ASVAB Arithmetic Reasoning Practice Test 208915 Results

	Your Results	Global Average
Questions	5	5
Correct	0	2.78
Score	0%	56%

Review

A circular logo is enlarged to fit the lid of a jar. The new diameter is 75% larger than the original. By what percentage has the area of the logo increased?

50% Answer Correctly

	25%
	15%
	20%
	37\(\frac{1}{2}\)%

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 75% the radius (and, consequently, the total area) increases by \( \frac{75\text{%}}{2} \) = 37\(\frac{1}{2}\)%

What is \( \frac{12\sqrt{40}}{6\sqrt{8}} \)?

71% Answer Correctly

	2 \( \sqrt{\frac{1}{5}} \)
	\(\frac{1}{5}\) \( \sqrt{2} \)
	2 \( \sqrt{5} \)
	\(\frac{1}{5}\) \( \sqrt{\frac{1}{2}} \)

Solution

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

\( \frac{12\sqrt{40}}{6\sqrt{8}} \)
\( \frac{12}{6} \) \( \sqrt{\frac{40}{8}} \)
2 \( \sqrt{5} \)

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
	10
	13
	24

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.

How many 2 gallon cans worth of fuel would you need to pour into an empty 20 gallon tank to fill it exactly halfway?

51% Answer Correctly

	5
	10
	5
	9

Solution

To fill a 20 gallon tank exactly halfway you'll need 10 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{10 \text{ gallons}}{2 \text{ gallons}} \) = 5

If \( \left|y - 6\right| \) - 6 = 2, which of these is a possible value for y?

62% Answer Correctly

	-5
	-8
	6
	-2

Solution

First, solve for \( \left|y - 6\right| \):

The value inside the absolute value brackets can be either positive or negative so (y - 6) must equal + 8 or -8 for \( \left|y - 6\right| \) to equal 8:

y - 6 = 8
y = 8 + 6
y = 14

y - 6 = -8
y = -8 + 6
y = -2

So, y = -2 or y = 14.