PSAT Math : PSAT Mathematics
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Example Questions
Example Question #24 : Algebra
If 3|x – 2| = 12 and |y + 4| = 8, then |x - y| can equal ALL of the following EXCEPT:
14
10
6
2
18
14
We must solve each absolute value equation separately for x and y. Remember that absolute values will always give two different values. In order to find these two values, we must set our equation to equal both a positive and negative value.
In order to solve for x in 3|x – 2| = 12,
we must first divide both sides of our equation by 3 to get |x – 2| = 4.
Now that we no longer have a coefficient in front of our absolute value, we must then form two separate equations, one equaling a positive value and the other equaling a negative value.
We will now get x – 2 = 4
and
x – 2 = –4.
When we solve for x, we get two values for x:
x = 6 and x = –2.
Do the same thing to solve for y in the equation |y + 4| = 8
and we get
y = 4 and y = –12.
This problem asks us to solve for all the possible solutions of |x - y|.
Because we have two values for x and two values for y, that means that we will have 4 possible, correct answers.
|6 – 4| = 2
|–2 – 4| = 6
|6 – (–12)| = 18
|–2 – (–12)| = 10
Example Question #42 : Linear / Rational / Variable Equations
No solutions.
No solutions.
Cross multiplying leaves 
Example Question #66 : How To Find The Solution To An Equation
If 
In evaluating, we can simply plug in 4 and 2 for 
Example Question #31 : How To Find The Solution To An Equation
Internet service costs $0.50 per minute for the first ten minutes and is $0.20 a minute thereafter. What is the equation that represents the cost of internet in dollars when time is greater than 10 minutes?
The first ten minutes will cost $5. From there we need to apply a $0.20 per-minute charge for every minute after ten. This gives
Example Question #32 : Equations / Inequalities
John goes on a trip of 
If we take the units and look at division, 
Example Question #71 : How To Find The Solution To An Equation
With a 
In general, 
The distance is the same going and coming; however, the head wind affects the rate. The equation thus becomes 
Solving for 
Example Question #34 : How To Find The Solution To An Equation
How much water should be added to 
Pure water is 0% and pure solution 100%. Let 
So the equation to solve becomes
and
Example Question #35 : How To Find The Solution To An Equation
Solve 
This problem is a good example of the substitution method of solving a system of equations. We start by rewritting the first equation in terms of 
Solving this equation gives 
Example Question #43 : Linear / Rational / Variable Equations
Joy bought some art supplies. She bought colored pencils for $1.25 per box and sketch pads for $2.25 each. Joy bought one more sketch pad than colored pencil boxes and spent $9.25. How many sketch pads did she buy?
Let 
So the equation to solve becomes 
Solving this equations leads to 2 colored pencil boxes and 3 sketch pads.
Example Question #72 : How To Find The Solution To An Equation
This question deals with absolute value equations which will normally gives you two solutions.
You need to solve two sets of equations for absolute value problems:
and
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