/math]?

If the solution to the inequality [math]a(x+4)>-2[/math] is [math]x<-3[/math], what is the value of [math]a[/math]?

$$|x+2|=a$$If [math]a>0[/math], then the equation above has two solutions. What is the summation of the solutions?

There are three distinct numbers [math]a, b[/math], and [math]c[/math] on a number line. If [math]|a-b|=|b-c|[/math]. Which of the following statements must be true?

If [math]a[/math] is a positive number and [math]b[/math] is a negative number, which of the following values could be negative?

$$|x-1|\leq3$$What is the summation of all integer solutions to the absolute inequality above?