Many of the math problems on tests are word problems. A word problem can include any kind of math, including simple arithmetic, fractions, decimals, percentages, and even algebra and geometry.
The hardest part of any word problem is translating English into math. When you read a problem, you can frequently translate it word for word from English statements into mathematical statements. At other times, however, a key word in the word problem hints at the mathematical operation to be performed. Here are the translation rules:
EQUALS key words: is, are, has
English 
Math 
The rookie is 20 years old. 
R = 20 
There are 7 hats. 
H = 7 
Officer Judi has commendations. 
J = 5 
ADDITION key words: sum; more, greater, or older than; total; all together
English 
Math 
The sum of two numbers is 10. 
X + Y = 10 
Karen has $5 more than Sam. 
K = 5 + S 
The base is 3" greater than the height. 
B = 3 + H 
Judi is 2 years older than Tony. 
J = 2 + T 
The total of three numbers is 25. 
A + B + C = 25 
How much do Joan and Tom have all together? 
J + T = ? 
SUBTRACTION key words: difference, less or younger than, fewer, remain, left over
English 
Math 
The difference between two numbers is 17. 
X – Y = 17 
Mike has 5 fewer cats than twice the number Jan has. 
M = 2 J – 5 
Jay is 2 years younger than Brett. 
J = B – 2 
After Carol ate 3 apples, R apples remained. 
R = A – 3 
MULTIPLICATION key words: of, product, times
English 
Math 
20% of the stolen radios 
.20 × M 
Half of the recruits 
× B 
The product of two numbers is 12. 
A ×B = 12 
DIVISION key word: per
English 
Math 
15 drops per teaspoon 

22 miles per gallon 

Distance Formula: Distance = Rate × Time
The key words are movement words like plane, train, boat, car, walk, run, climb, travel, and swim.
 How far did the plane travel in 4 hours if it averaged 300 miles per hour?
D = 300 × 4
D = 1,200 miles
 Ben walked 20 miles in 4 hours. What was his average speed?
20 = r × 4
5 miles per hour = r
Solving a Word Problem Using the Translation Table
Remember the problem at the beginning of this chapter about the jelly beans?
Juan ate of the jelly beans. Maria then ate of the remaining jelly beans, which left 10 jelly beans. How many jelly beans were there to begin with?
 60
 80
 90
 120
 140
We solved it by working backward. Now let's solve it using our translation rules.
Assume Juan started with J jelly beans. Eating of them means eating × J jelly beans. Maria ate a fraction of the remaining jelly beans, which means we must subtract to find out how many are left: J – × J = × J. Maria then ate , leaving of the × J jelly beans, or × × J jelly beans. Multiplying out × × J gives J as the number of jelly beans left. The problem states that there were 10 jelly beans left, meaning that we set × J equal to 10:
× J = 10
Solving this equation for J gives J = 60. Thus, the correct answer is choice a (the same answer we got when we worked backward). As you can see, both methods—working backwards and translating from text to math—work. You should use whichever method is more comfortable for you.
Math Word Problems Sample Questions
 Officer Miller pledged three dollars for every mile his son walked in the Police Athletic League Walkathon. If his son walks nine miles, how much will Officer Miller owe?
 $3.00
 $12.00
 $18.00
 $27.00
 Officer Beque has been writing six speeding tickets every week. At this rate, how long will it take for her to write 27 tickets?
 3 weeks
 3.5 weeks
 4 weeks
 4.5 weeks
 The chief 's administrative aide is able to type 85 words per minute. How many minutes will it take him to type a report containing 1,020 words?
 11
 12
 Chief Wallace is writing a budget request to upgrade the office computer. The request includes the purchase of 4 GB of RAM, which will cost $100, two new software programs at $350 each, an external hard drive that costs $249, and printer ink for $49.What is the total amount the budget request should be written for
 a. $998.00
 $1,098.00
 $1,349.00
 $1,398.00
Answer questions 5 and 6 based on the following information.
Mrs. O'Leary called a transit police detective to report that her overnight bag was stolen when she dozed off while waiting for the train departing New York City en route to Philadelphia. The overnight bag was worth approximately $150. The bag contained the following items:
 1 change of clothing, including dress, shoes, and underclothing valued at $200
 1 makeup case valued at $50
 2 bottles of perfume that were gifts for her granddaughters valued at $60 each
 1 pair of gold earrings valued at $200
 2 silver rings valued at $100 each
 $300 in cash
 You are the detective who received this report. Based on the items listed, what should you write on your report as the value of the stolen money and property?
 $770.00
 $1,070.00
 $1,100.00
 $1,220.00
 Two days later, after returning home, Mrs. O'Leary called to say that she had made some errors in her initial report. She discovered she had not taken the gold earrings on the trip nor had she taken one of the two silver rings. Your amended report should now indicate which figure as the value of the stolen money and property?
 $570.00
 $770.00
 $920.00
 $1,020.00
 Joan is preparing for the police applicant physical by getting into better shape. Last weekend she walked 25 miles in 4.5 hours. What was her average speed?
 4.5 miles per hour
 5 miles per hour
 5.5 miles per hour
 6 miles per hour
 If a patrol car is driven at the speed of 60 miles per hour for 45 minutes, how far will it have traveled?
 40 miles
 45 miles
 50 miles
 none of the above
Answers
 d. This is a simple multiplication calculation: 3 × 9 = 27.
 d. Divide the total number of tickets by the number Officer Beque writes weekly (27 ÷ 6) to obtain the answer.
 c. The calculation is similar to Question 3. Divide the total number of words in the report by the speed at which the administrative aide types (1,020 ÷ 85) to obtain the answer. In Question 3 the answers were presented to you in decimals; in this question you are given fractions, but your use of division is the same.
 b. This is an addition problem, but you must make sure that you read how many of each item at each cost to be sure you add up the proper numbers. Choice a omits one of the items; choices c and d could come from assuming 4 GB of RAM was $400 rather than $100 for that portion of the purchase.
 d. There are two ways to reach the total; you can add each item separately or you can multiply to obtain the total for perfume and rings (of which there were more than one) and then add the sums. If you made an error, you may have simply made an error in multiplication or addition or you may have forgotten to include all the items. If you did not answer this question correctly, go back and determine whether your errors were in the math or the reading of the question.
 c. If you totaled the items correctly in Question 5, you now have to subtract the value of the earrings ($200) and the value of one ring ($100), add these to total $300, and subtract that from the correct total. There are important lessons to be learned from these two questions. The most important one is to read and do your calculations carefully on these multipart questions; if you get the first part wrong, you are likely to also get the second part wrong. In many cases, the question developer predicts the errors you might make and provides choices to the second question that seem logical even if incorrect. Knowing this, you must read the question carefully. If you are permitted to write in your test booklet, consider placing a circle around all the items you will have to calculate and then underlining the numbers of each item so you remember whether there are two pairs of earrings or one ring or similar combinations of items.
 c. In this problem, you must divide the number of miles walked by the time it took (25 ÷ 4.5) to obtain the answer.
 b. Convert the 45 minutes to 0.75 hour, which is the time, then multiply: 60 mph × 0.75 = 45 miles.
Notice that question 8 presumes that you know that 45 minutes is or .75 of an hour. If you have forgotten how to convert fractions to decimals or generally feel uncomfortable with fractions, decimals, percents, or other math terms and functions, you should purchase one of the many math guides and workbooks that are available. There are also a number of internet sites that can provide you with math assistance. Reviewing a guidebook or an internet study site may help you overcome what has been called math anxiety—the fear many people have that they are unable to do even the simplest math problems.
Since most of the material you will be tested on does not require advanced math knowledge, do not permit yourself to tense up over these sections of the exam. Whether you are permitted to bring a calculator to the test or are expected to figure out the problems the oldfashioned way on paper, just relax and answer the questions.
Before explaining the nonmath number questions you are likely to see on your exam, here are some extra sample math questions.
Bonus Math Sample Questions
 Officers Cubera and Stubbs have been assigned to transport two prisoners from the stationhouse to the county jail. The total trip is miles. If they have completed miles, how many miles do they still have to go?
 Officers Kiergaard and Spuno made an arrest for possession of 28 ounces of marijuana, which was separated into ounce bags. How many packages of marijuana did they find in the suspect's possession?
 4
 6
 8
 10
 (500 ÷ 5) + 3 × 24 =
 100
 172
 2,472
 none of the above
 The Mission City Police Department has a higher than average percentage of women on its staff. If 20% of the staff in this department of 200 are women, how many women officers does Mission City employ?
 10
 20
 30
 40
 Of the 760 crimes committed in Copperville last month, 76 involved grand larceny. What percentage of the crimes involved grand larceny?
 .01%
 .76%
 1%
 10%
 The number of traffic summons issued by members of the Sun City traffic squad for the last six months was 127, 130, 135, 142, and 160.What was the average number of summonses per month?
 127
 135
 139
 142
Answers
 a. Because the fractions do not have the same bottom number, you have to work with the least common denominator.
 c. Divide the number of ounces by the number of bags (28 ÷ ) to obtain the answer.
 b. You must solve the division first: 500 ÷ 5 = 100. The equation now become 100 + 3 × 24. An acronym you can use to remember this is PEMDAS, which stands for parenthesis, exponents, multiplication, division, addition, subtraction. If you follow PEMDAS, after doing the math within the parenthesis, you do the multiplication: 3 × 24 = 72, which provides a much easier equation to work with, 100 + 72 = 172.
 d. To multiply the size of the department by the percentage of women, add a decimal point to arrive at .20 and multiply by the number of employees in the department: .20 × 200 = 40. You might know that 10% can be derived in your head by dropping the last 0, which in this instance would be 20 women. Since 20% is double 10%, you can now double the number of women to the correct answer of 40.
 d. This is a typical percent problem that involves finding what percent one number is of another number. It is a simple one because, if you remember from the previous question that the figure 10% will always involve dropping the last number, the figures 760 and 76 provide an immediate clue.
 c. To calculate an average, add up each item being averaged and divide by the total number of items. In this question, you must add: 127 + 130 + 135 + 142 + 160 = 694 and then divide by 5 = 138.8, a total which permits you to round it off to the next highest full number, 139.
Other NumberBased Questions
Police officers work with numbers that have nothing to do with solving math problems. You might be given an address, you might be given cross streets, or you might receive a notification from the dispatcher to be on the lookout for a certain license plate number or a particular make and model of a motor vehicle. Each of these will require you to have recall of letter and number combinations. The questions in this area, like so many others, actually test for two skills—your visual perception and your shortterm memory. Letter and number recall can be tested for in two ways; one involves giving you a grid and another provides multiplechoice questions that ask you to select the choice that matches a letterandnumber combination at the start of the question.
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