ASVAB Arithmetic Reasoning Practice Test 289571 Results

Your Results Global Average
Questions 5 5
Correct 0 3.00
Score 0% 60%

Review

1

In a class of 20 students, 6 are taking German and 9 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?

63% Answer Correctly
10
13
17
15

Solution

The number of students taking German or Spanish is 6 + 9 = 15. Of that group of 15, 5 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 15 - 5 = 10 who are taking at least one language. 20 - 10 = 10 students who are not taking either language.


2

How many 16-passenger vans will it take to drive all 56 members of the football team to an away game?

81% Answer Correctly
4 vans
6 vans
8 vans
5 vans

Solution

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{56}{16} \) = 3\(\frac{1}{2}\)

So, it will take 3 full vans and one partially full van to transport the entire team making a total of 4 vans.


3

The __________ is the smallest positive integer that is a multiple of two or more integers.

56% Answer Correctly

absolute value

greatest common factor

least common factor

least common multiple


Solution

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.


4

What is \( 8 \)\( \sqrt{50} \) + \( 8 \)\( \sqrt{2} \)

35% Answer Correctly
16\( \sqrt{50} \)
48\( \sqrt{2} \)
16\( \sqrt{2} \)
16\( \sqrt{100} \)

Solution

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

8\( \sqrt{50} \) + 8\( \sqrt{2} \)
8\( \sqrt{25 \times 2} \) + 8\( \sqrt{2} \)
8\( \sqrt{5^2 \times 2} \) + 8\( \sqrt{2} \)
(8)(5)\( \sqrt{2} \) + 8\( \sqrt{2} \)
40\( \sqrt{2} \) + 8\( \sqrt{2} \)

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

40\( \sqrt{2} \) + 8\( \sqrt{2} \)
(40 + 8)\( \sqrt{2} \)
48\( \sqrt{2} \)


5

Convert 7,056,000 to scientific notation.

64% Answer Correctly
7.056 x 10-6
70.56 x 105
7.056 x 105
7.056 x 106

Solution

A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

7,056,000 in scientific notation is 7.056 x 106