ASVAB Arithmetic Reasoning Practice Test Notes

Introduction

• Video Overview:
  • 16 practice test questions for the Arithmetic Reasoning subtest of the ASVAB and PCAT.
  • Testing conditions: 39 minutes for 16 questions; no calculators or reference sheets.
  • Tools allowed: Scratch paper and pencil.
  • Recommendation: Avoid paying for tutoring; free resources are sufficient.
  • Test difficulty: Similar to elementary to high school math.

Practice Questions Overview

Question 1: Banana Purchase

• Problem: Andy spends $4.68 on bananas, each costing $0.78.
• Solution: Use long division to determine quantity: 468/78 = 6 bananas.

Question 2: Yarn Percentage

• Problem: Determine what percentage of yarn was green.
• Solution Steps:
  • Total balls: 10 white + 3 green + 2 yellow = 15.
  • Green percentage: (3/15) = 1/5 = 20%.

Question 3: Climbing Distances

• Problem: Calculate total climbing distance for Ray.
• Solution Steps:
  • Convert mixed fractions: 9 1/3 + 8 5/6.
  • Find common denominator and add: 17 + 7/6 = 18 1/6 feet.

Question 4: Service Call Charges

• Problem: Calculate a service bill with a flat fee and hourly rate.
• Solution: Flat fee $35 + ($25/hour x 3 hours) = $110 total.

Question 5: Glasses from Juice

• Problem: Number of 5 1/4 oz glasses from a 31 1/2 oz container.
• Solution Steps:
  • Convert to improper fractions and divide: 63/2 ÷ 21/4 = 6 glasses.

Question 6: Music Concert Intermission

• Problem: Intermission percentage of the concert.
• Solution Steps:
  • Convert duration to minutes: 3 hours = 180 minutes.
  • Intermission time: 27/180 = 15%.

Question 7: James’ Earnings

• Problem: Calculate total earnings including overtime.
• Solution Steps:
  • Regular earnings: 40 hours x $12 = $480.
  • Overtime: 10 hours x $18 = $180.
  • Total earnings: $480 + $180 = $660.

Question 8: Successive Discounts

• Problem: Price after applying successive discounts.
• Solution Steps:
  • Initial price: $40.
  • First 10% discount: $36.
  • Second 10% discount: $32.40.
  • Final 20% discount: $25.92.

Question 9: Garden Area Calculation

• Problem: Find the area of a rectangular garden.
• Solution Steps:
  • Perimeter provided: 24 feet.
  • Width is half the length, solve for L: Length = 8, Width = 4.
  • Area = L x W = 32 square feet.

Question 10: Excavated Dirt Volume

• Problem: Calculate dirt volume for a swimming pool.
• Solution Steps:
  • Use volume formula for rectangular prism.
  • Dimensions: 25 x 18 x 4 = 1,800 cubic feet.

Question 11: Box Surface Area

• Problem: Approximate surface area of a box.
• Solution Steps:
  • Box dimensions: 8, 12, 9.
  • Use surface area formula: 2(LW + WH + LH) = 552 square inches.

Question 12: Jacket Price Increase

• Problem: Calculate percent increase in jacket price.
• Solution Steps:
  • Old price: $60, New price: $90.
  • Percentage increase = 50%.

Question 13: Trip Time Calculation

• Problem: Total driving time for a trip.
• Solution Steps:
  • Distance = Rate x Time.
  • Calculate time for each leg and sum: Total = 12 hours.

Question 14: Loan Repayment

• Problem: Total loan repayment including interest.
• Solution Steps:
  • Principal: $1,500, Rate: 7%, Time: 2 years.
  • Interest = $210.
  • Total repayment: $1,710.

Question 15: Painted Box Surface Area

• Problem: Area painted on a box excluding the bottom.
• Solution Steps:
  • Calculate surface area excluding base: 31 square feet.

Question 16: Average Age Calculation

• Problem: Calculate average age of students.
• Solution Steps:
  • Use weighted average formula.
  • Result: Average age = 14.2 years.

Question 17: Tank Capacities

• Problem: Maximum capacity of two tanks.
• Solution Steps:
  • Solve equations for each tank's capacity.
  • Total capacity: 264 gallons.

Question 18: Tennis Court Area Difference

• Problem: Difference in area between singles and doubles courts.
• Solution Steps:
  • Calculate both areas.
  • Difference: 72 square feet.