{{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 yon 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】
B
【答案解析】Opposite angles of a parallelogram are congruent, or equal. Therefore, (s-6)=(r-4). Select one variable and solve:
s-6=r-4
s=r+2
If s=r+2, then s must be greater than r, and Quantity B is greater than Quantity A.
单选题
【正确答案】
B
【答案解析】Because [*] is less than [*] subtracting [*] from 1 will result in a larger number than will subtracting [*] from 1. Therefore, Quantity B is greater Quantity A.
单选题
【正确答案】
B
【答案解析】To solve this problem, pay attention to the location of the negative sign. Quantity A=-(4 × 4] =-16. Quantity B = (-4 × -4) = 16.
单选题
【正确答案】
C
【答案解析】To easily solve this problem, recognize that (4x) (7y) = 28xy. Therefore, no matter what value you assign to either x or y, the quantities will be the same.
单选题
【正确答案】
A
【答案解析】To solve this problem set up 3 equations:
Mike = Tom - 3
Mark = Tim + 8
Tom = Tim + 9
Substitute (Tim+9) for Tom in the first equation:
Mike = Tim + 9 - 3 = Tim + 6.
If Mike = Tim + 6 and Mark = Tim + 8, then Mark = Mike + 2. Therefore, Mark's age is greater Mike's age, and Quantity A is greater than Quantity B.
单选题
【正确答案】
A
【答案解析】To solve this problem, let x be the radius of each racquetball. The height of the six racquetballs, then, is 12x, because the diameter is equal to 2x. The racquetballs are circles, so the circumference of each racquetball is 2πx. Quantity A, the sum of the circumferences of three racquetballs, is 6πx. The value of n is approximately 3.14, so 6πx will be greater than 12x, and Quantity A is greater than Quantity B.
单选题
【正确答案】
A
【答案解析】The number of male dogs is 17-5 or 12. The fraction of male dogs in the kennel is [*]. The ratio of female to male dogs is [*]. Therefore, Quantity A is greater than Quantity B.
单选题
In an office supply shop, pens that normally sell for 89 cents each are
on sale at 2 for $1.29. How much can be saved by purchasing 12 of these pens at
the sales price?
【正确答案】
B
【答案解析】Normally, 12 pens would cost 12($0.89), or $10.68. At the sales price, 12 pens cost 6($1.29), or $7.74. This gives you a savings of $10.68-$7.74, or $2.94.
单选题
If the average (arithmetic mean) of 7 consecutive numbers is 16, what
is the sum of the least and greatest of the 7 integers?
【正确答案】
【答案解析】To solve this problem, first set the least of the seven values to z. When the least of the seven numbers is x, the remaining numbers are x+1, x+2, x+3, x+4, x+5, and x+6, because the numbers are consecutive. Because the average of the seven numbers is 16, then [x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)+[x+6)] divided by 7=16. Solve for x:
[*]
The smallest number, x, is 13, and the largest number is x+6. Therefore the largest number is equal to 13+6, or 19, and the sum of these two numbers is 13+19, or 32.
填空题
If 3x+4y=17 and 5x+2y=23, what is the value of x-y?
单选题
In the figure above, a small circle, with radius x, is inside a larger
circle, with radius 6. What is the area, in terms of x, of the shaded
region?
【正确答案】
【答案解析】To solve this problem, first calculate the area of the larger circle: A=πr2=π62=36π. Next, calculate the area of the smaller circle: A=x2π. Finally, subtract the area of the smaller circle from the area of the larger circle: 36π-x2π.
多选题
If |4-3x|＜5, which of the following is a possible value of
x?
Select {{U}}all{{/U}} such values.
Select {{U}}all{{/U}} such values.
【正确答案】
A、B
【答案解析】This problem tests your knowledge of absolute values and inequalities. |4-3x|＜5 can be written as two separate inequalities: 4-3x＜5 and 4-3x＞-5. Because the original inequality was a "less than," the word in between the two new inequalities must be AND.
Solve both inequalities as follows:
4-3x＜5
-3x＜1
[*]
When you multiply both sides of an inequality by a negative number, you must reverse the inequality sign.
[*]
Now move on to the next inequality.
4-3x＞-5
-3x＞-9
x＜3
Answer choices A and B are both greater than [*] and less than 3.
单选题
The number 0.001 is how many times greater than the number
(0.0001)2?
【正确答案】
C
【答案解析】To solve this problem, first square the value 0.0001:
(0.0001)2 = 0.00000001
This value is equivalent to 1 × 10-8, because the decimal point is moved 8 places to the left. On the other hand, 0.001 is equivalent to 1 × 10-3, because the decimal point is moved 3 places to the left. Thus, because [*], 0.001 is 105 times greater than (0.0001)2.
(0.0001)2 = 0.00000001
This value is equivalent to 1 × 10-8, because the decimal point is moved 8 places to the left. On the other hand, 0.001 is equivalent to 1 × 10-3, because the decimal point is moved 3 places to the left. Thus, because [*], 0.001 is 105 times greater than (0.0001)2.