ASVAB Arithmetic Reasoning Practice Test 75 Results

Your Results Global Average
Questions 5 5
Correct 0 3.26
Score 0% 65%

Review

1

Simplify \( \frac{24}{72} \).

77% Answer Correctly
\( \frac{3}{8} \)
\( \frac{8}{19} \)
\( \frac{10}{19} \)
\( \frac{1}{3} \)

Solution

To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 8 factors [1, 2, 3, 4, 6, 8, 12, 24] making 24 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{24}{72} \) = \( \frac{\frac{24}{24}}{\frac{72}{24}} \) = \( \frac{1}{3} \)


2

53% Answer Correctly
1
9.0
0.8
3.2

Solution


1


3

What is \( 3 \)\( \sqrt{12} \) - \( 8 \)\( \sqrt{3} \)

38% Answer Correctly
-5\( \sqrt{36} \)
-2\( \sqrt{3} \)
24\( \sqrt{36} \)
24\( \sqrt{3} \)

Solution

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

3\( \sqrt{12} \) - 8\( \sqrt{3} \)
3\( \sqrt{4 \times 3} \) - 8\( \sqrt{3} \)
3\( \sqrt{2^2 \times 3} \) - 8\( \sqrt{3} \)
(3)(2)\( \sqrt{3} \) - 8\( \sqrt{3} \)
6\( \sqrt{3} \) - 8\( \sqrt{3} \)

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

6\( \sqrt{3} \) - 8\( \sqrt{3} \)
(6 - 8)\( \sqrt{3} \)
-2\( \sqrt{3} \)


4

Which of the following is a mixed number?

82% Answer Correctly

\({7 \over 5} \)

\({5 \over 7} \)

\(1 {2 \over 5} \)

\({a \over 5} \)


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.


5

A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 20% off." If Ezra buys two shirts, each with a regular price of $33, how much money will he save?

70% Answer Correctly
$6.60
$16.50
$1.65
$3.30

Solution

By buying two shirts, Ezra will save $33 x \( \frac{20}{100} \) = \( \frac{$33 x 20}{100} \) = \( \frac{$660}{100} \) = $6.60 on the second shirt.