ASVAB Arithmetic Reasoning Practice Test 915951 Results

	Your Results	Global Average
Questions	5	5
Correct	0	3.28
Score	0%	66%

Review

On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 45% of his shots. If the guard takes 15 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

	24
	27
	14
	10

Solution

If the guard hits 45% of his shots and takes 15 shots he'll make:

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{45}{100} \) = \( \frac{45 x 15}{100} \) = \( \frac{675}{100} \) = 6 shots

The center makes 25% 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 = \( \frac{6}{\frac{25}{100}} \) = 6 x \( \frac{100}{25} \) = \( \frac{6 x 100}{25} \) = \( \frac{600}{25} \) = 24 shots

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

Convert a^-5 to remove the negative exponent.

68% Answer Correctly

	\( \frac{1}{a^5} \)
	\( \frac{-1}{-5a} \)
	\( \frac{1}{a^{-5}} \)
	\( \frac{-5}{a} \)

Solution

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

Simplify \( \frac{28}{76} \).

77% Answer Correctly

	\( \frac{5}{6} \)
	\( \frac{7}{19} \)
	\( \frac{3}{7} \)
	\( \frac{4}{11} \)

Solution

To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{28}{76} \) = \( \frac{\frac{28}{4}}{\frac{76}{4}} \) = \( \frac{7}{19} \)

What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?

69% Answer Correctly

	46
	44
	54
	53

Solution

The equation for this sequence is:

a_n = a_n-1 + 3(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 + 3(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46

Which of these numbers is a factor of 36?

69% Answer Correctly

	13
	12
	24
	23

Solution

The factors of a number are all positive integers that divide evenly into the number. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.