ASVAB Arithmetic Reasoning Practice Test 329303 Results

	Your Results	Global Average
Questions	5	5
Correct	0	2.56
Score	0%	51%

Review

Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 10 small cakes per hour. The kitchen is available for 4 hours and 32 large cakes and 170 small cakes need to be baked.

How many cooks are required to bake the required number of cakes during the time the kitchen is available?

41% Answer Correctly

	6
	7
	9
	12

Solution

If a single cook can bake 5 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 5 x 4 = 20 large cakes during that time. 32 large cakes are needed for the party so \( \frac{32}{20} \) = 1\(\frac{3}{5}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 10 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 10 x 4 = 40 small cakes during that time. 170 small cakes are needed for the party so \( \frac{170}{40} \) = 4\(\frac{1}{4}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 2 + 5 = 7 cooks.

On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 60% 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

	35
	31
	45
	42

Solution

If the guard hits 60% of his shots and takes 30 shots he'll make:

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{60}{100} \) = \( \frac{60 x 30}{100} \) = \( \frac{1800}{100} \) = 18 shots

The center makes 40% 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 = \( \frac{18}{\frac{40}{100}} \) = 18 x \( \frac{100}{40} \) = \( \frac{18 x 100}{40} \) = \( \frac{1800}{40} \) = 45 shots

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

What is \( 4 \)\( \sqrt{112} \) + \( 6 \)\( \sqrt{7} \)

35% Answer Correctly

	22\( \sqrt{7} \)
	10\( \sqrt{784} \)
	24\( \sqrt{16} \)
	10\( \sqrt{112} \)

Solution

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

4\( \sqrt{112} \) + 6\( \sqrt{7} \)
4\( \sqrt{16 \times 7} \) + 6\( \sqrt{7} \)
4\( \sqrt{4^2 \times 7} \) + 6\( \sqrt{7} \)
(4)(4)\( \sqrt{7} \) + 6\( \sqrt{7} \)
16\( \sqrt{7} \) + 6\( \sqrt{7} \)

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

16\( \sqrt{7} \) + 6\( \sqrt{7} \)
(16 + 6)\( \sqrt{7} \)
22\( \sqrt{7} \)

What is -6z⁶ x 7z²?

75% Answer Correctly

	z⁶
	-42z⁶
	z⁸
	-42z⁸

Solution

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

-6z⁶ x 7z²
(-6 x 7)z^{(6 + 2)}
-42z⁸

If \( \left|b - 3\right| \) + 3 = 8, which of these is a possible value for b?

62% Answer Correctly

	7
	8
	0
	2

Solution

First, solve for \( \left|b - 3\right| \):

The value inside the absolute value brackets can be either positive or negative so (b - 3) must equal + 5 or -5 for \( \left|b - 3\right| \) to equal 5:

b - 3 = 5
b = 5 + 3
b = 8

b - 3 = -5
b = -5 + 3
b = -2

So, b = -2 or b = 8.