### All PSAT Math Resources

## Example Questions

### Example Question #1 : How To Find Out When An Equation Has No Solution

Solve for .

**Possible Answers:**

No solutions.

**Correct answer:**

No solutions.

Cross multiplying leaves , which is not possible.

### Example Question #131 : Gre Quantitative Reasoning

If is defined for all numbers and to be , then what is ?

**Possible Answers:**

**Correct answer:**

In evaluating, we can simply plug in 4 and 2 for and respectively. We then get .

### Example Question #131 : Algebra

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?

**Possible Answers:**

**Correct answer:**

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 #42 : Linear / Rational / Variable Equations

John goes on a trip of kilometers at a speed of kilometers an hour. How long did the trip take?

**Possible Answers:**

**Correct answer:**

If we take the units and look at division, will yield hours as a unit. Therefore the answer is .

### Example Question #131 : Gre Quantitative Reasoning

With a head wind a plane can fly a certain distance in five hours. The return flight takes an hour less. How fast was the plane flying?

**Possible Answers:**

**Correct answer:**

In general, .

The distance is the same going and coming; however, the head wind affects the rate. The equation thus becomes .

Solving for gives .

### Example Question #31 : How To Find The Solution To An Equation

How much water should be added to of 90% cleaning solution to yield 50% cleaning solution?

**Possible Answers:**

**Correct answer:**

Pure water is 0% and pure solution 100%. Let = water to be added.

in general where is the volume and is the percent.

So the equation to solve becomes

and

### Example Question #211 : Algebra

Solve and

**Possible Answers:**

**Correct answer:**

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 to get and then substutite the into the second equation to get

.

Solving this equation gives and substituting this value into one of the original equations gives , thus the correct answer is .

### Example Question #31 : 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?

**Possible Answers:**

**Correct answer:**

Let = # of color pencil boxes and = # of sketch pads purchased.

So the equation to solve becomes .

Solving this equations leads to 2 colored pencil boxes and 3 sketch pads.

### Example Question #42 : Equations / Inequalities

**Possible Answers:**

**Correct answer:**

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

### Example Question #41 : How To Find The Solution To An Equation

Steve sells cars. His monthly salary is $1,000. He gets a $500 commission for each car he sells. If Steve wants to make $7,500 this month, how many cars would he have to sell?

**Possible Answers:**

**Correct answer:**

Let = money earned and = number of cars sold

So

and solving shows that he needs to sell 13 cars to make $7,500.

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