ASVAB Arithmetic Reasoning Practice Test 440736 Results

	Your Results	Global Average
Questions	5	5
Correct	0	2.98
Score	0%	60%

Review

What is \( 2 \)\( \sqrt{48} \) - \( 2 \)\( \sqrt{3} \)

38% Answer Correctly

	4\( \sqrt{48} \)
	0\( \sqrt{16} \)
	4\( \sqrt{144} \)
	6\( \sqrt{3} \)

Solution

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

2\( \sqrt{48} \) - 2\( \sqrt{3} \)
2\( \sqrt{16 \times 3} \) - 2\( \sqrt{3} \)
2\( \sqrt{4^2 \times 3} \) - 2\( \sqrt{3} \)
(2)(4)\( \sqrt{3} \) - 2\( \sqrt{3} \)
8\( \sqrt{3} \) - 2\( \sqrt{3} \)

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

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

In a class of 24 students, 8 are taking German and 8 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?

63% Answer Correctly

	10
	23
	18
	12

Solution

The number of students taking German or Spanish is 8 + 8 = 16. Of that group of 16, 2 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 16 - 2 = 14 who are taking at least one language. 24 - 14 = 10 students who are not taking either language.

What is \( \frac{-2a^6}{9a^2} \)?

60% Answer Correctly

	-\(\frac{2}{9}\)a^{\(\frac{1}{3}\)}
	-4\(\frac{1}{2}\)a⁸
	-\(\frac{2}{9}\)a⁴
	-\(\frac{2}{9}\)a^-4

Solution

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-2a^6}{9a^2} \)
\( \frac{-2}{9} \) a^{(6 - 2)}
-\(\frac{2}{9}\)a⁴

A circular logo is enlarged to fit the lid of a jar. The new diameter is 65% larger than the original. By what percentage has the area of the logo increased?

51% Answer Correctly

	27\(\frac{1}{2}\)%
	20%
	32\(\frac{1}{2}\)%
	22\(\frac{1}{2}\)%

Solution

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 65% the radius (and, consequently, the total area) increases by \( \frac{65\text{%}}{2} \) = 32\(\frac{1}{2}\)%

If a car travels 180 miles in 3 hours, what is the average speed?

86% Answer Correctly

	60 mph
	20 mph
	35 mph
	55 mph

Solution

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

speed = \( \frac{\text{distance}}{\text{time}} \)
speed = \( \frac{180mi}{3h} \)
60 mph