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Free practice questions/GMAT Focus Edition

GMAT Focus Edition — Word Problems: Rates, Work & Mixtures

6 free practice questions with full explanations.

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Question 1

A car travels 240 miles at a constant speed, then returns the same 240 miles at a speed 20 mph faster, taking 1 hour less for the return trip. What was the speed of the car on the way there?

  • A) 40 mph
  • B) 48 mph
  • C) 60 mph
  • D) 80 mph
Show answer & explanation

Correct answer: C) 60 mph

Let the initial speed be r. Time there = 240/r, time back = 240/(r+20). 240/r - 240/(r+20) = 1. Testing r=60: 240/60=4, 240/80=3, difference=1. Correct.

Question 2

Machine A can complete a job in 6 hours, and Machine B can complete the same job in 3 hours. Working together, how many hours will it take them to complete the job?

  • A) 1
  • B) 1.5
  • C) 2
  • D) 2.5
Show answer & explanation

Correct answer: C) 2

Combined rate = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2 job per hour. Time = 1/(1/2) = 2 hours.

Question 3

A chemist mixes a 10% saline solution with a 30% saline solution to create 20 liters of a 25% saline solution. How many liters of the 30% solution are used?

  • A) 5
  • B) 10
  • C) 12
  • D) 15
Show answer & explanation

Correct answer: D) 15

Let x = liters of 30% solution, (20-x) = liters of 10% solution. 0.30x + 0.10(20-x) = 0.25(20). 0.30x + 2 - 0.10x = 5. 0.20x = 3. x = 15.

Question 4

Two trains start at the same time from stations 300 miles apart and travel toward each other. Train A travels at 55 mph and Train B travels at 45 mph. How long until they meet?

  • A) 2 hours
  • B) 2.5 hours
  • C) 3 hours
  • D) 3.5 hours
Show answer & explanation

Correct answer: C) 3 hours

Combined speed = 55 + 45 = 100 mph. Time = 300/100 = 3 hours.

Question 5

Pipe A can fill a tank in 4 hours. Pipe B can fill the same tank in 12 hours. If both pipes are opened together, how long will it take to fill the tank?

  • A) 2 hours
  • B) 3 hours
  • C) 4 hours
  • D) 6 hours
Show answer & explanation

Correct answer: B) 3 hours

Combined rate = 1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3 tank per hour. Time = 1/(1/3) = 3 hours.

Question 6

It takes 8 workers 15 days to build a wall. If 4 more workers join, and all workers work at the same rate, how many days will it take to build the same wall?

  • A) 8
  • B) 9
  • C) 10
  • D) 12
Show answer & explanation

Correct answer: C) 10

Total work = 8 workers x 15 days = 120 worker-days. With 12 workers: 120/12 = 10 days.

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