GMAT
Problem solving and Data Sufficiency
Problem Solving (10)
1. The denominator of a certain fraction is twice as great as the numerator. If 4 are added to
both the numerator and denominator, the new fraction would be 5/8. What is the
denominator of the fraction?
A. 3
B. 6
C. 9
D. 12
E. 13
2. A rectangular door measures 5 feet in width by 6 feet, 8 inches in height. What is the
distance from one corner of the door to the diagonally opposite corner?
A. 8 feet, 3 inches
B. 8 feet, 4 inches
C. 9 feet
D. 9 feet, 4 inches
E. 9 feet, 6 inches
3. A store sells a six-pack of soda for $2.70. If this represents a savings of 10 percent of the
individual price of cans of soda, then what is the price of a single can of soda?
A. $0.35
B. $0.40
C. $0.45
D. $0.50
E. $0.55
4. There are 8 teams in a certain league and each team play each of the other teams exactly
once. If each game is played by 2 teams, what is the total number of games played?
A. 15
B. 16
C. 28
D. 56
E. 64
5. The distance from City 1 to City 22 is 825 kilometers. On an accurate map showing both
cities, 1 centimeter represents 75 kilometers. On the map, how man millimeters separate
City 1 and City 2? [Note: 1 centimeter = 10 millimeters.]
A. 10
B. 45
C. 60
D. 90
E. 110
6. For the past x laps around the track. Steven’s average time per lap was 51 seconds. If a
lap of 39 seconds would reduce his average time per lap to 49 seconds, what is the value
of x?
A. 2
B. 5
C. 6
D. 10
E. 12
2, 4, 6, 8, n, 3, 5, 7, 9
7. In the list above, if n is an integer between 1 and 10, inclusive, then the median must be
A. either 4 or 5
B. either 5 or 6
C. either 6 or 7
D. n
E. 5.50
8. If a portion of $ 10,000 is invested at 6%and the remaining portion is invested at 5%, and
if x represents the amount invested at 6%, what is the annual income in dollars from the
5% investment?
A. .05(10,000 – x)
B. .05(x + 10,000)
C. 5(x – 10,000)
D. 5(10,000 – x)
E. .05(x – 10,000)
9. A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the
carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high
as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?
A. 20
B. 40
C. 60
D. 80
E. 100
10. If x + 5 > 2 and x – 3 < 7, the value of x must be between which of the following pairs of
numbers?
A. -3 and 10
B. -3 and 4
C. 2 and 7
D. 3 and 4
E. 3 and 10
Data Sufficiency Test (10)
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
1. If Ms. Smith’ income was 20 percent more for 1991 than it was for 1990, how
much was g=her income for 1991?
(1) Ms. Smith’s income for the first 6 months of 1990 was $17,500 and her
income for the last 6 months of 1990 was $20,000.
(2) Ms. Smith’s income for 1991 was $7,500 greater than her income for
1990.
2. If n + k = m, what is the value of k?
(1) n = 10
(2) m + 10 = n
3. If Beth spent $400 of her earnings last month on rent, how much did Beth earn last
month?
(1) Beth saved 1/3 of her earning last month and spent half of the remainder
on rent.
(2) Beth earned twice as much this month as last month.
4. What is the numerical ration P: Q: R?
(1) The ratio P: Q is 1:2.
(2) R = 5
5. If he total price of five grocery items is $6.05, what is the price of the most
expensive of these items?
(1) The price of the most expensive item is exactly 50 percent greater than
the price of each of the other four items.
(2) The price of each item (except the most expensive item) is $1.10.
6. What is the value of xy – yz?
(1) y = 2
(2) x – z = 5
7. If Amy drove the distance from her home to the beach in less than 2 hours, was her
average speed greater than 60 miles per hour?
(1) The distance that Amy drove from her home to the beach was less than 125
miles.
(2) The distance that Amy drove from her home to the beach was greater than 122
miles.
8. Code letters X, Y, and Z each represent one digit in the three-digit prime number XYZ.
If neither X nor Y is an odd integer, what is the number represented by XYZ?
(1) The sum of three digits is 7.
(2) X – Y > 2
9. How many people are directors of both company K and company R?
(1) There were 17 directors present at a joint meeting of the directors of company
K and company R, and no directors were absent.
(2) Company K has 12 directors and company R has 8 directors.
10. In a certain office, 50 percent of the employees are college graduates and 60 percent of
the employees are over 40 years old. If 30 percent of those over 40 have master’s
degrees, how many of the employees over 40 have master’s degrees?
(1) Exactly 100 of the employees are college graduates.
(2) Of the employees 40 years old or less, 25 percent have master’s degrees.