ASVAB Arithmetic Reasoning Practice Test 296140 Results

Your Results Global Average
Questions 5 5
Correct 0 2.79
Score 0% 56%

Review

1

What is \( 9 \)\( \sqrt{75} \) + \( 5 \)\( \sqrt{3} \)

35% Answer Correctly
14\( \sqrt{225} \)
14\( \sqrt{3} \)
45\( \sqrt{75} \)
50\( \sqrt{3} \)

Solution

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

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

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

45\( \sqrt{3} \) + 5\( \sqrt{3} \)
(45 + 5)\( \sqrt{3} \)
50\( \sqrt{3} \)


2

Which of the following is not an integer?

77% Answer Correctly

-1

0

1

\({1 \over 2}\)


Solution

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.


3

What is 3\( \sqrt{4} \) x 2\( \sqrt{3} \)?

41% Answer Correctly
5\( \sqrt{12} \)
6\( \sqrt{3} \)
5\( \sqrt{3} \)
12\( \sqrt{3} \)

Solution

To multiply terms with radicals, multiply the coefficients and radicands separately:

3\( \sqrt{4} \) x 2\( \sqrt{3} \)
(3 x 2)\( \sqrt{4 \times 3} \)
6\( \sqrt{12} \)

Now we need to simplify the radical:

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


4

Solve 3 + (5 + 4) ÷ 2 x 4 - 32

52% Answer Correctly
\(\frac{2}{3}\)
12
3\(\frac{1}{2}\)
1

Solution

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

3 + (5 + 4) ÷ 2 x 4 - 32
P: 3 + (9) ÷ 2 x 4 - 32
E: 3 + 9 ÷ 2 x 4 - 9
MD: 3 + \( \frac{9}{2} \) x 4 - 9
MD: 3 + \( \frac{36}{2} \) - 9
AS: \( \frac{6}{2} \) + \( \frac{36}{2} \) - 9
AS: \( \frac{42}{2} \) - 9
AS: \( \frac{42 - 18}{2} \)
\( \frac{24}{2} \)
12


5

A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 50% off." If Frank buys two shirts, each with a regular price of $14, how much money will he save?

70% Answer Correctly
$4.20
$2.10
$3.50
$7.00

Solution

By buying two shirts, Frank will save $14 x \( \frac{50}{100} \) = \( \frac{$14 x 50}{100} \) = \( \frac{$700}{100} \) = $7.00 on the second shirt.