ASVAB Arithmetic Reasoning Practice Test 860430 Results

Your Results Global Average
Questions 5 5
Correct 0 2.94
Score 0% 59%

Review

1

What is \( \frac{2}{6} \) + \( \frac{8}{14} \)?

60% Answer Correctly
\( \frac{3}{42} \)
\(\frac{19}{21}\)
\( \frac{5}{8} \)
\( \frac{7}{42} \)

Solution

To add 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:

\( \frac{2 x 7}{6 x 7} \) + \( \frac{8 x 3}{14 x 3} \)

\( \frac{14}{42} \) + \( \frac{24}{42} \)

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

\( \frac{14 + 24}{42} \) = \( \frac{38}{42} \) = \(\frac{19}{21}\)


2

Which of the following is an improper fraction?

70% Answer Correctly

\(1 {2 \over 5} \)

\({2 \over 5} \)

\({a \over 5} \)

\({7 \over 5} \)


Solution

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.


3

What is \( 3 \)\( \sqrt{75} \) + \( 9 \)\( \sqrt{3} \)

35% Answer Correctly
27\( \sqrt{225} \)
12\( \sqrt{3} \)
27\( \sqrt{75} \)
24\( \sqrt{3} \)

Solution

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

3\( \sqrt{75} \) + 9\( \sqrt{3} \)
3\( \sqrt{25 \times 3} \) + 9\( \sqrt{3} \)
3\( \sqrt{5^2 \times 3} \) + 9\( \sqrt{3} \)
(3)(5)\( \sqrt{3} \) + 9\( \sqrt{3} \)
15\( \sqrt{3} \) + 9\( \sqrt{3} \)

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

15\( \sqrt{3} \) + 9\( \sqrt{3} \)
(15 + 9)\( \sqrt{3} \)
24\( \sqrt{3} \)


4

Which of these numbers is a factor of 28?

69% Answer Correctly
8
29
30
7

Solution

The factors of a number are all positive integers that divide evenly into the number. The factors of 28 are 1, 2, 4, 7, 14, 28.


5

A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 45% off." If Ezra buys two shirts, each with a regular price of $13, how much will he pay for both shirts?

57% Answer Correctly
$18.85
$5.85
$14.95
$20.15

Solution

By buying two shirts, Ezra will save $13 x \( \frac{45}{100} \) = \( \frac{$13 x 45}{100} \) = \( \frac{$585}{100} \) = $5.85 on the second shirt.

So, his total cost will be
$13.00 + ($13.00 - $5.85)
$13.00 + $7.15
$20.15