ASVAB Arithmetic Reasoning Practice Test 850721 Results

Your Results Global Average
Questions 5 5
Correct 0 3.35
Score 0% 67%

Review

1

If all of a roofing company's 6 workers are required to staff 2 roofing crews, how many workers need to be added during the busy season in order to send 4 complete crews out on jobs?

55% Answer Correctly
9
19
12
6

Solution

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 6 workers at the company now and that's enough to staff 2 crews so there are \( \frac{6}{2} \) = 3 workers on a crew. 4 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 4 x 3 = 12 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 12 - 6 = 6 new staff for the busy season.


2

What is the greatest common factor of 80 and 80?

77% Answer Correctly
80
3
44
78

Solution

The factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 10 factors [1, 2, 4, 5, 8, 10, 16, 20, 40, 80] making 80 the greatest factor 80 and 80 have in common.


3

Solve 4 + (5 + 4) ÷ 3 x 5 - 32

52% Answer Correctly
\(\frac{8}{9}\)
1\(\frac{2}{7}\)
2
10

Solution

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

4 + (5 + 4) ÷ 3 x 5 - 32
P: 4 + (9) ÷ 3 x 5 - 32
E: 4 + 9 ÷ 3 x 5 - 9
MD: 4 + \( \frac{9}{3} \) x 5 - 9
MD: 4 + \( \frac{45}{3} \) - 9
AS: \( \frac{12}{3} \) + \( \frac{45}{3} \) - 9
AS: \( \frac{57}{3} \) - 9
AS: \( \frac{57 - 27}{3} \)
\( \frac{30}{3} \)
10


4

Solve for \( \frac{2!}{6!} \)

67% Answer Correctly
\( \frac{1}{504} \)
\( \frac{1}{5} \)
\( \frac{1}{60480} \)
\( \frac{1}{360} \)

Solution

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{2!}{6!} \)
\( \frac{2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4 \times 3} \)
\( \frac{1}{360} \)


5

Which of the following is a mixed number?

82% Answer Correctly

\({a \over 5} \)

\({5 \over 7} \)

\(1 {2 \over 5} \)

\({7 \over 5} \)


Solution

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.