A. if Quantity A is greater;
B. if Quantity B is greater;
C. if the two quantities are equal;
D. if it is impossible to determine which quantity is greater.
Note: The given information, if any, is always centered above the two quantifies. In any question, if a symbol or letter appears more than once, it represents the same thing each time.
单选题
【正确答案】
A
【答案解析】The only positive divisors of 19 are 1 and 19. Quantity A: 1 + 19 = 20.
Quantity B: 1 × 19 = 19. Quantity A is greater.
单选题
【正确答案】
A
【答案解析】Since (a, b) is on the positive portion of the x-axis, a is positive and b = 0；so a + b is positive. Also, since (c, d) is on the negative portion of the y-axis, c is negative and d = 0; so c + d is negative. Quantity A is greater.
单选题
【正确答案】
D
【答案解析】By the distributive law, Quantity A is 5 r + 5 t. Subtract 5 r from each quantity, and compare 5 t and t. They are equal if t = 0 and unequal otherwise. Neither quantity is always greater, and the two quantities are not always equal (D).
单选题
【正确答案】
A
【答案解析】Quantity A: there are 5 positive multiples of 5 less than 26: 5, 10, 15, 20, 25; their average is 15, the middle one [KEY FACT E5].
Quantity B: there are 3 positive multiples of 7 less than 26:7, 14, 21; their average is 14.
Quantity A is greater.
单选题
【正确答案】
B
【答案解析】[*]
Therefore, d- c = cd, which is positive. Then, d- c is positive, and so d ＞ c.
Quantity B is greater.
单选题
【正确答案】
C
【答案解析】The simplest solution is to realize that there is one palindrome between 100 and 109 (101), one between 390 and 399 (393), one between 880 and 889 (888), and in general, one out of every 10 numbers. So the probability is [*]. The answer is (C).
**The more direct solution is to count the number of palindromes. Either systematically make a list and notice that there are 10 of them between 100 and 199, and 10 in each of the hundreds from the 100s to the 900s, for a total of 90; or use the counting principle: the first digit can be chosen in any of 9 ways, the second in any of 10 ways, and the third, since it must match the first, can be chosen in only 1 way (9 × 10 × 1 = 90).
Since there are 900 three-digit numbers, the
probability is [*]
单选题
Jack and Jill each bought the same TV set using a 10% off coupon. Jack's cashier took 10% offthe price and then added 8.5% sales tax. Jill's cashier first added the tax and then took 10% offthe total price.
【正确答案】
C
【答案解析】Let P = the price of the TV set. Then Jack paid 1.085(.90P), whereas Jill paid .90(1.085P). The quantities are equal (C).
**Use TACTIC 2, Chapter 9, and choose a convenient number: assume the TV cost $100. Jack paid $90 plus $7.65 tax (8.5% of $90) for a total of $97.65. Jill's cashier rang up $100 plus $8.50 tax and then deducted $10.85 (10% of $108.50) for a final cost of $97.65.
单选题
【正确答案】
A
【答案解析】Quantity A: Since the hypotenuse is 2, the length of each leg is
[*]
[*]
Quantity B: Since the hypotenuse is 2, the shorter leg is 1, the longer leg is [*], and the area is [*] , which is less than 1 because [*] is less than 2.
Quantity A is greater.
单选题
Directions: Questions 9-20 have three different formats. Unless a
question has its own directions that specifically state otherwise, each question
has five answer choices, exacdy one of which is correct. If it is now June, what
month will it be 400 months from now?
【正确答案】
D
【答案解析】Since 400 = 12 × 33 + 4,100 months is 4 months more than 33 years. 33 years from June it will again be June, and 4 months later it will be October. [See Section 11-P]
**Look for a pattern. Since there are 12 months in a year, after every 12 months it will again be June; i.e., it will be June after 12, 24, 36, 48, ... , 120, ... ,360 months. So, 396 (33 × 12) months from now, it will again be June. Count 4 more months to October.
填空题
Directions: The answer to the following question is a fraction. Enter the numerator in the upper box and the denominator in the lower box. If 
of the members of the school chorus are boys, what is the ratio of girls to boys in the chorus?
of the members of the school chorus are boys, what is the ratio of girls to boys in the chorus?
填空题
Directions: For the following question, enter your answer in the box, What is the volume of a cube whose total surface area is 54?
单选题
If A is 25 kilometers east of B, which is 12 kilometers south of C, which is 9 kilometers west of D, how far is it, in kilometers, from A to D?
【正确答案】
A
【答案解析】Use TACTIC 1 in Chapter 7: draw a diagram. In the figure below, form rectangle BCDE by drawing DE⊥AB.
[*]
Then, BE = 9, AE = 16, and DE = 12. Finally, DA = 20, because right triangle AED is a 3-4-5 triangle in which each side is multiplied by 4. If you don't realize that, use the Pythagorean theorem to get DA:
(DA)2 = (AE)2 + (DE)2 = 256 + 144 = 400[*]DA = 20.
[*]
Then, BE = 9, AE = 16, and DE = 12. Finally, DA = 20, because right triangle AED is a 3-4-5 triangle in which each side is multiplied by 4. If you don't realize that, use the Pythagorean theorem to get DA:
(DA)2 = (AE)2 + (DE)2 = 256 + 144 = 400[*]DA = 20.
多选题
Directions: For the following question, consider each of the choices
separately and select all that apply. In triangle ABC, AB = AC = 2. Which of the
following could be the area of triangle ABC ? Indicate all possible areas.
【正确答案】
A、B、C、D
【答案解析】·If m∠A = 90°, then the area of triangle ABC is [*].
So choice D is possible.
[*]
· If angle A is either acute or obtuse and we treat AC as the base of the triangle, then the height, h, is less than 2, and so
[*]
[*]
In fact, h can be any positive number less than 2. So choices A, B, and C are also possible. Since h cannot be greater than 2, choices E and F are not possible.