Common Word Problems
This handout is devoted to the reoccurring word problems that appear
on the GMAT. Remember to continue Plugging in and Backsolving for
problems that you cannot set up algebraically.
 Dirt


Formula 
You may have to use the formula a couple times in one problem
If a car travels at an average speed of 70 kilometers per hour for 4
hours, how many kilometers does it travel?
On a 400-mile trip, car X traveled half the distance at 40 miles per hour
and the other half at 50 miles per hour. What was the average speed of
car X?
 Work

2 or 3 individuals who work at different rates
 Formula 
If machine X can produce 1,000 bolts in 4 hours and machine Y can
produce 1,000 bolts in 5 hours, in how many hours can machines X and
Y, working together at these constant rates, produce 1,000 bolts?

2 different size groups who work at the same rate
 Formula 
If 5 workers take an hour to dig a ditch, how long should it take 12
workers to dig a ditch of the same size?
 Proportion
If 5 shirts cost $44, then at this rate, what is the cost of 8 shirts?
 Ratio

Use the ratio box
If ¾ of the employees in a supermarket are not college graduates, what
is the ratio of the number of college graduates to those who are not
college graduates?
Last year, the ratio of the number of tennis matches that Central
College’s women’s team won to the number of matches they lost was
7:3. What percent of their matches did the team win?
There are 90 red and blue marbles in a bag in a ratio of 5:13
respectively. How many blue marbles are there?
1
 Measurement

Convert
A train travels at a constant rate of 25 meters per second. How many
kilometers does it travel in 5 minutes? (1 kilometer = 1,000 meters)
 Average

Finding the average
The temperature at noon in Coldtown, USA was 5F on Monday, 10F
on Tuesday, -2F below zero on Wednesday, -5F below zero on
Thursday, 0F on Friday, 4F on Saturday, and -1F below zero on
Sunday. What was the average temperature at noon for the week?

Finding the missing element
 Formula 
 Sum of the numbers = Sum of average that many times
If the average annual income of 10 workers is $15,665 and two of the
workers each make $20,000 for the year, what is the average annual
income of the remaining 8 workers?
 Mixture

Formula 
If 6 pounds of nuts that cost $1.20 per pound are mixed with 2 pounds
of nuts that cost $1.60 per pound, what is the cost per pound of the
mixture?
 Percentage

Regular
 Translate
 “Per”
What is 45 percent of 7/12 of 240?

Try __________ ___ to solve this type
The price of an item is discounted by 20 percent and then this reduced
price is discounted by an additional 30 percent. These two discounts
are equal to an overall discount of what percent?

“What was the percentage change?”
 Formula 
If the price of an item increases from $24 to $30, what is the percent
increase in price?

“What was the original amount?”
 Formula 
 Try __________ to solve this type
2
A certain customer paid $24 for a dress. If that price represented a 25
percent discount on the original price of the dress, what was the
original price of the dress?

Interest



Formula 
Simple vs. Compound
You will often have to take the annual rate and divide among the year; semiannually,
quarterly, or monthly
If $8,000 is invested at 6 percent simple annual interest, how much
interest is earned after 3 months?
 Profit

Profit = _________ – __________
A certain appliance costs a merchant $30. At what price should the
merchant sell the appliance in order to make a gross profit of 50 percent
of the cost of the appliance?
 Venn Diagrams

Remember the center must be subtracted from the two sets
In a survey, 60% of those surveyed owned a car and 80% of those
surveyed owned a TV. If 55% owned both a car and a TV, what
percent of those surveyed owned a car or a TV or both?
In a certain production lot, 40 percent of the toys are red and the
remaining toys are green. Half of the toys are small and half are large.
If 10 percent of the toys are red and small, and 40 toys are green and
large, how many of the toys are red and large?
 Permutations

Each time you have to make a choice, draw a space
If there are 3 different roads from Syracuse to Binghamton and 4
different roads from Binghamton to Scranton, how many different
routes are there from Syracuse to Scranton that go through
Binghamton?
A club has 20 members. They are electing a president and a vicepresident. How many different outcomes of the election are possible?
(Assume the president and vice-president must be different members of
the club.)
3
A train travels at an average speed of 50 miles
per hour for 2 ½ hours and then travels at a speed
of 70 miles per hour for 1 ½ hours. How far did
the train travel in the entire 4 hours?
A) 120
B) 185
C) 210
D) 230
E) 240
Pam and Sue drove to a business meeting 120
miles away in the same car. Pam drove to the
meeting and Sue drove back along the same
route. If Pam drove at 60 miles per hour and Sue
drove at 50 miles per hour, how much longer, in
minutes, did it take Sue to travel the distance
than it did Pam?
A) 4
B) 10
C) 20
D) 24
E) 30
A train travels at an average speed of 20 mph
through urban areas, 50 mph through suburban
areas, and 75 mph through rural areas. If a trip
consists of traveling half an hour through urban
areas, 3 ½ hours through suburban areas, and 3
hours through rural areas, what is the train’s
average speed for the entire trip?
A) 48 1/3
B) 50
C) 54 3/7
D) 58 4/7
E) 59 2/7
The distance from Cleveland to Buffalo is 200
miles. A train takes 3 ½ hours to go from
Buffalo to Cleveland and 4 ½ hours to go back
from Cleveland to Buffalo. What was the
average speed of the train for the round trip from
Buffalo to Cleveland and back?
A) 25.39
B) 26
C) 49.5
D) 50
E) 50.79
A car is traveling on a straight highway. At 10
o’clock, it passes a truck traveling in the same
direction. The truck continues on the highway
traveling at 50 mph while the car travels at 65
mph. How far apart are the car and the truck at 2
o’clock?
A) 15 miles
B) 30 miles
C) 60 miles
D) 200 miles
E) 260 miles
Stan drove for h hours at a constant rate of r
miles per hour. How many miles did he go
during the final 20 minutes of his drive?
A) 20r
B) hr
3
C) 3hr
D) hr
E)
20
r
3
Two airplanes are 300 miles apart and flying
directly toward each other. One is flying at 200
mph, and the other at 160mph. How long will it
take for the two planes to meet?
A) 36 minutes
B) 50 minutes
C) 1 hour and 12 minutes
D) 1 hour and 40 minutes
E) 1 hour and 41 minutes
Doreen can wash her car in 15 minutes, while
her younger brother Dave takes twice as long to
do the same job. If they work together, how
many minutes will the job take them?
A) 5
B) 7 ½
C) 10
D) 22 ½
E) 30
If 15 workers can pave a certain number of
driveways in 24 days, how many days will 40
workers take, working at the same rate, to do
the same job?
A) 9
B) 12
C) 20
D) 25
E) 64
4
If Paul can paint a fence in 2 hours and Fred can
paint the same fence in 3 hours, Paul and Fred
working together can paint the fence in how
many hours?
A) 5
B) 2 ½
C) 1 1/5
D) 1
E) 5/6
There are two taps, tap 1 and tap 2, in a keg. If
both taps are opened, the keg is drained in 20
minutes. If tap 1 is closed and tap 2 is open, the
keg will be drained in 30 minutes. If tap 2 is
closed and tap 1 is open, how long will it take to
drain the keg? 1 hour
A) 10 minutes
B) 40 minutes
C) 45 minutes
D) 50 minutes
E) 60 minutes
When both floodgates A and B are open, a
reservoir drains in 3 1/3 days. If floodgate A
alone drains the reservoir in 10 days, how many
days does it take floodgate B alone to drain the
reservoir?
A) 4
B) 5
C) 6 2/3
D) 10
E) 12
A worker is digging a ditch. He gets 2 assistants
who work 2/3 as fast as he does. If all 3 work on
a ditch, they should finish it in what fraction of
the time that the worker takes working alone?
A) 3/7
B) 1/2
C) 3/4
D) 4/3
E) 7/3
Machine A and Machine B are each used to
manufacture 660 sprockets. It takes machine A
10 hours longer to produce 660 sprockets than
machine B. Machine B produces 10 percent
more sprockets per hour than machine A. How
many sprockets per hour does machine A
produce?
A) 6
B) 6.6
C) 60
D) 100
E) 110
If 4 boys can shovel a driveway in 2 hours, how
many minutes will it take 5 boys to do the job?
A) 60
B) 72
C) 96
D) 120
E) 150
If Sam can finish a job in 3 hours and Mark can
finish a job in 12 hours, in how many hours
could they finish the job if they worked on it
together at their respective rates?
A) 1
B) 2 2/5
C) 2 5/8
D) 3 ¼
E) 4
If Art and Rita can do a job in 4 hours when
working together at their respective constant
rates and Art can do the job alone in 6 hours, in
how many hours can Rita do the job alone?
A) 2
B) 8
C) 8 ½
D) 10
E) 12
A worker makes a basket in 2/3 of an hour. If
the worker works for 7 ½ hours, how many
baskets will he make?
A) 5
B) 10
C) 11 ¼
D) 12
E) 15
If m is proportional to n and m = 5 when n = 4,
what is the value of m when n = 18?
A) 11
B) 14.4
C) 20
D) 22.5
E) 25
The concession stand at Cinema City sells
popcorn in three sizes: large, super, and jumbo.
One day, Cinema City sold 240 bags of popcorn,
and the ratio of large to super to jumbo was
8:17:15. How many super bags of popcorn were
sold that day?
A) 48
B) 90
C) 102
D) 108
E) 120
5
If the ratio of juniors to seniors on a team is 3:5,
what percent of the team members are seniors?
A) 37.5%
B) 40%
C) 60%
D) 62.5%
E) It cannot be determined from the
information given
The average of 5, 10, 15, and z is 20. What is z?
A) 0
B) 20
C) 25
D) 45
E) 50
The average of 10 numbers is –10. If the sum of 6
of them is 100, what is the average of the other 4?
A) –100
B) –50
C) 0
D) 50
E) 100
Sheila took five chemistry tests during the
semester and the average of her test scores was
85. If her average after the first three tests was
83, what was the average of her fourth and fifth
tests?
A) 83
B) 85
C) 87
D) 88
E) 90
How many liters of a solution that is 15 percent
salt must be added to 5 liters of a solution that is
8 percent salt so that the resulting solution is 10
percent salt?
A) 2
B) 6
C) 7
D) 10
E) 13
A solution is 90 percent glycerin. If there are 4
gallons of the solution, how much water, in
gallons, must be added to make a 75-percent
glycerin solution?
A) 1.8
B) 1.4
C) 1.2
D) 1.0
E) 0.8
Amanda bought a $60 sweater on sale at 5% off.
How much did she pay, including 5% sales tax?
A) $54.15
B) $57.00
C) $57.75
D) $59.85
E) $60.00
A coat was sold for $75. The coat was sold for
150% of the cost of the coat. How much did the
coat cost?
A) $11.25
B) $50.00
C) $63.75
D) $112.50
E) $225.00
What was the percentage discount on a which
originally cost $5,000 was reduced to $4,800?
A) 200%
B) 96%
C) 40%
D) 4.16%
E) 4%
If 25% of 260 equals 6.5% of a, what is a?
A) 10
B) 65
C) 100
D) 130
E) 1000
From 1989 to 1990, the number of applicants to
a college increased 15% to 5060? How many
applicants were there in 1989?
A) 759
B) 4301
C) 4400
D) 5819
E) 5953
During his second week on the job, Mario earned
$110. This represented a 25% increase over his
earnings of the previous week. How much did
he earn during his first week of work?
A) $82.50
B) $85.00
C) $88.00
D) $137.50
E) $146.67
6
A Merchant was selling an item at a certain
price, then marked it down 20% for a spring sale.
During the summer, he marked the item down
another 20% from its spring price. If the item
sold at the summer price, what percent of the
original price did it sell for?
A) 40%
B) 60%
C) 64%
D) 67%
E) 80%
From 1994 to 1995 the sales of a book decreased
by 80%. If the sales in 1996 were the same as in
1994, by what percent did they increase from
1995 to 1996?
A) 80
B) 100
C) 120
D) 400
E) 500
If x% of y is 10, what is y?
A) 10
x
B) 100
x
C) 1000
D)
E)
x
x
100
x
10
Ms. Lopez deposits $100 in an account that pays
20% interest, compounded semiannually. How
much money will there be in the account at the
end of one year?
A) $118.00
B) $120.00
C) $121.00
D) $122.00
E) $140.00
How much interest will $10,000 earn in 9
months at an annual rate of 6%?
A) $450
B) $540
C) $560
D) $600
E) $667
What will $1000 be worth after three years if it
earns interest at the rate of 5% compounded
annually?
A) $1,150
B) $1,155
C) $1,157.63
D) $1,158.52
E) $1,160
If $10,000 is invested at 10 percent annual
interest, compounded semiannually, what is the
balance after 1 year?
A) $10,010
B) $10,015
C) $11,000
D) $11,025
E) $12,100
Half the graduating class of a college was
accepted by a business school. One-third of the
class was accepted by a law school. If one-fifth
of the class was accepted to both types of school,
what fraction of the class was accepted only by a
law school.
A) 1/60
B) 2/15
C) 1/3
D) 1/2
E) 4/5
At a school of 50 students, 20 students are
enrolled in history and 12 are enrolled in
mathematics. If 8 are enrolled in both classes,
how many are enrolled in neither?
A) 10
B) 18
C) 24
D) 26
E) 40
In a certain town 40% of the people have brown
hair, 25% have brown eyes, and 10% have both
brown hair and brown eyes. What percentage of
the people in the town have neither brown hair
nor brown eyes?
A) 35
B) 40
C) 45
D) 50
E) 55
7
7 basketball teams play in a league against each
other. At the end of the season, how many
different ways could the top 3 teams end up in
the rankings?
A) 6
B) 42
C) 210
D) 5,040
E) 5,045
At a restaurant, you must choose an appetizer, a
main course, and a dessert. If there are 2
possible appetizers, 3 possible main courses, and
5 possible desserts, how many different meals
could you order?
A) 60
B) 30
C) 10
D) 6
E) 3
8