GRE Quantitative Reasoning Practice: Work, Mixture and Interest Problems
- Work, Mixture and Interest Problems
- 10 questions
- 15 minutes
Word problems on the GRE usually hide a simple equation: a rate times a time, a part over a whole, or a total divided by a count. Write that equation before you calculate, and check that your answer makes sense in the story.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
Pipe A can fill a tank in 4 hours, and pipe B can fill the same tank in 6 hours.
Working together, how long do the two pipes take to fill the empty tank?
Correct answer: C
Together they fill 1/4 + 1/6 = 5/12 of the tank per hour, so the time is 12/5 hours = 2.4 hours, which is 2 hours 24 minutes. The value 5 hours is the average of the two times, but working together must be faster than either pipe alone.
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Question 2
A chemist has 20 liters of a solution that is 30% acid.
How many liters of pure water must be added to make a solution that is 20% acid?
Correct answer: D
The 6 liters of acid stay the same. For them to be 20% of the new volume, the volume must be 6 ÷ 0.20 = 30 liters, so 10 liters of water are added. The value 2 comes from taking 10% of 20, which ignores that the total volume grows.
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Question 3
An account earns 4% interest compounded annually. $5,000 is deposited, and nothing else is deposited or withdrawn.
What is the balance after 2 years?
Correct answer: B
Each year multiplies the balance by 1.04: 5,000 × 1.04 × 1.04 = 5,408. The value $5,400 is simple interest, which ignores the interest earned on the first year's interest.
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Question 4
Two trains leave the same station at the same time and travel in opposite directions, one at 55 miles per hour and the other at 65 miles per hour.
After how many hours are the trains 300 miles apart?
Correct answer: A
Moving in opposite directions, the distance between them grows by 55 + 65 = 120 miles each hour, so 300 ÷ 120 = 2.5 hours. Using the difference of the speeds (10) would be right only if they traveled in the same direction.
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Question 5
An employee's salary is raised by 10%, and a year later the new salary is raised by 20%.
By what percent is the final salary greater than the original salary?
Correct answer: D
The salary is multiplied by 1.10 and then by 1.20, which is 1.32 in total, a 32% increase. Adding the percents gives 30%, which misses the 20% raise on the first 10%.
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Question 6
The average (arithmetic mean) of five numbers is 18. When one of the numbers is removed, the average of the remaining four numbers is 16.
What number was removed?
Correct answer: E
The five numbers add up to 5 × 18 = 90 and the remaining four to 4 × 16 = 64, so the removed number is 90 − 64 = 26.
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Question 7
A store prices an item 40% above its cost and then sells it at 25% off that price.
The selling price is what percent greater than the cost?
Correct answer: A
The selling price is 1.40 × 0.75 = 1.05 times the cost, so it is 5% above cost. Subtracting the percents (40 − 25 = 15) ignores that the discount is taken from the higher marked price.
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Question 8
In a class of 20 students the average test score is 70, and in a class of 30 students the average score on the same test is 80.
What is the average score of all 50 students together?
Correct answer: C
The total of all scores is 20 × 70 + 30 × 80 = 1,400 + 2,400 = 3,800, and 3,800 ÷ 50 = 76. The value 75 averages the two class averages without weighting the larger class more.
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Question 9
A loan earns simple interest at 5% per year.
What principal earns $360 in interest in 3 years?
Correct answer: B
Simple interest is principal × rate × time, so P × 0.05 × 3 = 360 and P = 360 ÷ 0.15 = 2,400. The value $7,200 forgets the 3 years and uses 360 ÷ 0.05.
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Question 10
Six identical machines, working at the same constant rate, produce 270 parts in 5 hours.
At this rate, how many parts can 10 such machines produce in 8 hours?
Correct answer: E
One machine makes 270 ÷ (6 × 5) = 9 parts per hour, so 10 machines in 8 hours make 9 × 10 × 8 = 720 parts.
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