In this section use scrap paper to solve each problem. Then decide which is the best of the choices given and fill in the corresponding oval on the Answer Sheet.
{{U}}Directions:{{/U}} In the following type of question, two quantities appear, one in Column A and one in Column B. You must compare them. The correct answer to the question is
A if the quantity in Column A is greater
B if the quantity in Column B is greater
C if the two quantities are equal
D if it is impossible to determine which quantity is greater
{{U}}Notes:{{/U}} Sometimes information about one or both of the quantities is centered above the two columns. If the same symbol appears in both columns, it represents the same thing each time. Directions: In the following questions, choose the best answer from the five choices listed.
 
【正确答案】
【答案解析】
【正确答案】
D
【答案解析】, which is clearly more than 65%, it appears that Column B is greater. Be careful! That would be true if a were positive, but no restrictions are placed on a. If a = 0, the columns are equal; if a is negative, Column A is greater. Neither column is always greater, and the two columns are not always equal (D).
**Use TACTIC 1, Chapter 12. Just let a = 0, and then let a = 1.
 【正确答案】
D
【答案解析】Use TACTIC 4, Chapter 12. Could the columns be equal? Could c = 5? Sure, if this is a 3-4-5 right triangle. Must c = 5? No; if the triangle is not a right triangle, c could be less than or more than 5. Neither column is always greater, and the columns are not always equal (D). (Note: Since the figure may not be drawn to scale, do not assume that the triangle has a right angle.)
 【正确答案】
C
【答案解析】
ColumnA:(a+b)2=a2 + 2ab + b2 = a2 + b2 (since ab = 0). Column B: (a -b)2 = a2-2ab + b2 = a2 + b2 (since ab = 0). The columns are equal (C). **Use TACTIC 1, Chapter 12: Pick two numbers whose product is 0; say a = 0 and b = 1. Then (a + b)2 = (0 + 1)2 = 1 and (a -b)2 = (0 -1)2 = 1. Eliminate A and B and try other values where either a or b is 0 (since ab = 0). The two expressions are always equal. |