### All SAT Mathematics Resources

## Example Questions

### Example Question #1 : Calculating Percents

What is decreased by ?

**Possible Answers:**

**Correct answer:**

A decrease of is the same thing as a decrease of , since , which reduces to . A convenient way to handle percent decreases is to think that if has been taken away, then is left. So you can multiply by to get .

### Example Question #1 : Calculating Percents

If of a number is , what is that number?

**Possible Answers:**

**Correct answer:**

A great way to set up a percent calculation like this is as a proportion:

That translates to ( out of ) is equal to out of an unknown number.

You can then simplify the fraction to to make the calculation faster. If you then have:

You have two options. One, you can recognize that the difference between the numerators is that the second fraction is twice the second, and you can then say that the denominator must also be double, giving you , meaning .

Or you can cross-multiply and solve, giving you:

### Example Question #1 : Calculating Percents

is of a number. What is that number?

**Possible Answers:**

**Correct answer:**

A great way to calculate this type of percentage problem is by setting up a proportion:

This translates to ( out of ) is equal to out of an unknown number. When you then cross-multiply, you’ll see that the math sets up nicely for quick calculation:

Since is , you can likely do this math in your head to find that , giving you the correct answer, .

### Example Question #3 : Calculating Percents

Keith completed a -kilometer race, during which he walked for of the distance and ran the rest. How many kilometers did he run?

**Possible Answers:**

**Correct answer:**

If Keith walked of the distance, that means he ran of the distance. So you can calculate of . can be expressed as , which reduces to , making the calculation by hand much quicker. of is , making the correct answer.

### Example Question #4 : Calculating Percents

is of half of a number. What is that number?

**Possible Answers:**

**Correct answer:**

Here it is helpful to recognize that is the same thing as . So if is of something, it is of that thing, meaning you can multiply by to get . And we know that then is half of the number they’re looking for, so if we multiply by we have the number: .

### Example Question #2 : Calculating Percents

At a manufacturing factory, of all widgets are found to be defective. If the plant were to produce widgets, how many would be defective?

**Possible Answers:**

**Correct answer:**

There are a couple of math shortcuts that can make this question much quicker than calculating the “long way” of multiplying times without a calculator.

Option 1 is to realize that “percent” means “out of one hundred.” defective means that out of every are defective; since , the total number of widgets, is of , you can then say that of are defective -- if out of are defective, then ( of ) out of ( of ) would be defective. This gives you the correct answer, .

Option 2 is similar: you can express as the fraction , which reduces to . If you then know that out of every widgets is defective, and you have a total of widgets, which is times , you’ll have defective widgets.

### Example Question #5 : Calculating Percents

What is increased by ?

**Possible Answers:**

**Correct answer:**

To increase by , you’d use the expression . But instead of doing the decimal multiplication, you can express as . That makes your job significantly easier, using:

Since equals , if you take of that you’ll just have . Add to the original and you have the correct answer, .

### Example Question #3 : Calculating Percents

Tamara spent of her -hour workweek in meetings. How many hours that week was she NOT in meetings?

**Possible Answers:**

**Correct answer:**

To calculate efficiently, you can first calculate by just moving the decimal point one place to the left. That means that of is (or just ). Then to get , take half of what you had as . Since here is , then is half that: . Add those together, and you have . Here that means that is equal to . If she worked total hours and were in meetings, then the other were not in meetings.

### Example Question #6 : Calculating Percents

If of a number is , what is that number?

**Possible Answers:**

**Correct answer:**

A great way to perform a calculation like this is to set up a proportion. If you know that , you can then cross-multiply and solve for . (That proportion means that , out of , is equal to out of some other number.) Solving, you’d have:

Simplify the first fraction:

Cross-multiply:

Divide by to isolate :

The correct answer is .

### Example Question #7 : Calculating Percents

If is of , what is ?

**Possible Answers:**

**Correct answer:**

One great way to set up a percent calculation like this is to follow the language of the prompt. The word “is” means equals, and “per cent” means “divided by ,” so this prompt literally translates to the equation:

You can then reduce the fraction by factoring out a from both numerator and denominator, leaving:

Then if you multiply both sides by , you’re just about ready to solve:

Since divided by is , you can then multiply to get to , the correct answer.