求教TTMath8中的两题

marco_polo

Q9:
If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

A.1/4 
B.3/8 
C.1/2 
D.5/8 
E.3/4 
Answer: D
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请教解题方法

Q29:
The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998.  Was the annual rent collected by the corporation from the building more in 1999 than in 1997?
(1)   x > y
(2)  xy/100 < x–y
 
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
答案B，为什么不能选D，设1997年的annual rent是1，1998年是（1+x%），1999年是（1+x%）(1+y%)。如果X>Y，是否就能得出（1+x%）(1+y%)>1？

dianecarton

设1997年为A,98年为B,99年为C,

(1)(B-A)/A=X%--->A=B/(1+X%) 只能知道(X-Y)的正负,但没办法判断与XY大小   独立不充分

(2)(C-B)/B=-Y%--->C=(1-Y%)B 求(C-A)/A的正负 即求[(1-Y%)B-B/(1+X%)]/[B/(1+X%)]=(X-Y)/100-(XY/100) 独立充分

[此贴子已经被作者于2008-3-9 2:14:57编辑过]

marco_polo

thanks dianecarton. actually, I don't clearly down your explanation of condition (1). the rent in 1999 is C, then C=B(1-y%)=A(1+x%)(1-y%). if x>y, shall I concludeA(1+x%)(1-y%)>C?