ASVAB Arithmetic Reasoning Practice Test 680400 Results

	Your Results	Global Average
Questions	5	5
Correct	0	2.95
Score	0%	59%

Review

Which of the following statements about exponents is false?

47% Answer Correctly

	b⁰ = 1
	all of these are false
	b¹ = b
	b¹ = 1

Solution

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

A bread recipe calls for 2\(\frac{1}{4}\) cups of flour. If you only have 1\(\frac{1}{8}\) cups, how much more flour is needed?

62% Answer Correctly

	1\(\frac{1}{8}\) cups
	2\(\frac{5}{8}\) cups
	2\(\frac{1}{8}\) cups
	1\(\frac{1}{2}\) cups

Solution

The amount of flour you need is (2\(\frac{1}{4}\) - 1\(\frac{1}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{18}{8} \) - \( \frac{9}{8} \)) cups
\( \frac{9}{8} \) cups
1\(\frac{1}{8}\) cups

What is the next number in this sequence: 1, 5, 13, 25, 41, __________ ?

69% Answer Correctly

	61
	69
	64
	67

Solution

The equation for this sequence is:

a_n = a_n-1 + 4(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

A circular logo is enlarged to fit the lid of a jar. The new diameter is 75% larger than the original. By what percentage has the area of the logo increased?

51% Answer Correctly

	25%
	37\(\frac{1}{2}\)%
	22\(\frac{1}{2}\)%
	17\(\frac{1}{2}\)%

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 75% the radius (and, consequently, the total area) increases by \( \frac{75\text{%}}{2} \) = 37\(\frac{1}{2}\)%

Convert b^-3 to remove the negative exponent.

68% Answer Correctly

	\( \frac{-1}{-3b} \)
	\( \frac{1}{b^3} \)
	\( \frac{-1}{b^{-3}} \)
	\( \frac{-3}{b} \)

Solution

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