ASVAB Arithmetic Reasoning Practice Test 301652 Results

Your Results Global Average
Questions 5 5
Correct 0 3.37
Score 0% 67%

Review

1

Convert b-3 to remove the negative exponent.

68% Answer Correctly
\( \frac{1}{b^{-3}} \)
\( \frac{-1}{-3b} \)
\( \frac{3}{b} \)
\( \frac{1}{b^3} \)

Solution

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.


2

\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?

56% Answer Correctly

distributive property for division

commutative property for division

distributive property for multiplication

commutative property for multiplication


Solution

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).


3

What is 2b5 + 7b5?

66% Answer Correctly
9b25
9b5
9b10
5b-5

Solution

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

2b5 + 7b5
(2 + 7)b5
9b5


4

Which of these numbers is a factor of 28?

69% Answer Correctly
17
2
1
6

Solution

The factors of a number are all positive integers that divide evenly into the number. The factors of 28 are 1, 2, 4, 7, 14, 28.


5

Simplify \( \frac{24}{68} \).

78% Answer Correctly
\( \frac{5}{8} \)
\( \frac{10}{17} \)
\( \frac{6}{17} \)
\( \frac{1}{4} \)

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 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{24}{68} \) = \( \frac{\frac{24}{4}}{\frac{68}{4}} \) = \( \frac{6}{17} \)