单选题
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 quantities. 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】[*]
For any positive numbers a and b, if a ＜ b,[*]
[*]
单选题
【正确答案】
B
【答案解析】It is irrelevant that 700 ＜ n ＜ 800. Every factor of n is a factor of 2n, but 2 is a prime factor of 2n, which is not a factor of n (since n is odd). 2n has more prime factors than n. Quantity B is greater.
单选题
【正确答案】
B
【答案解析】Since x ＜ y, the average of x and y is less than y, so having another y raises the average. Quantity B is greater.
** Plug in the numbers: say x = 2 and y = 4.
Quantity A: the average of 2 and 4 is 3.
Quantity B: the average of 2, 4, and 4 is 10 ÷ 3 = 3.333, which is more than 3; the second 4 raised the average.
单选题
【正确答案】
A
【答案解析】In any triangle, if one side is longer than a second side, the angle opposite the longer side is greater than the angle opposite the shorter side, so c ＞ d. Quantity A is greater. (It is irrelevant that the third angle is 135°.)
单选题
【正确答案】
B
【答案解析】[*]
单选题
【正确答案】
D
【答案解析】Could x and y be equal? Yes, the two small triangles could be right triangles, and x and y could each be 40. Must they be equal? No, see the figure below, in which clearly x ＜ y. Neither quantity is always greater, and the quantities are not always equal.
[*]
单选题
【正确答案】
B
【答案解析】I Don't waste time using the slope formula; just make a quick sketch.
[*]
Note that I slopes downward, so its slope is negative, whereas m slopes upward, so its slope is positive. Quantity B is greater.