ASVAB Arithmetic Reasoning Practice Test 328682 Results

	Your Results	Global Average
Questions	5	5
Correct	0	2.84
Score	0%	57%

Review

Which of the following is not an integer?

77% Answer Correctly

	-1
	\({1 \over 2}\)
	0
	1

Solution

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

Convert z^-4 to remove the negative exponent.

68% Answer Correctly

	\( \frac{-4}{-z} \)
	\( \frac{-1}{-4z^{4}} \)
	\( \frac{1}{z^{-4}} \)
	\( \frac{1}{z^4} \)

Solution

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

Which of the following statements about exponents is false?

47% Answer Correctly

	b¹ = 1
	b¹ = b
	b⁰ = 1
	all of these are false

Solution

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

If all of a roofing company's 16 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 9 complete crews out on jobs?

55% Answer Correctly

	20
	7
	6
	13

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 16 workers at the company now and that's enough to staff 4 crews so there are \( \frac{16}{4} \) = 4 workers on a crew. 9 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 9 x 4 = 36 total workers to staff the crews during the busy season. The company already employs 16 workers so they need to add 36 - 16 = 20 new staff for the busy season.

What is \( 8 \)\( \sqrt{32} \) + \( 8 \)\( \sqrt{2} \)

35% Answer Correctly

	16\( \sqrt{32} \)
	40\( \sqrt{2} \)
	16\( \sqrt{16} \)
	16\( \sqrt{64} \)

Solution

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

8\( \sqrt{32} \) + 8\( \sqrt{2} \)
8\( \sqrt{16 \times 2} \) + 8\( \sqrt{2} \)
8\( \sqrt{4^2 \times 2} \) + 8\( \sqrt{2} \)
(8)(4)\( \sqrt{2} \) + 8\( \sqrt{2} \)
32\( \sqrt{2} \) + 8\( \sqrt{2} \)

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

32\( \sqrt{2} \) + 8\( \sqrt{2} \)
(32 + 8)\( \sqrt{2} \)
40\( \sqrt{2} \)