ASVAB Arithmetic Reasoning Practice Test 654679 Results

	Your Results	Global Average
Questions	5	5
Correct	0	3.01
Score	0%	60%

Review

Which of these numbers is a factor of 64?

68% Answer Correctly

	62
	64
	63
	29

Solution

The factors of a number are all positive integers that divide evenly into the number. The factors of 64 are 1, 2, 4, 8, 16, 32, 64.

What is the next number in this sequence: 1, 3, 7, 13, 21, __________ ?

69% Answer Correctly

	23
	27
	31
	39

Solution

The equation for this sequence is:

a_n = a_n-1 + 2(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31

What is 7c² - 4c²?

71% Answer Correctly

	-3c^-2
	3c^-2
	3c²
	11c^-4

Solution

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

7c² - 4c²
(7 - 4)c²
3c²

If a mayor is elected with 75% of the votes cast and 82% of a town's 44,000 voters cast a vote, how many votes did the mayor receive?

49% Answer Correctly

	25,617
	30,307
	18,762
	27,060

Solution

If 82% of the town's 44,000 voters cast ballots the number of votes cast is:

(\( \frac{82}{100} \)) x 44,000 = \( \frac{3,608,000}{100} \) = 36,080

The mayor got 75% of the votes cast which is:

(\( \frac{75}{100} \)) x 36,080 = \( \frac{2,706,000}{100} \) = 27,060 votes.

On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 50% 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

	17
	12
	20
	22

Solution

If the guard hits 50% of his shots and takes 10 shots he'll make:

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{50}{100} \) = \( \frac{50 x 10}{100} \) = \( \frac{500}{100} \) = 5 shots

The center makes 30% 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 = \( \frac{5}{\frac{30}{100}} \) = 5 x \( \frac{100}{30} \) = \( \frac{5 x 100}{30} \) = \( \frac{500}{30} \) = 17 shots

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