ASVAB Arithmetic Reasoning Practice Test 745944 Results

	Your Results	Global Average
Questions	5	5
Correct	0	2.75
Score	0%	55%

Review

The __________ is the greatest factor that divides two integers.

67% Answer Correctly

	absolute value
	greatest common multiple
	greatest common factor
	least common multiple

Solution

The greatest common factor (GCF) is the greatest factor that divides two integers.

What is the next number in this sequence: 1, 5, 13, 25, 41, __________ ?

68% Answer Correctly

	66
	64
	61
	68

Solution

The equation for this sequence is:

a_n = a_n-1 + 4(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 + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

Which of the following statements about exponents is false?

46% 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).

A circular logo is enlarged to fit the lid of a jar. The new diameter is 60% larger than the original. By what percentage has the area of the logo increased?

50% Answer Correctly

	27\(\frac{1}{2}\)%
	17\(\frac{1}{2}\)%
	30%
	32\(\frac{1}{2}\)%

Solution

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 60% the radius (and, consequently, the total area) increases by \( \frac{60\text{%}}{2} \) = 30%

On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 35% of his shots. If the guard takes 30 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
	18
	28
	33

Solution

If the guard hits 35% of his shots and takes 30 shots he'll make:

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{35}{100} \) = \( \frac{35 x 30}{100} \) = \( \frac{1050}{100} \) = 10 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 = \( \frac{10}{\frac{30}{100}} \) = 10 x \( \frac{100}{30} \) = \( \frac{10 x 100}{30} \) = \( \frac{1000}{30} \) = 33 shots

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