ASVAB Arithmetic Reasoning Practice: Multi-step Math Problems

Practice questions

1. Luz filled up her 10-gallon gas tank with regular unleaded fuel for $30. Tony used premium fuel, which costs 25 percent more per gallon, to fill his 10-gallon gas tank. Assuming both of their gas tanks were empty, how much did Tony spend?

   A. $37.75 B. $3.75 C. $37.50 D. $30

2. If one side of a square is increased by 6 cm and an adjacent side is decreased by 2 cm, a rectangle with a perimeter of 28 cm is formed. What is the area of the rectangle?

   A. 19 cm² B. 25 cm² C. 31 cm² D. 33 cm²

Answers and explanations

1. The correct answer is Choice (C).

   Write an equation that lets x represent the cost of 1 gallon of unleaded fuel. Ten gallons cost Luz $30, so

   

   Because premium fuel costs 25 percent more, it costs 125 percent of the price of unleaded fuel, so let 1.25x represent the amount Tony spent per gallon. Unleaded gas costs $3 per gallon, so figure out how much Tony spent per gallon by replacing x in his equation with 3:

   $3(1.25) = $3.75

   Each gallon of premium fuel costs $3.75 and Tony bought 10 gallons, so multiply 3.75 by 10 to find out how much Tony spent:

   

   Tony spent $37.50 on fuel.

2. The correct answer is Choice (D).

   This problem requires you to take a few steps to arrive at the answer.

   Create a table that lets you visualize what to use in your equation, letting x represent the length of one side of the square:

   

   The problem gives you the perimeter of the rectangle, so use the perimeter formula to find the dimensions — you'll need them to find the rectangle's area. Remember that P = 2l + 2w, where P represents perimeter, l represents length, and w represents width:

   

   Now you know that the original square's sides each measured 5 centimeters. As the problem tells you, one side was increased by 6 centimeters to create the rectangle, while the other was decreased by 2 centimeters. That makes one side 11 centimeters and the other 3 centimeters. You can find the area of the rectangle with the formula A = lw, where A represents the area, l represents the length, and w represents the width:

   

   The rectangle's area is 33 square centimeters.