### Federal Law Enforcement Written Entrance Test

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

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

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

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

Mathematical Ratio Sample Questions

5. 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

6. On the blue prints to the new courthouse, 1/4 inch equals 1 foot of actual length. The blue prints show the judge's bench as being a line 2 inches long. How long is the actual length of the judge's bench?

A.  5 feet

B.  8 feet

C.  9 feet

D.  10 feet

E.  None of these

7. What is the ratio of 12 to 30 in its simplest form?

A.  12:15

B.  24:60

C.  2:5

D.  6:15

E.  None of these

Mathematical Taxation Rate Sample Questions

8. 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

9. 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

10. 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

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
```

11. 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
```