ASVAB Arithmetic Reasoning Practice Test 977898 Results

	Your Results	Global Average
Questions	5	5
Correct	0	2.73
Score	0%	55%

Review

Betty scored 80% on her final exam. If each question was worth 2 points and there were 100 possible points on the exam, how many questions did Betty answer correctly?

57% Answer Correctly

	27
	40
	41
	47

Solution

Betty scored 80% on the test meaning she earned 80% of the possible points on the test. There were 100 possible points on the test so she earned 100 x 0.8 = 80 points. Each question is worth 2 points so she got \( \frac{80}{2} \) = 40 questions right.

A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 3 to 2 and the ratio of baseball to basketball cards is 3 to 1, what is the ratio of football to basketball cards?

53% Answer Correctly

	9:2
	5:2
	3:6
	1:1

Solution

The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.

On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 70% of his shots. If the guard takes 20 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

	39
	50
	28
	29

Solution

If the guard hits 70% of his shots and takes 20 shots he'll make:

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{70}{100} \) = \( \frac{70 x 20}{100} \) = \( \frac{1400}{100} \) = 14 shots

The center makes 50% 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 = \( \frac{14}{\frac{50}{100}} \) = 14 x \( \frac{100}{50} \) = \( \frac{14 x 100}{50} \) = \( \frac{1400}{50} \) = 28 shots

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

The total water usage for a city is 35,000 gallons each day. Of that total, 35% is for personal use and 65% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?

58% Answer Correctly

	1,800
	7,000
	10,500
	3,900

Solution

65% of the water consumption is industrial use and 35% is personal use so (65% - 35%) = 30% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{30}{100} \) x 35,000 gallons = 10,500 gallons.

Convert 3,963,000 to scientific notation.

62% Answer Correctly

	3.963 x 10^-5
	3.963 x 10⁶
	3.963 x 10⁷
	0.396 x 10⁷

Solution

A number in scientific notation has the format 0.000 x 10^exponent. 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:

3,963,000 in scientific notation is 3.963 x 10⁶