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Set Timing
You will have 62 minutes to complete the following section.
You are not allowed to use a calculator.
A booklet is recommended for taking notes.
Problem Solving question type
Each Problem Solving question consists of a quantitative question and 5 answer choices. Solve the problem and select the best of the given answer choices.
Note that all numbers given are real numbers.
Figures are drawn as accurately as possible, except when explicitly stated otherwise.
Data Sufficiency question type
Each Data Sufficiency question consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question.
In questions that ask you to find a numerical quantity, data provided in the statements are considered sufficient only if it is possible to determine exactly one numerical value for the quantity.
You must answer each question by choosing from 5 Data Sufficiency answer choices:
(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 (1) and (2) TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
These 5 answer choices are presented (in this exact order) for every Data Sufficiency question.
Note that all numbers given are real numbers. Figures are not necessarily drawn to scale.
Set Timing
You will have 62 minutes to complete the following section.
You are not allowed to use a calculator.
A booklet is recommended for taking notes.
Problem Solving question type
Each Problem Solving question consists of a quantitative question and 5 answer choices. Solve the problem and select the best of the given answer choices.
Note that all numbers given are real numbers.
Figures are drawn as accurately as possible, except when explicitly stated otherwise.
Data Sufficiency question type
Each Data Sufficiency question consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question.
In questions that ask you to find a numerical quantity, data provided in the statements are considered sufficient only if it is possible to determine exactly one numerical value for the quantity.
You must answer each question by choosing from 5 Data Sufficiency answer choices:
(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 (1) and (2) TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
These 5 answer choices are presented (in this exact order) for every Data Sufficiency question.
Note that all numbers given are real numbers. Figures are not necessarily drawn to scale.
The table above gives the coffee consumption in 1994 for five countries. If the total coffee consumption of these countries was 40 percent of the world’s coffee consumption, what was the world’s coffee consumption, in millions of kilograms, in 1994?
4,320
4,470
5,400
6,480
6,700
What is the sum of the integers from -190 to 195, inclusive?
0
5
875
965
375
Is the standard deviation of the salaries of Company Y’s employees greater than the standard deviation of the salaries of Company Z’s employees?
(1) The average (arithmetic mean) salary of Company Y’s employees is greater than the average salary of Company Z’s employees.
(2) The median salary of Company Y’s employees is greater than the median salary of Company Z’s employees.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
Square S is inscribed in circle T. If the perimeter of S is 24, what is the circumference of T?
6 π
12 π
3 √2 π
6 √2 π
12 √2 π
The operation @ is defined for all nonzero numbers a and b by a @ b = a/b – b/a. If x and y are nonzero numbers, which of the following statements must be true?
I. x @ xy = x(1 @ y)
II. x @ y = -( y @ x)
III. 1/x @ 1/y = y @ x
I only
II only
III only
I and II
II and III
What was the price at which a merchant sold a certain appliance?
(1) The merchant’s gross profit on the appliance was 20 percent of the price at which the merchant sold the appliance.
(2) The price at which the merchant sold the appliance was $50 more than the merchant’s cost of the appliance.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
An attorney charged a fee for estate planning services for a certain estate. The attorney’s fee was what percent of the assessed value of the estate?
(1) The assessed value of the estate was $1.2 million.
(2) The attorney charged $2,400 for the estate planning services.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient
Is the sum of the integers x and y a prime number?
(1) x is an even prime number.
(2) y is a prime number between 10 and 20.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
There are 11 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?
120
720
1,060
1,520
1,980
If w, x, y, and z are integers such that 1<w < x < y < z and wxyz = 462, then z =?
7
11
14
21
42
The sum of three integers is 40. The largest integer is 3 times the middle integer, and the smallest integer is 23 less than the largest integer. What is the product of the three integers?
1,104
972
672
294
192
If a and b are positive, is (a-1+ b-1)-1 less than (a-1 b-1)-1 ?
(1) a = 2b
(2) a + b > 1
(2) a + b > 1
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
33.3 %
40%
50%
60%
66.6 %
If x is an integer, which of the following must be an odd integer?
2x + 2
4x + 3
12x - 6
13x
14x
A collection of 36 cards consists of 4 sets of 9 cards each. The 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?
(1) The units digit of the sum of the numbers on the remaining 35 cards is 6.
(2) The sum of the numbers on the remaining 35 cards is 176.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
If xy ≠ 0, is x/y = 1?
(1) x2 = y2
(2) xy > 0
(1) x2 = y2
(2) xy > 0
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
A construction company was paid a total of $500,000 for a construction project. The
company’s only costs for the project were for labor and materials. Was the company’s
profit for the project greater than $150,000?
company’s only costs for the project were for labor and materials. Was the company’s
profit for the project greater than $150,000?
(1) The company’s total cost was three times its cost for materials.
(2) The company’s profit was greater than its cost for labor.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
AMOUNT OF BACTERIA PRESENT
| Time | Amount |
| 1:00 P.M. | 10.0 grams |
| 4:00 P.M. | x grams |
| 7:00 P.M. | 14.4 grams |
Data for a certain biology experiment are given in the table above. If the amount of
bacteria present increased by the same fraction during each of the two 3-hour periods
shown, how many grams of bacteria were present at 4:00 P.M.?
bacteria present increased by the same fraction during each of the two 3-hour periods
shown, how many grams of bacteria were present at 4:00 P.M.?
12.0
12.1
12.2
12.3
12.4
The value of (9×107 )(9×108 ) is closest to which of the following?
0%
0
0%
0
0%
0
0%
0
0%
0
A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?
0
1/9
2/9
1/3
1
There are 8 books on a shelf, of which 2 are paperbacks and 6 are hardbacks. How many possible selections of 4 books from this self include at least one paperback?
40
45
50
55
60
In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?
3/5
2/3
3/4
4/5
5/6
Of the goose eggs laid at a certain pond, 2/3 hatched, and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?
280
400
540
600
840
If 1050 – 74 is written as an integer in base 10 notation, what is the sum of the digits in that integer?
424
433
440
449
467
In the rectangular solid above, the three sides shown have areas 12, 15, and 20, respectively. What is the volume of the solid?
60
120
450
1,800
3,600
There are 8 magazines lying on a table; 4 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?
1/2
2/3
32/35
11/12
13/14
What is the remainder when the two digit, positive integer x is divided by 3?
(1) The sum of the digits of x is 5.
(2) The remainder when x is divided by 9 is 5
(1) The sum of the digits of x is 5.
(2) The remainder when x is divided by 9 is 5
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient.
In Town X, 64 percent of the population are employed, and 48 percent of the population are employed males. What percent of the employed people in Town X are females?
16%
25%
32%
40%
52%
If k = -1, which of the following is (are) true?
I. kk = k
II. |k| = -k
III. k0 = -k
I only
I and II only
I and III only
II and III only
I, II, and III
Is the sum of p2 and q2 greater than 1?
(1) p is greater than 1/2.
(2) q is greater than 1/2.
(1) p is greater than 1/2.
(2) q is greater than 1/2.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient.
What is the median number of employees assigned per project for the projects at
Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to
each project.
(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to
each project.
Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to
each project.
(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to
each project.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient.
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