A rectangular photograph is surrounded by a border that is 1 inch wide on each side.  The total area of the photograph and the border is M square inches.  If the border had been 2 inches wide on each side, the total area would have been (M + 52) square inches.  What is the perimeter of the photograph, in inches?

A.        34
B.        36
C.        38
D.        40
E.        42
Answer:

Q34:
The operation Θ is defined by x Θ y =   +   for all nonzero numbers x and y.  If z is a number greater than 1, which of the following must be true?


  I.  x Θ (-z) = 0
         II.  z Θ   = 1
        III.    Θ   = z


A.        I only
B.        I and II only
C.        I and III only
D.        II and III only
E.        I, II, and III
  Answer:

回答第一题时，设相片的长、阔为 x 与 y。那么加了一条一寸阔的边后，长、阔就是 x + 2 与 y + 2。

所以 (x + 2)(y + 2) = m
xy + 2x + 2y = m – 4 .........................................................(1)

如果边阔改为 2 寸，长、阔就变成 x + 4 与 y + 4。那么面积就是 m + 52。
(x + 4)(y + 4) = m + 52
xy + 4x + 4y = m + 52 – 16 = m + 36 .............................(2)

(2) – (1) 的结果是 2x + 2y = 40。而 2x + 2y 正是相片的周长。

第二题有个符号不显示，不知道题目是什么。