ASVAB Arithmetic Reasoning Practice Test 631030 Results

Your Results Global Average
Questions 5 5
Correct 0 3.04
Score 0% 61%

Review

1

On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 45% of his shots. If the guard takes 15 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
24
27
13
11

Solution
If the guard hits 45% of his shots and takes 15 shots he'll make:

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{45}{100} \) = \( \frac{45 x 15}{100} \) = \( \frac{675}{100} \) = 6 shots

The center makes 25% 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 = \( \frac{6}{\frac{25}{100}} \) = 6 x \( \frac{100}{25} \) = \( \frac{6 x 100}{25} \) = \( \frac{600}{25} \) = 24 shots

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


2

What is \( \frac{2}{7} \) x \( \frac{1}{6} \)?

72% Answer Correctly
\(\frac{16}{45}\)
\(\frac{1}{21}\)
\(\frac{1}{3}\)
\(\frac{8}{15}\)

Solution

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{7} \) x \( \frac{1}{6} \) = \( \frac{2 x 1}{7 x 6} \) = \( \frac{2}{42} \) = \(\frac{1}{21}\)


3

If \(\left|a\right| = 7\), which of the following best describes a?

67% Answer Correctly

a = -7

a = 7

a = 7 or a = -7

none of these is correct


Solution

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).


4

What is (a3)2?

80% Answer Correctly
2a3
a-1
a6
a5

Solution

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

(a3)2
a(3 * 2)
a6


5

What is \( 8 \)\( \sqrt{48} \) - \( 8 \)\( \sqrt{3} \)

38% Answer Correctly
64\( \sqrt{16} \)
0\( \sqrt{48} \)
24\( \sqrt{3} \)
0\( \sqrt{-7} \)

Solution

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

8\( \sqrt{48} \) - 8\( \sqrt{3} \)
8\( \sqrt{16 \times 3} \) - 8\( \sqrt{3} \)
8\( \sqrt{4^2 \times 3} \) - 8\( \sqrt{3} \)
(8)(4)\( \sqrt{3} \) - 8\( \sqrt{3} \)
32\( \sqrt{3} \) - 8\( \sqrt{3} \)

Now that the radicands are identical, you can subtract them:

32\( \sqrt{3} \) - 8\( \sqrt{3} \)
(32 - 8)\( \sqrt{3} \)
24\( \sqrt{3} \)