ASVAB Arithmetic Reasoning Practice Test 586258 Results

Your Results Global Average
Questions 5 5
Correct 0 2.93
Score 0% 59%

Review

1

If all of a roofing company's 8 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 8 complete crews out on jobs?

55% Answer Correctly
13
17
8
18

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 8 workers at the company now and that's enough to staff 4 crews so there are \( \frac{8}{4} \) = 2 workers on a crew. 8 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 8 x 2 = 16 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 16 - 8 = 8 new staff for the busy season.


2

What is \( 9 \)\( \sqrt{80} \) + \( 3 \)\( \sqrt{5} \)

35% Answer Correctly
12\( \sqrt{400} \)
27\( \sqrt{80} \)
12\( \sqrt{80} \)
39\( \sqrt{5} \)

Solution

To add these radicals together their radicands must be the same:

9\( \sqrt{80} \) + 3\( \sqrt{5} \)
9\( \sqrt{16 \times 5} \) + 3\( \sqrt{5} \)
9\( \sqrt{4^2 \times 5} \) + 3\( \sqrt{5} \)
(9)(4)\( \sqrt{5} \) + 3\( \sqrt{5} \)
36\( \sqrt{5} \) + 3\( \sqrt{5} \)

Now that the radicands are identical, you can add them together:

36\( \sqrt{5} \) + 3\( \sqrt{5} \)
(36 + 3)\( \sqrt{5} \)
39\( \sqrt{5} \)


3

A bread recipe calls for 3\(\frac{5}{8}\) cups of flour. If you only have 1\(\frac{1}{8}\) cups, how much more flour is needed?

62% Answer Correctly
\(\frac{7}{8}\) cups
1\(\frac{1}{2}\) cups
2\(\frac{1}{2}\) cups
2\(\frac{1}{4}\) cups

Solution

The amount of flour you need is (3\(\frac{5}{8}\) - 1\(\frac{1}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{29}{8} \) - \( \frac{9}{8} \)) cups
\( \frac{20}{8} \) cups
2\(\frac{1}{2}\) cups


4

What is \( \frac{2}{8} \) ÷ \( \frac{4}{8} \)?

68% Answer Correctly
2
4
\(\frac{1}{2}\)
\(\frac{2}{5}\)

Solution

To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{8} \) ÷ \( \frac{4}{8} \) = \( \frac{2}{8} \) x \( \frac{8}{4} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{8} \) x \( \frac{8}{4} \) = \( \frac{2 x 8}{8 x 4} \) = \( \frac{16}{32} \) = \(\frac{1}{2}\)


5

What is \( \frac{12\sqrt{63}}{6\sqrt{9}} \)?

71% Answer Correctly
\(\frac{1}{7}\) \( \sqrt{2} \)
\(\frac{1}{2}\) \( \sqrt{7} \)
2 \( \sqrt{7} \)
2 \( \sqrt{\frac{1}{7}} \)

Solution

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{12\sqrt{63}}{6\sqrt{9}} \)
\( \frac{12}{6} \) \( \sqrt{\frac{63}{9}} \)
2 \( \sqrt{7} \)