ASVAB Arithmetic Reasoning Practice Test 280413 Results

Your Results Global Average
Questions 5 5
Correct 0 2.42
Score 0% 48%

Review

1

A circular logo is enlarged to fit the lid of a jar. The new diameter is 30% larger than the original. By what percentage has the area of the logo increased?

51% Answer Correctly
17\(\frac{1}{2}\)%
15%
35%
32\(\frac{1}{2}\)%
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 30% the radius (and, consequently, the total area) increases by \( \frac{30\text{%}}{2} \) = 15%

2

Which of the following statements about exponents is false?

47% Answer Correctly

b1 = 1

b0 = 1

all of these are false

b1 = b
Solution

A number with an exponent (be) 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).

3

A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 10% off." If Bob buys two shirts, each with a regular price of $10, how much will he pay for both shirts?

57% Answer Correctly
$1.00
$19.00
$10.50
$13.00
Solution

By buying two shirts, Bob will save $10 x \( \frac{10}{100} \) = \( \frac{$10 x 10}{100} \) = \( \frac{$100}{100} \) = $1.00 on the second shirt.

So, his total cost will be
$10.00 + ($10.00 - $1.00)
$10.00 + $9.00
$19.00

4

What is \( 5 \)\( \sqrt{27} \) + \( 8 \)\( \sqrt{3} \)

35% Answer Correctly
13\( \sqrt{81} \)
40\( \sqrt{81} \)
13\( \sqrt{9} \)
23\( \sqrt{3} \)
Solution

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

5\( \sqrt{27} \) + 8\( \sqrt{3} \)
5\( \sqrt{9 \times 3} \) + 8\( \sqrt{3} \)
5\( \sqrt{3^2 \times 3} \) + 8\( \sqrt{3} \)
(5)(3)\( \sqrt{3} \) + 8\( \sqrt{3} \)
15\( \sqrt{3} \) + 8\( \sqrt{3} \)

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

15\( \sqrt{3} \) + 8\( \sqrt{3} \)
(15 + 8)\( \sqrt{3} \)
23\( \sqrt{3} \)

5

Solve 3 + (3 + 5) ÷ 3 x 5 - 32

52% Answer Correctly
1\(\frac{2}{3}\)
1\(\frac{4}{5}\)
7\(\frac{1}{3}\)
\(\frac{6}{7}\)
Solution

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

3 + (3 + 5) ÷ 3 x 5 - 32
P: 3 + (8) ÷ 3 x 5 - 32
E: 3 + 8 ÷ 3 x 5 - 9
MD: 3 + \( \frac{8}{3} \) x 5 - 9
MD: 3 + \( \frac{40}{3} \) - 9
AS: \( \frac{9}{3} \) + \( \frac{40}{3} \) - 9
AS: \( \frac{49}{3} \) - 9
AS: \( \frac{49 - 27}{3} \)
\( \frac{22}{3} \)
7\(\frac{1}{3}\)