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Mathematical Questions
For most individuals, this is probably the hardest part of a written law enforcement test. Some people become
very discouraged when they read what appears to be a complicated math problem. The truth is, in order to solve
these arithmetic questions you do not need a degree in mathematics. You can find the answer by doing some simple multiplication, division, subtraction and addition. You will also need an understanding of certain terms in order to score high on this section of the test.
Averaging is the result obtained by dividing a sum by the number of quantities added. For example the
average of 2, 10, 12 is the sum of 24 divided by the quantity of 3 which equals 8.
When averaging two rates such as miles per hour the question may not state the length of the distance
traveled. As long as the distances are the same, such as in a return trip, you need to make up a simple length
in order to do your calculations.
Ratio is the relationship in numbers between two similar things. This can be expressed as a fraction
such as 1/3 or by using a colon 1:3. Ratios are read inserting the word to as 1 to 3.
Taxation rate is a percentage that has to be paid which is based on a fixed ratio. In calculating tax
rates it is sometimes helpful to change the tax rate percentage into a decimal. For example 25% = .25
Cross Multiplying can be used when you are working with fractions that equal each other but one fraction
has a missing number. By multiplying the top numbers with the opposite bottom numbers you can determine the
missing number.
The questions will be given to you as a numerical question or as a short statement of the facts involving
numerical amounts. Read the questions carefully and think about what you need to do in order to determine
the correct answer. In this portion of the test, the last answer to each question will be none of these.
This makes it difficult in guessing the correct answer. You must take the time to do some accurate calculations.
You cannot use a calculator in figuring out the answers. You will be given scratch paper that you can use to do
your calculations.
Mathematical Averaging Sample Questions
1. An odometer on a squad car shows that the car has been driven
a total of 735 miles during a one week period. What is the
average number of miles the car was driven each day during that
one week period?
A. 105 miles
B. 123 miles
C. 147 miles
D. 245 miles
E. None of these
Answer to #1
2. A hot air balloon has flown a distance of 2,400 miles in 25 days
flying 12 hours each day. What is the average speed the balloon was
traveling?
A. 6 mph
B. 7 mph
C. 8 mph
D. 9 mph
E. None of these
Answer to #2
3. The police chased a suspect vehicle for 150 miles traveling at a speed of 75 miles per hour.
After apprehending the suspect, they made the same trip back to the police station at 50 miles per hour.
What was the average speed the squad car was traveling for both trips?
A. 55 mph
B. 60 mph
C. 62.5 mph
D. 65 mph
E. None of these
Answer to #3
4. A motorist leaves his home and drives his vehicle at a rate of 40 miles per hour. His vehicle breaks
down and he walks the same route back to his house at a rate of 5 miles per hour. What is the average
rate he was traveling for both trips?
A. 2.2
B. 4.5
C. 8.0
D. 8.8
E. None of these
Answer to #4
Mathematical Ratio Sample Questions
1. A Secret Service office has 10 male agents and 5 female agents. The ratio of male agents to the
number of agents in the office is:
A. 15:10
B. 5:10
C. 10:5
D. 10:15
E. None of these
Answer to #1
2. On the blue prints to the new courthouse, 1/4 inch equals 1 foot of actual length. The blue prints
show the judges bench as being a line 2 inches long. How long is the actual length of the judges bench?
A. 5 feet
B. 8 feet
C. 9 feet
D. 10 feet
E. None of these
Answer to #2
3. The ratio of 12 to 30 is:
A. 12:15
B. 24:60
C. 6:15
D. 12:100
E. None of these
Answer to #3
Mathematical Taxation Rate Sample Questions
1. An agent just bought a new pair of handcuffs for $25.00. The sales tax is computed at a rate of 5%.
What will be his total cost for the handcuffs?
A. $25.25
B. $25.50
C. $26.00
D. $26.25
E. None of these
Answer to #1
2. The Agents Benevolent Fund needs to raise $4,410. They are considering taxing the souvenir items
sold through their mail order catalog. It is estimated that the mail order sales will be $147,000
this year. What tax rate will yield $4,410?
A. 1%
B. 2%
C. 3%
D. 4%
E. None of these
Answer to #2
3. The tax rate on purchasing gasoline is 2%. If the total tax paid is $60, what is the total dollar
amount of gasoline purchased?
A. $120
B. $3,000
C. $6,000
D. $12,000
E. None of these
Answer to #3
Cross Multiplying Sample Questions
When working with fractions, cross multiplying can often help you find the correct answer.
For example, if the equation is:
1 2
---- = ----
8 ?
you would cross multiply 1 x ? and 2 x 8 which gives you the answer of ? = 16. 1/8 = 2/16.
You can also use this formula when dealing with letters instead of numbers.
A 500
---- = ----
B ?
Cross multiplying gives you A? = 500B. You can then determine what ? is by dividing 500B
by A. The correct answer is:
500B
? = ------
A
You can also use cross multiplying in figuring percentages. An easy one would be what is 10%
of 50? You should know that the answer is 5 and cross multiplying gives you the same answer.
10 x 500
---- = ---- 100x = 500 x = ----- x=5
100 50 100
1. A new police car will travel M miles on G gallons of gasoline. How many gallons of gasoline
will be needed to travel Z number of miles?
A. B. C. D.
MG MZ GZ Z
----- ----- ----- -----
Z G M GM
Answer to #1
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