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Free practice questions/GRE General Test

GRE General Test — Word Problems

30 free practice questions with full explanations.

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Question 1

A rectangular garden has a length that is 3 feet more than its width. If the area is 108 square feet, what is the width?

  • A) 6 feet
  • B) 8 feet
  • C) 9 feet
  • D) 10 feet
  • E) 12 feet
Show answer & explanation

Correct answer: C) 9 feet

Let width = w, length = w+3. w(w+3) = 108. w^2 + 3w - 108 = 0. Factoring: (w-9)(w+12) = 0. Since width must be positive, w = 9.

Question 2

A theater sold 250 tickets for a total of $3,150. Adult tickets cost $15 and child tickets cost $9. How many adult tickets were sold?

  • A) 100
  • B) 120
  • C) 140
  • D) 150
  • E) 160
Show answer & explanation

Correct answer: D) 150

Let a = adult tickets, c = child tickets. a + c = 250 and 15a + 9c = 3150. From the first equation, c = 250 - a. Substituting: 15a + 9(250-a) = 3150 -> 15a + 2250 - 9a = 3150 -> 6a = 900 -> a = 150.

Question 3

A car depreciates in value by 15% each year. If a car is purchased for $20,000, what is its approximate value after 2 years?

  • A) $14,000
  • B) $14,450
  • C) $15,000
  • D) $17,000
  • E) $18,500
Show answer & explanation

Correct answer: B) $14,450

Value after 2 years = 20,000 x (0.85)^2 = 20,000 x 0.7225 = $14,450.

Question 4

Working at a constant rate, a team of 4 workers can complete a project in 15 days. If 2 more workers of the same productivity join the team, how many days would the project take?

  • A) 8
  • B) 9
  • C) 10
  • D) 11
  • E) 12
Show answer & explanation

Correct answer: C) 10

Total work = 4 workers x 15 days = 60 worker-days. With 6 workers: 60 / 6 = 10 days.

Question 5

A car travels 180 miles using 6 gallons of gas. At this rate, how many miles can it travel on 10 gallons?

  • A) 320
  • B) 270
  • C) 300
  • D) 250
  • E) 280
Show answer & explanation

Correct answer: C) 300

Rate=180/6=30 miles/gallon. 30x10=300.

Question 6

A shirt priced at $45 is discounted 20%. What is the sale price?

  • A) $32
  • B) $36
  • C) $34
  • D) $38
  • E) $40
Show answer & explanation

Correct answer: B) $36

45 x 0.80 = $36.

Question 7

If 5 workers can complete a task in 12 days, how many days would it take 6 workers at the same rate?

  • A) 10
  • B) 8
  • C) 9
  • D) 11
  • E) 14
Show answer & explanation

Correct answer: A) 10

Total work=5x12=60 worker-days. /6=10 days.

Question 8

The ratio of cats to dogs at a shelter is 3:4. If there are 28 dogs, how many cats are there?

  • A) 18
  • B) 24
  • C) 20
  • D) 25
  • E) 21
Show answer & explanation

Correct answer: E) 21

Ratio 3:4. Each part=28/4=7. Cats=3x7=21.

Question 9

A train travels 240 miles in 4 hours at a constant speed. At this same speed, how long would it take to travel 360 miles?

  • A) 5 hours
  • B) 5.5 hours
  • C) 6 hours
  • D) 6.5 hours
  • E) 7 hours
Show answer & explanation

Correct answer: C) 6 hours

Speed = 240/4 = 60 mph. Time for 360 miles = 360/60 = 6 hours.

Question 10

An investor puts $8,000 into an account earning simple interest. After 3 years, the account has grown to $9,200. What is the annual simple interest rate?

  • A) 4%
  • B) 5%
  • C) 6%
  • D) 8%
  • E) 15%
Show answer & explanation

Correct answer: B) 5%

Interest earned = 9,200 - 8,000 = 1,200 over 3 years. Simple interest: 1,200 = 8,000 x r x 3, so r = 1,200/24,000 = 0.05 = 5%.

Question 11

A mixture is made by combining 3 liters of a solution that is 20% acid with 2 liters of a solution that is 45% acid. What is the acid concentration of the resulting 5-liter mixture?

  • A) 25%
  • B) 28%
  • C) 30%
  • D) 32.5%
  • E) 35%
Show answer & explanation

Correct answer: C) 30%

Total acid = (3 x 0.20) + (2 x 0.45) = 0.60 + 0.90 = 1.50 liters. Concentration = 1.50/5 = 0.30 = 30%.

Question 12

Working alone, Pipe A can fill a tank in 4 hours, and Pipe B can fill the same tank in 6 hours. If both pipes are opened together, how long will it take to fill the tank?

  • A) 2 hours
  • B) 2.4 hours
  • C) 3 hours
  • D) 4.8 hours
  • E) 5 hours
Show answer & explanation

Correct answer: B) 2.4 hours

Pipe A's rate = 1/4 tank/hr, Pipe B's rate = 1/6 tank/hr. Combined rate = 1/4 + 1/6 = 3/12 + 2/12 = 5/12 tank/hr. Time = 1 / (5/12) = 12/5 = 2.4 hours.

Question 13

A car rental company charges a flat fee of $40 plus $0.25 per mile driven. If a customer's total bill was $77.50, how many miles did they drive?

  • A) 130
  • B) 140
  • C) 150
  • D) 160
  • E) 170
Show answer & explanation

Correct answer: C) 150

77.50 = 40 + 0.25m. 37.50 = 0.25m. m = 150.

Question 14

Sarah is twice as old as her brother Tom. In 5 years, Sarah will be 1.5 times as old as Tom. How old is Tom now?

  • A) 5
  • B) 8
  • C) 10
  • D) 12
  • E) 15
Show answer & explanation

Correct answer: A) 5

Let Tom's age = t, Sarah's age = 2t. In 5 years: 2t + 5 = 1.5(t + 5). 2t + 5 = 1.5t + 7.5. 0.5t = 2.5. t = 5.

Question 15

A car travels at 55 mph for 2 hours and then at 65 mph for 3 hours. What is the total distance traveled?

  • A) 265 miles
  • B) 285 miles
  • C) 305 miles
  • D) 325 miles
  • E) 345 miles
Show answer & explanation

Correct answer: C) 305 miles

Distance = (55 x 2) + (65 x 3) = 110 + 195 = 305 miles.

Question 16

Two hoses fill a pool together in 6 hours. If one hose alone would take 10 hours, how long would the other hose alone take to fill the pool?

  • A) 12 hours
  • B) 15 hours
  • C) 18 hours
  • D) 20 hours
  • E) 24 hours
Show answer & explanation

Correct answer: B) 15 hours

Combined rate = 1/6. One hose's rate = 1/10. Other hose's rate = 1/6 - 1/10 = 5/30 - 3/30 = 2/30 = 1/15. So the other hose takes 15 hours alone.

Question 17

A store discounts an item by 20%, then further discounts the sale price by an additional 10%. What is the total percent discount from the original price?

  • A) 28%
  • B) 30%
  • C) 22%
  • D) 18%
  • E) 25%
Show answer & explanation

Correct answer: A) 28%

Final price = original x 0.80 x 0.90 = original x 0.72, meaning the final price is 72% of the original -- a 28% total discount.

Question 18

An account earns simple interest. A deposit of $6,000 grows to $7,200 after 4 years. What is the annual interest rate?

  • A) 4%
  • B) 5%
  • C) 6%
  • D) 8%
  • E) 10%
Show answer & explanation

Correct answer: B) 5%

Interest earned = 7,200 - 6,000 = 1,200 over 4 years. 1,200 = 6,000 x r x 4. r = 1,200/24,000 = 0.05 = 5%.

Question 19

A train travels 180 miles in 3 hours. At this same average speed, how far would it travel in 5 hours?

  • A) 240 miles
  • B) 260 miles
  • C) 280 miles
  • D) 300 miles
  • E) 320 miles
Show answer & explanation

Correct answer: D) 300 miles

Speed = 180/3 = 60 mph. Distance in 5 hours = 60 x 5 = 300 miles.

Question 20

A jacket originally priced at $150 is discounted by 30%, and then the discounted price is subject to 6% sales tax. What is the final price?

  • A) $105.00
  • B) $109.20
  • C) $111.30
  • D) $115.50
  • E) $120.00
Show answer & explanation

Correct answer: C) $111.30

Discounted price = 150 x 0.70 = $105. With 6% tax: 105 x 1.06 = $111.30.

Question 21

A mother is currently 4 times as old as her daughter. In 8 years, she will be 2.5 times as old as her daughter. How old is the daughter now?

  • A) 6
  • B) 8
  • C) 10
  • D) 12
  • E) 14
Show answer & explanation

Correct answer: B) 8

Let daughter's age = d, mother's age = 4d. In 8 years: 4d + 8 = 2.5(d + 8). 4d + 8 = 2.5d + 20. 1.5d = 12. d = 8.

Question 22

Two pumps working together can drain a pool in 4 hours. If one pump alone would take 6 hours, how long would the other pump alone take?

  • A) 8 hours
  • B) 10 hours
  • C) 12 hours
  • D) 14 hours
  • E) 16 hours
Show answer & explanation

Correct answer: C) 12 hours

Combined rate = 1/4. One pump's rate = 1/6. Other pump's rate = 1/4 - 1/6 = 3/12 - 2/12 = 1/12. So the other pump takes 12 hours alone.

Question 23

A recipe requires 3 cups of flour for every 2 cups of sugar. If a baker uses 15 cups of flour, how many cups of sugar are needed?

  • A) 12
  • B) 9
  • C) 7.5
  • D) 10
  • E) 8
Show answer & explanation

Correct answer: D) 10

Ratio flour:sugar = 3:2. 15 cups flour is 5x the base ratio (3x5=15), so sugar = 2x5 = 10 cups.

Question 24

A car travels 240 miles using 8 gallons of gas. At this rate, how many gallons would it need to travel 420 miles?

  • A) 14
  • B) 12
  • C) 15
  • D) 16
  • E) 13
Show answer & explanation

Correct answer: A) 14

Rate = 240/8 = 30 miles/gallon. 420/30 = 14 gallons.

Question 25

Working alone, Pump A can fill a tank in 6 hours, and Pump B can fill the same tank in 3 hours. Working together, how long would it take to fill the tank?

  • A) 1.5 hours
  • B) 2 hours
  • C) 2.5 hours
  • D) 4.5 hours
  • E) 3 hours
Show answer & explanation

Correct answer: B) 2 hours

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

Question 26

An investment of $2,000 grows at 5% simple annual interest. What is the total value after 3 years?

  • A) $2,315
  • B) $2,205
  • C) $2,300
  • D) $2,100
  • E) $2,315.25
Show answer & explanation

Correct answer: C) $2,300

Simple interest = principal x rate x time = 2000 x 0.05 x 3 = $300. Total = 2000 + 300 = $2,300.

Question 27

A jacket priced at $80 is discounted 25%. What is the sale price?

  • A) $55
  • B) $58
  • C) $60
  • D) $64
  • E) $65
Show answer & explanation

Correct answer: C) $60

80 x 0.75 = $60.

Question 28

A community garden allocates plots in a ratio of 3 vegetable plots for every 2 flower plots. If the garden has 40 total plots, how many are vegetable plots?

  • A) 16
  • B) 20
  • C) 22
  • D) 24
  • E) 28
Show answer & explanation

Correct answer: D) 24

Total ratio parts = 3+2=5. Each part = 40/5=8. Vegetable plots = 3x8=24.

Question 29

The ratio of managers to staff at a company is 2:9. If there are 54 staff, how many managers are there?

  • A) 10
  • B) 11
  • C) 13
  • D) 14
  • E) 12
Show answer & explanation

Correct answer: E) 12

Each part = 54/9=6. Managers=2x6=12.

Question 30

If 8 workers can complete a task in 15 days, how many days would it take 10 workers at the same rate?

  • A) 12
  • B) 10
  • C) 11
  • D) 13
  • E) 14
Show answer & explanation

Correct answer: A) 12

Total work=8x15=120 worker-days. /10=12 days.

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