ASVAB Arithmetic Reasoning Practice Test 730496 Results

	Your Results	Global Average
Questions	5	5
Correct	0	2.81
Score	0%	56%

Review

What is $ 4 $$ \sqrt{12} $ - $ 5 $$ \sqrt{3} $

38% Answer Correctly

	-1$ \sqrt{3} $
	-1$ \sqrt{12} $
	3$ \sqrt{3} $
	20$ \sqrt{12} $

Solution

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

4$ \sqrt{12} $ - 5$ \sqrt{3} $
4$ \sqrt{4 \times 3} $ - 5$ \sqrt{3} $
4$ \sqrt{2^2 \times 3} $ - 5$ \sqrt{3} $
(4)(2)$ \sqrt{3} $ - 5$ \sqrt{3} $
8$ \sqrt{3} $ - 5$ \sqrt{3} $

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

8$ \sqrt{3} $ - 5$ \sqrt{3} $
(8 - 5)$ \sqrt{3} $
3$ \sqrt{3} $

If all of a roofing company's 4 workers are required to staff 2 roofing crews, how many workers need to be added during the busy season in order to send 7 complete crews out on jobs?

55% Answer Correctly

	8
	10
	15
	14

Solution

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 4 workers at the company now and that's enough to staff 2 crews so there are $ \frac{4}{2} $ = 2 workers on a crew. 7 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 7 x 2 = 14 total workers to staff the crews during the busy season. The company already employs 4 workers so they need to add 14 - 4 = 10 new staff for the busy season.

Frank loaned Bob $1,500 at an annual interest rate of 2%. If no payments are made, what is the interest owed on this loan at the end of the first year?

74% Answer Correctly

	$30
	$32
	$78
	$8

Solution

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = ($ \frac{6}{100} $) x $1,500
i = 0.02 x $1,500
i = $30

Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 13 small cakes per hour. The kitchen is available for 2 hours and 22 large cakes and 150 small cakes need to be baked.

How many cooks are required to bake the required number of cakes during the time the kitchen is available?

41% Answer Correctly

	12
	11
	14
	10

Solution

If a single cook can bake 3 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 3 x 2 = 6 large cakes during that time. 22 large cakes are needed for the party so $ \frac{22}{6} $ = 3$\frac{2}{3}$ cooks are needed to bake the required number of large cakes.

If a single cook can bake 13 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 13 x 2 = 26 small cakes during that time. 150 small cakes are needed for the party so $ \frac{150}{26} $ = 5$\frac{10}{13}$ cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 4 + 6 = 10 cooks.

What is $ \frac{4}{9} $ x $ \frac{2}{8} $?

72% Answer Correctly

	1
	$\frac{1}{9}$
	$\frac{2}{81}$
	$\frac{8}{81}$

Solution

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

$ \frac{4}{9} $ x $ \frac{2}{8} $ = $ \frac{4 x 2}{9 x 8} $ = $ \frac{8}{72} $ = $\frac{1}{9}$

	-1\( \sqrt{3} \)
	-1\( \sqrt{12} \)
	3\( \sqrt{3} \)
	20\( \sqrt{12} \)

	1
	\(\frac{1}{9}\)
	\(\frac{2}{81}\)
	\(\frac{8}{81}\)