ASVAB Arithmetic Reasoning Practice Test 287850 Results

Your Results Global Average
Questions 5 5
Correct 0 3.61
Score 0% 72%

Review

1

What is (a5)3?

80% Answer Correctly
a15
a-2
a2
3a5
Solution

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

(a5)3
a(5 * 3)
a15

2

How many hours does it take a car to travel 35 miles at an average speed of 35 miles per hour?

86% Answer Correctly
2 hours
9 hours
8 hours
1 hour
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 = \( \frac{35mi}{35mph} \)
1 hour

3

Solve for \( \frac{2!}{3!} \)

67% Answer Correctly
\( \frac{1}{6720} \)
\( \frac{1}{3} \)
\( \frac{1}{8} \)
1680
Solution

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{2!}{3!} \)
\( \frac{2 \times 1}{3 \times 2 \times 1} \)
\( \frac{1}{3} \)
\( \frac{1}{3} \)

4

A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 45% off." If Roger buys two shirts, each with a regular price of $38, how much money will he save?

70% Answer Correctly
$1.90
$9.50
$17.10
$7.60
Solution

By buying two shirts, Roger will save $38 x \( \frac{45}{100} \) = \( \frac{$38 x 45}{100} \) = \( \frac{$1710}{100} \) = $17.10 on the second shirt.

5

What is \( \frac{4}{6} \) - \( \frac{5}{14} \)?

61% Answer Correctly
\(\frac{13}{42}\)
2 \( \frac{4}{42} \)
\( \frac{4}{13} \)
1 \( \frac{9}{42} \)
Solution

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 7}{6 x 7} \) - \( \frac{5 x 3}{14 x 3} \)

\( \frac{28}{42} \) - \( \frac{15}{42} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{28 - 15}{42} \) = \( \frac{13}{42} \) = \(\frac{13}{42}\)