ASVAB Arithmetic Reasoning Practice Test 487196 Results

Your Results Global Average
Questions 5 5
Correct 0 2.70
Score 0% 54%

Review

1

On average, the center for a basketball team hits 45% of his shots while a guard on the same team hits 50% of his shots. If the guard takes 10 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?

42% Answer Correctly
9
11
15
10

Solution
If the guard hits 50% of his shots and takes 10 shots he'll make:

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{50}{100} \) = \( \frac{50 x 10}{100} \) = \( \frac{500}{100} \) = 5 shots

The center makes 45% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{5}{\frac{45}{100}} \) = 5 x \( \frac{100}{45} \) = \( \frac{5 x 100}{45} \) = \( \frac{500}{45} \) = 11 shots

to make the same number of shots as the guard and thus score the same number of points.


2

Cooks are needed to prepare for a large party. Each cook can bake either 4 large cakes or 14 small cakes per hour. The kitchen is available for 4 hours and 20 large cakes and 450 small cakes need to be baked.

How many cooks are required to bake the required number of cakes during the time the kitchen is available?

41% Answer Correctly
10
5
9
11

Solution

If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 20 large cakes are needed for the party so \( \frac{20}{16} \) = 1\(\frac{1}{4}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 14 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 14 x 4 = 56 small cakes during that time. 450 small cakes are needed for the party so \( \frac{450}{56} \) = 8\(\frac{1}{28}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 2 + 9 = 11 cooks.


3

Convert 1,973,000 to scientific notation.

63% Answer Correctly
1.973 x 107
1.973 x 10-5
1.973 x 10-6
1.973 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:

1,973,000 in scientific notation is 1.973 x 106


4

What is \( 4 \)\( \sqrt{112} \) + \( 8 \)\( \sqrt{7} \)

35% Answer Correctly
32\( \sqrt{16} \)
32\( \sqrt{112} \)
24\( \sqrt{7} \)
12\( \sqrt{112} \)

Solution

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

4\( \sqrt{112} \) + 8\( \sqrt{7} \)
4\( \sqrt{16 \times 7} \) + 8\( \sqrt{7} \)
4\( \sqrt{4^2 \times 7} \) + 8\( \sqrt{7} \)
(4)(4)\( \sqrt{7} \) + 8\( \sqrt{7} \)
16\( \sqrt{7} \) + 8\( \sqrt{7} \)

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

16\( \sqrt{7} \) + 8\( \sqrt{7} \)
(16 + 8)\( \sqrt{7} \)
24\( \sqrt{7} \)


5

Which of the following is a mixed number?

83% Answer Correctly

\({7 \over 5} \)

\(1 {2 \over 5} \)

\({5 \over 7} \)

\({a \over 5} \)


Solution

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.