ASVAB Arithmetic Reasoning Practice - 6

There are 5 blue marbles, 4 red marbles, and 3 yellow marbles in a box. If Jim randomly selects a marble from the box, what is the probability of selecting a red or yellow marble?

• $\frac{1}{4}$

• $\frac{1}{3}$

• $\frac{7}{12}$

• $\frac{3}{4}$

Answer explanation

The correct answer is $\frac{7}{12}$ . A probability is the likelihood of a successful event occurring divided by the total number of events possible. In this case, a successful event is selecting either a red or a yellow marble and the total number of events possible is the total number of marbles. Combine the number of red and yellow marbles: 4 + 3 = 7, and divide this by the total number of marbles: 5 + 4 + 3 = 12. The probability is $\frac{7}{12}$

If Kayla left a $10.47 tip on a breakfast that cost $87.25, what percentage was the tip?

• $8.3\%$

• $12\%$

• $13\%$

• $14\%$

Answer explanation

The correct answer is 12%. If you want to know what percent A is of B, you divide A by B, then take that number and move the decimal place two spaces to the right:10.47 ÷ 87.25 = 0.12.

Move the decimal two spaces to the right to find the percentage: = 12%

A phone company charges $2 for the first five minutes of a phone call and 30 cents per minute thereafter. If Malik makes a phone call that lasts 25 minutes, what will be the total cost of the phone call?

• $8.00

• $8.50

• $9.00

• $9.50

Answer explanation

The correct answer is $8.00. The total cost of the phone call can be represented by the equation:

TC = $2.00 + $0.3x,

where x is the duration of the call after the first five minutes.

In this case, x = 20. Substitute the known values into the equation and solve for the total cost:

TC = $2.00 + $0.3 * 20

TC = $2.00 + $6.00

TC= $8.00

If 10 inches on a map represents an actual distance of 100 feet, then what actual distance does 25 inches on the map represent?

• 25 feet

• 100 feet

• 150 feet

• 250 feet

Answer explanation

The correct answer is 250 feet. First calculate the number of feet that 1 inch represents:

100 ft ÷ 10 in = 10 ft/in

Then multiply this by the total number of inches:

25 in × 10 ft/in = 250 ft

Tags

CCSS.7.G.A.1

CCSS.7.RP.A.1

CCSS.7.RP.A.2

CCSS.7.RP.A.3

Five years ago, Amy was three times as old as Mike. If Mike is 10 years old now, how old is Amy?

• 15

• 20

• 25

• 30

Answer explanation

The correct answer is 20. You can et up a table comparing the situation five years ago to the situation today to keep things organized.

Mike is 10 years old now, so he must have been 5 years old five years ago.

Amy was 3 times as old as Mike five years ago, so Amy must have been 15 five years ago.

Add 5 years to Amy’s age five years ago to calculate her age now. Amy is 15 + 5 = 20 years old now.

At a used book store, Valentina purchased three books for $2.65 each. If she paid with a $20 bill, how much change did she receive?

• $12.05

• $13.15

• $13.85

• $17.35

Answer explanation

The correct answer is $12.05. Three books at $2.65 would equal a total of $7.95. The change would equal $20 − $7.95 = $12.05.

Tags

CCSS.3.NBT.A.2

CCSS.3.OA.A.3

CCSS.3.OA.D.8

Mia earns $8.10 per hour and worked 40 hours. Charlotte earns $10.80 per hour. How many hours would Charlotte need to work to equal Mia’s earnings over 40 hours?

• 25

• 27

• 28

• 30

Answer explanation

The correct answer is 30. Begin by calculating Mia’s total earnings after 40 hours:

40 hours × $8.10 per hour = $324

Next, divide this total by Charlotte’s hourly rate to find the number of hours Charlotte would need to work:

$324 ÷ $10.80 per hour = 30 hours

Aisha wants to paint the walls of a room. She knows that each can of paint contains one gallon. A half gallon will completely cover a 55 square feet of wall. Each of the four walls of the room is 10 feet high. Two of the walls are 10 feet wide and two of the walls are 15 feet wide. How many 1-gallon buckets of paint does Aisha need to buy in order to fully paint the room?

• 4

• 5

• 9

• 10

Answer explanation

The correct answer is 5. The total number of buckets necessary will be the total area of the walls divided by the total area covered by each bucket. First, calculate the area of the walls Aisha wants to paint. Two of the walls are 10 × 10 and two of the walls are 10 × 15:

2 (10 × 10) = 200 sq. ft.

2 (10 × 15) = 300 sq. ft.

So the total square footage of the walls is 500.

If a half gallon of paint will cover 55 square feet, then each gallon will cover 2 × 55 = 110 square feet. Four gallons can only cover 440 square feet. Five gallons will cover 550 square feet, which will be enough for the entire area of the walls.

There are 4 red marbles and 8 green marbles in a box. If Emma randomly selects a marble from the box, what is the probability of her selecting a red marble?

• $\frac{1}{3}$

• $\frac{1}{2}$

• $\frac{2}{3}$

• $\frac{4}{5}$

Answer explanation

The correct answer is $\frac{1}{3}$ . The probability of a successful event is the ratio of the number of successful events to the total number of events. In this case, a successful event is selecting a red marble from the box. The total number of events is the total number of marbles in the box:

$P\left(red\right)=\frac{number\ of\ red\ marbles}{total\ number\ of\ marbles}$

$P\left(red\right)=\frac{4}{12}=\frac{1}{3}$

Oscar purchased a new hat that was on sale for $5.06. The original price was $9.20. What percentage discount was the sale price?

• 4.5%

• 41.4%

• 45%

• 55%

Answer explanation

The correct answer is (C). The percentage discount is the reduction in price divided by the original price. The difference between original price and sale price is:

$9.20 − $5.06 = $4.14

The percentage discount is this difference divided by the original price:

$4.14 ÷ $9.20 = 0.45

Convert the decimal to a percentage by multiplying by 100%:

0.45 × 100% = 45%