# Arithmetic Reasoning & Math Knowledge

The two quantitative sections of the AFOQT are designed to test your understanding of basic math terms and problem-solving methods taught in high school and lower level college courses. Much like the Graduate Record Examination (GRE), there are three content areas of which the bulk of your quantitative study should focus: Arithmetic, Algebra & Geometry.

Arithmetic Reasoning Subtest Information: Time: 29 Minutes; Items: 25

Math Knowledge Subtest Information: Time: 22 Minutes; Items: 25

## AFOQT Mathematical Concepts to Master:

### I. Arithmetic

• Properties/Types of Integers:
• Divisibility
• Factorization
• Prime Numbers
• Remainders
• Odd & Even Integers
• Arithmetic Operations
• Exponents & Roots
• Concepts You Should Be Familiar With:
• Estimation
• Percent
• Ratio
• Rate
• Absolute Value
• The Number Line
• Decimal Representation
• Number Sequences

### II. Algebra

• Operations with Exponents
• Factoring & Simplifying Algebraic Expressions
• Relations
• Functions
• Equations & Inequalities (Solving Simultaneous Equations & Inequalities)
• Setting Up Equations to Solve Word Problems

### III. Geometry

• Parallel & Perpendicular Lines
• Circles (Find Area: (3.14)(r^2))
• Triangles (Area & Perimeter)
• Isósceles, Equilateral
• Pythagorean Theorem
• Rectangles, Squares (Area & Perimeter)
• Cylinders (Area, Volume)

(Answers provided at the bottom of the page)

## Practice Questions

1
Of 7,562 college students, 3,451 have taken part in some intramural sport program. What percentage of students have played intramural sports?
A
56.7%
B
65.2%
C
45.6%
D

57.2%
E
34.6%
2
A shipping container has a length of 327 feet and a width of 15.3 feet. If the height is 12.6 feet, what is the volume of the container (rounded to the nearest whole number)?
A
19,975 cubic feet
B
82,357 cubic feet
C
23,965 cubic feet
D
63,039 cubic feet
E
76,346 cubic feet
3
If a pound of rice costs \$4.20, how much does ¾ pound cost?
A
\$4.00
B
\$3.75
C
\$3.35
D
\$3.95
E
\$3.15
4
Of 4,906 participants surveyed by an energy company, 80% are in favor of increasing the solar energy program, while 9% are not. How many people are in favor of increasing the solar energy program?
A
2,446
B
3,451
C
7,394
D
4,276
E
3,925
5
The temperature in Calgary is -1°C. Using the formula F° = C°x (9/5) + 32, what is the temperature in degrees Fahrenheit?
A
30.2
B
32
C
29
D
29.8
E
33
6
Which of the following choices completes this equation: ( ) = (9 x 2) + (4 x 3)
A
(10 + 3)
B
(10 x 3)
C
(36 + 6)
D
(9 x 6)
E
(5 x 4)
7
A triangle has angles A (55°) and B (65°). What is the measure of angle C?
A
60°
B
65°
C
70°
D
75°
E
80°
8
Which is another way to write 5.97 x 10^3?
A
0.597
B
5.97
C
59,700
D
597
E
5,970
9
How many inches are there in 3 4/9 yards (rounded to nearest whole number)?
A
36 in
B
24 in
C
82 in
D
124 in
E
187 in
10
Which value of ‘x’ will make the number sequence 4x + 27 ≤ 90 true?
A
14
B
19
C
16
D
17
E
20
11
If x > 0, what is the median of the data set consisting of -3x, -6x, x, -9x, and 5x?
A
-3x
B
-6x
C
x
D
-9x
E
5x
12
A game’s card set consists of 7 orange cards and 21 blue cards. If a player randomly selects one of these cards, what is the probability it will be orange?
A
2/5
B
3/8
C
1/4
D
1/3
E
2/3
13
What is the value of x when 5x – 5 = 6x + 8?
A
11
B
30
C
-13
D
3
E
-3
14
What is the value of a when 6a – 1 = 2(a + 1)?
A
3/4
B
3/8
C
1/2
D
0
E
5/2
15
In square meters, what is the area of a rectangle with a diagonal of 25 meters and a width of 15 meters?
A
250
B
225
C
275
D
300
E
350
16
Three consecutive even integers have a sum of 102. If x represents the least number in the set, what equation can be used to determine the value of the sum of the integers?
A
x + (x + 2) + (x + 4) = 102
B
x + (x + 1) + (x + 3) = 102
C
x + (x + 1) + (x + 2) = 102
D
x + 2x + 4x = 102
E
x + x + x = 102
17
Allison drove from her house to a friend’s house 420 kilometers away. She left at 10:30 a.m. and arrived at 3:50 p.m., making one stop along the way for a snack. If Allison’s average speed for the trip whilst driving was 90 kilometers per hour, how long was her snack break?
A
10 minutes
B
20 minutes
C
40 minutes
D
1 hour
E
1 hour and 20 minutes
18
Each person in a room is a freshman or a sophomore. The number of freshman in the room is 7 times the number of sophomores. Which of the following could be the number of people in the room? Indicate ALL such numbers.
A
14
B
26
C
35
D
48
E
49
19
Lauren bought a new cell phone, cell phone case and an external battery charger. The cell phone cost \$149.99, the case cost \$24.99 and the charger was \$29.99. If the tax on each item was 9.5%, which of the following is closest to the amount Lauren spent?
A
\$175
B
\$200
C
\$210
D
\$224
E
\$250
20
The exterior angle of triangle XYZ at vertex X is 130° and the exterior angle at vertex Y is 110°. What is the interior angle at vertex Z?
A
40°
B
60°
C
70°
D
110°
E
120°

1. C (3451/7562=.4563)
2. D (V=LxWxH)
3. E (\$4.20/4 = \$1.05; \$4.20-\$1.05=\$3.15)
4. E (3925/4906)
5. A (-1×1.8+32=30.2)
6. B (10×3) = 30 ; 12+18 = 30
7. A (angles of a triangle add up to 180 deg)
8. E
9. D
10. A
11. A (-9x, -6x, -3x, x, 5x; Since we know x is positive, the terms can be placed in order from smallest to largest. By definition the median is the middle term in this list)
12. C (There are a total of 28 cards – 7 orange; 21 blue. Therefore the probability of selecting an orange card is: 7/28 = 1/4)
13. C (The goal here is to isolate the variable to one side with the constants on the other. By subtracting 5x from both sides, you can rewrite the equation as: -5 = x + 8. This simplifies to x = -13 when 8 is subtracted from both sides)
14. A (After distributing the 2, the equation is equivalent to 6a -1 = 2a + 2. Simplifying, 4a = 3, so a = 3/4)
15. D (The diagonal forms a right triangle with the width and the length acting as legs. Using the Pythagorean theorem, the length of the triangle will be √25^2 – 15^2 = √400 = 20, and the area will be 20 x 15 = 300)
16. A
17. C
18. D (If the number of sophomores in the room is x, then the number of freshman is 7x. The total number of people in the room is 7x + x = 8x. The number of people in the room (8x) must be a multiple of 8.)
19. D
20. B (The sum of the exterior angles of any polygon is 360°, so the exterior angle at vertex Z is 360°-130°-110° = 120°. However, this is not the value of the question asked. Since the sum of the interior angle of a polygon and its exterior angle is 180°, the interior angle at vertex Z is 180°-120° = 60°)