# Page 2 Mathematics Study Guide for the Wonderlic Personnel Test™

### Ratio

The tricky part of these problems is that they give you fractions and multiples to work with. Instead of saying, “It takes 1 hour to make 9 dolls,” they say, “It takes $\frac{1}{3}$ hour to make 3 dolls.” You have to figure out how many dolls can be made in 1 hour to answer the question, “How long does it take them to make 27 dolls?”

Similarly, the problem might give you information for more than one, like this:

Cindy could buy 7 bunches of carrots for $10.50. How much would 3 bunches cost? If you quickly find the cost of one bunch of carrots, you can easily find the cost of 3. One bunch, in this case, costs$1.50, so 3 bunches would run $4.50. Try these problems yourself before looking below them at the solution in parentheses. Problem 1 The boss gave each employee a$20 bonus for each 4 new accounts started. What would an employee’s bonus be if 11 new accounts were created?

(Start by dividing 20 by 4 in your head to arrive at the bonus for each one new account, which is $5.00. Then, multiply 5 by 11 to get$55.00.)

Problem 2

If you raised enough money for $\frac{1}{6}$ of a CD by working 1 hour, how many hours would you have to work to earn enough to buy 3 CDs?

(First, establish that $6 \cdot \frac{1}{6} = 1$, so you would have to work 6 hours to earn enough money for each one CD. You want 3 CDs, so multiply 6 hours by 3 to get 18 hours.)

### Average

If you’re quick with numbers and calculating with pencil and paper, you’ll want to try this type of problem on the Wonderlic® test. As long as you follow this procedure, you should arrive at the correct answer. If doing so, however, takes you more than about 14 seconds, skip “finding the average” questions when you take the actual test.

When asked to find the average, add the given items together and divide by the number of items in the list. You may have to wade through some explanation and determine which numbers to use, for example:

There were 11 workers on the job on Monday through Friday, but only 4 each on Saturday and Sunday. What is the average number of workers on the job per day?

6
7
8
9
10

This would give you a series of the numbers 11, 11, 11, 11, 11, 4, and 4. Add them together and arrive at 63. Divide by 7 (the number of items in the list) and get 9, the correct answer.

Quick Trick: There is a chance you will see an extra-easy (read “extra-quick”) problem in this category. Be alert for average problems that list an odd-numbered series of numbers that occur in sequence, like 11, 12, 13, 14, and 15. You can quickly see, since there are no numbers missing in the sequence and there is a “middle” number, that the answer to this one is 13. Be careful, though—this does not work with even-numbered series like 14, 15, 16, 17, 18, and 19. This series has six items, so there is no “middle” number.

### Percentages

There are two types of percentage questions possible on the Wonderlic® test. With either type, one of the best ways to solve the problem quickly is to create a proportion and cross multiply to find the answer. This is what that would look like if you were solving each type of problem:

#### Questions that Give You Numbers and Ask for a Percentage

Terrence’s football team had 60 players on its roster, but only 54 showed up for the first practice. What percentage of his team attended the practice?

Remember that you put two ratios together with an = sign to create a proportion. Use the information you have and put an x for the information you seek. You know that 54 out of 60 players attended, so the first fraction (ratio) is:

What you don’t know is what percentage this is, so that becomes the second fraction (ratio) in the proportion. Any percentage can be expressed as some number over 100 and you don’t know this particular one, so it would be:

Put these two ratios together and you have:

Then, cross multiply to solve for x (the number you need) and you get:

If there are zeroes on both sides of the equal sign, you can cancel those out, so it becomes:

This division can be done in your head because you know 6 goes into 54 nine times. Add the zero and you have your answer: 90, or 90%.

#### Questions That Give You a Percentage and Ask for a Number

The same process can be used if you are given a percentage and need to find a number, like this:

Carlton needed to score at least 75% on his algebra test to pass the class. If there were 80 questions on the test, how many must Carlton answer correctly?

(cancel zeroes on both sides)

One important thing to remember when attempting the percentage questions on the Wonderlic® test is to be sure you know what the question is asking. For instance, the question may give you information about how many people were present at an event, but then ask you what percentage were absent. This just adds a bit of subtraction to your procedure but it’s necessary to get the right answer. Consider this question, for example:

The attendance at the concert filled 90% of the available seats in the auditorium. If there are 400 seats in the auditorium, how many seats were empty?

Here, the proportion will give you the number of seats that were full and then you’ll have to subtract that from the total number of seats to get the answer.

Quick Trick: If you are familiar with some fraction equivalencies and some common conversions between fractions and percentages, it could speed up your calculations for percentage problems. For example, if you know that 12 out of 18 is $\frac{2}{3}$ and you know that $\frac{2}{3}$ is about 66%, finding a percentage can be really speedy! Here are some common percentage conversions to memorize:

Here are some common percentage conversions to memorize: