{{U}}General Information:{{/U}}
Numbers: All of the numbers used in this section are real numbers.
Figures: Assume that the position of all points, angles, etc. are in the order shown and the measures of angles are positive.
Straight lines can be assumed to be straight.
All figures lie in a plane unless otherwise stated.
The figures given for each question provide information to solve the problem. The figures are not drawn to scale unless otherwise stated. To solve the problems, use your knowledge of mathematics; do not estimate lengths and sizes of the figures to answer questions.
Multiple-choice Questions
Select One Answer Choice
{{U}}Directions:{{/U}} These questions are multiple-choice questions that ask you to select only one answer choice from a list of five choices.
Select One or More Answer Choices
{{U}}Directions:{{/U}} Select one or more answer choices according to the specific question directions.
If the question does not specify how many answer choices to select, select all that apply. The correct answer may be just one of the choices or as many as all of the choices, depending on the question.
No credit is given unless you select all of the correct choices and no others.
If the question specifies how many answer choices to select, select exactly that number of choices.
Numeric Entry Questions
{{U}}Directions:{{/U}} Enter your answer in the answer box(es) below the question. Equivalent forms of the correct answer, such as 2.5 and 2.50, are all correct. Fractions do not need to be reduced to lowest terms.
Enter the exact answer unless the question asks you to round your answer.
Quantitative Comparison Questions
{{U}}Directions:{{/U}} Some questions give you two quantities, Quantity A and Quantity B. Compare the two quantities and choose one of the following answer choices:
A if Quantity A is greater;
B if Quantity B is greater;
C if the two quantities are equal;
D if you cannot determine the relationship based on the given information.
Note: Information and/or figures pertaining to one or both of the quantities may appear above the two columns. Any information that appears in both columns has the same meaning for both Quantity A and Quantity B.
You will also be asked Data Interpretation questions, which are grouped together and refer to the same table, graph, or other data presentation. These questions ask the examinee to interpret or analyze the given data. The types of questions may be Multiple-choice (both types) or Numeric Entry.
Each of Questions 1 to 7 presents two quantities, Quantity A and Quantity B. Compare the two quantities. You may use additional information centered above the quantities if such information is given. Choose one of the following answer choices:
A. if Quantity A is greater;
B. if Quantity B is greater;
C. if the two quantities are equal;
D. if you cannot determine the relationship based on the given information.
单选题
【正确答案】
C
【答案解析】Because the triangle in this problem is a right triangle, use the Pythagorean Theorem to compute the length of the hypotenuse, c, as follows:
c2=62+82
c2=36+64=100
Thus c=10, and Quantity A and Quantity B are equal.
If you recognized that the triangle is a 3-4-5 triangle you could have quickly arrived at the correct answer.
c2=62+82
c2=36+64=100
Thus c=10, and Quantity A and Quantity B are equal.
If you recognized that the triangle is a 3-4-5 triangle you could have quickly arrived at the correct answer.
单选题
【正确答案】
B
【答案解析】To solve this problem, compute the averages of both lists of numbers. For Quantity A, the average of 11, 13, and 15 is [*], or [*], which equals 13. For Quantity B, the average of 12, 14, and 16 is [*], or [*] which equals 14. Therefore, Quantity B is greater than Quantity A.
Another way to solve this problem is to note that all of the numbers in Quantity B are greater than those in Quantity A. Therefore, the average of Quantity B will be greater than the average of Quantity A.
单选题
【正确答案】
D
【答案解析】To solve this problem, try some test values for r, s, and t. Because it is given in the problem that they are negative numbers, r＜0, s＜0, and t＜0. Let r=-1, s=-2 and t=-4. The sum is -7 (-1+-2+-4), but the product is -8 (-1×-2×-4), making the product less than the sum. Now, let r=-0.5, s=-1 and t=-2. The sum is -3.5 (-0.5+-1+-2), but the product is -1 (-0.5×-1×-2), making the product greater than the sum. Therefore, you cannot determine the relationship based on the given information.
单选题
【正确答案】
B
【答案解析】To determine the relationship, solve the equation 3x+4=28 for x. First, subtract 4 from both sides. Then divide both sides by 3 to get x=8. Thus, Quantity B (21) is greater than Quantity A (8).
单选题
【正确答案】
A
【答案解析】Given that a＜0, the quantity 1-a would be greater than 1, because subtracting a negative number has the effect of adding a positive number. The quantity a- 1 is such that a number is being subtracted from a negative number, increasing the magnitude in the negative direction, thus the quantity is less than -1. Therefore, Quantity A is greater than Quantity B.
单选题
【正确答案】
C
【答案解析】Because 0＜x＜1, then 8.5＜(8.5+x)＜9.5. Using the rules for rounding (.5 or higher rounds up), the quantity (8.5+x) will always round to 9 when 0＜x＜1. Therefore, quantities A and B are equal.
单选题
【正确答案】
D
【答案解析】While it may seem obvious that 5a would be greater than [*], consider the case when a＜0. For example 5(-5)=-25 while [*]=-1. Thus when a＞0, 5a is greater than [*]. However, when a＜0, 5a is less than [*]. Therefore, you cannot determine the relationship between Quantity A and Quantity B based on the given information.
单选题
If 65 percent of the people who purchase a certain model of a car are male, what is the ratio of the number of males who purchase the model to the number of females who purchase the model?
A. 
B. 
C. 
D. 
E. 
B.
C.
D.
E.
【正确答案】
B
【答案解析】Because 65 percent of the people are male, then the rest of the 100 percent must be female; therefore, 100-65, or 35 percent of the people are female. If 100 people purchased this particular model of car, then the ratio of males to females would be [*] which reduces to [*].
单选题
Which of the following is the sum of two positive integers whose
product is 36?
【正确答案】
C
【答案解析】To solve this problem, consider the pairs of positive integers whose product is 36: i and 36; 2 and 24; 3 and 12; 4 and 9; and 6 and 6. The only pair whose sum is an answer choice is 3+12, or 15.
填空题
There are six members on a committee, four of whom are women and two of whom are men. The members agree to randomly pull two names out of a hat to serve as Chair and Secretary for the group, respectively. What is the probability that both of the men are chosen? Give the probability as a fraction.
单选题
If the degree measures of the angles of a triangle are in the ratio
2:3:4, what is the degree measure of the smallest angle?
【正确答案】
C
【答案解析】If the degree measures of the angles of a triangle are in the ratio 2:3:4, then the smallest angle will constitute [*], or [*] of the sum of the three angles of the triangle. Because all triangles are composed of three angles whose sum is 180°, the degree measure of the smallest angle is [*] of 180°, or 40°.
多选题
If4 more than twice n is a negative number and 6 more than n is a
positive number, which of the following numbers could be the value of
n?
Select {{U}}all{{/U}} such numbers.
Select {{U}}all{{/U}} such numbers.
【正确答案】
A、B、C
【答案解析】To solve this problem, first translate the words into their mathematical equivalents:
4 more than twice n translates to 4 + 2n. You are given that this quantity is a negative number, which translates to 4 + 2n ＜ 0.
6 more than n translates to 6 + n. You are given that this quantity is a positive number, which translates to 6 + n ＞ 0.
Solve each inequality as follows:
4+2n＜0
n＜-2
6+n＞0
n＞-6
So, n could be any number less than -2 and greater than -6.
单选题
If a+c=13 and b-c=6, then a+b=?
【正确答案】
C
【答案解析】Given that a+c=13 and b-c=6, the quantity a+b can be determined by substitution. If a + c= 13, then c= 13 - a. Substituting c=13-a into b-c=6 yields the following:
b-(13-a)=6
b-13+a=6
b+a=6+13
a+b=19