ASVAB Arithmetic Reasoning Practice Test 357262 Results

	Your Results	Global Average
Questions	5	5
Correct	0	2.74
Score	0%	55%

Review

If a mayor is elected with 67% of the votes cast and 85% of a town's 11,000 voters cast a vote, how many votes did the mayor receive?

50% Answer Correctly

	6,826
	8,135
	7,106
	6,265

Solution

If 85% of the town's 11,000 voters cast ballots the number of votes cast is:

(\( \frac{85}{100} \)) x 11,000 = \( \frac{935,000}{100} \) = 9,350

The mayor got 67% of the votes cast which is:

(\( \frac{67}{100} \)) x 9,350 = \( \frac{626,450}{100} \) = 6,265 votes.

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 6 complete crews out on jobs?

55% Answer Correctly

	4
	1
	11
	12

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. 6 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 6 x 2 = 12 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 12 - 8 = 4 new staff for the busy season.

Which of the following is not a prime number?

65% Answer Correctly

	2
	9
	5
	7

Solution

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 60% of his shots. If the guard takes 10 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?

42% Answer Correctly

	19
	17
	14
	12

Solution

If the guard hits 60% of his shots and takes 10 shots he'll make:

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{60}{100} \) = \( \frac{60 x 10}{100} \) = \( \frac{600}{100} \) = 6 shots

The center makes 50% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{6}{\frac{50}{100}} \) = 6 x \( \frac{100}{50} \) = \( \frac{6 x 100}{50} \) = \( \frac{600}{50} \) = 12 shots

to make the same number of shots as the guard and thus score the same number of points.

What is \( \frac{-8y^7}{3y^2} \)?

60% Answer Correctly

	-2\(\frac{2}{3}\)y¹⁴
	-2\(\frac{2}{3}\)y^{\(\frac{2}{7}\)}
	-2\(\frac{2}{3}\)y⁵
	-\(\frac{3}{8}\)y⁵

Solution

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-8y^7}{3y^2} \)
\( \frac{-8}{3} \) y^{(7 - 2)}
-2\(\frac{2}{3}\)y⁵