ASVAB Arithmetic Reasoning Practice Test 3777 Results

Your Results Global Average
Questions 5 5
Correct 0 3.12
Score 0% 62%

Review

1

How many hours does it take a car to travel 65 miles at an average speed of 65 miles per hour?

85% Answer Correctly
1 hour
3 hours
4 hours
9 hours

Solution

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

speed = \( \frac{\text{distance}}{\text{time}} \)

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{65mi}{65mph} \)
1 hour


2

A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 9 to 2 and the ratio of baseball to basketball cards is 9 to 1, what is the ratio of football to basketball cards?

53% Answer Correctly
81:2
9:4
1:1
1:8

Solution

The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.


3

What is \( \frac{2}{6} \) x \( \frac{1}{8} \)?

72% Answer Correctly
\(\frac{1}{56}\)
\(\frac{1}{24}\)
\(\frac{1}{20}\)
\(\frac{1}{3}\)

Solution

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

\( \frac{2}{6} \) x \( \frac{1}{8} \) = \( \frac{2 x 1}{6 x 8} \) = \( \frac{2}{48} \) = \(\frac{1}{24}\)


4

Simplify \( \sqrt{80} \)

62% Answer Correctly
2\( \sqrt{10} \)
6\( \sqrt{10} \)
4\( \sqrt{5} \)
5\( \sqrt{5} \)

Solution

To simplify a radical, factor out the perfect squares:

\( \sqrt{80} \)
\( \sqrt{16 \times 5} \)
\( \sqrt{4^2 \times 5} \)
4\( \sqrt{5} \)


5

What is \( 8 \)\( \sqrt{20} \) - \( 9 \)\( \sqrt{5} \)

38% Answer Correctly
72\( \sqrt{20} \)
-1\( \sqrt{5} \)
-1\( \sqrt{20} \)
7\( \sqrt{5} \)

Solution

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

8\( \sqrt{20} \) - 9\( \sqrt{5} \)
8\( \sqrt{4 \times 5} \) - 9\( \sqrt{5} \)
8\( \sqrt{2^2 \times 5} \) - 9\( \sqrt{5} \)
(8)(2)\( \sqrt{5} \) - 9\( \sqrt{5} \)
16\( \sqrt{5} \) - 9\( \sqrt{5} \)

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

16\( \sqrt{5} \) - 9\( \sqrt{5} \)
(16 - 9)\( \sqrt{5} \)
7\( \sqrt{5} \)