请教GWD#29的一道题，急！！！

yazhouwu

Q3:
If n is an integer and xⁿ – x^-n = 0, what is the value of x ?
(1)x is an integer.
(2)n ≠ 0

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E，我选B

我之前的理解是这样的:
题干：=> (x^n)^2  =1  => x^n = +1 or -1
1) x is integer =>
   if n = 0, x could be any nonzero integer
   if n is even integer, x = +1 or -1
   if n is odd integer, x = +1 or -1
  thus, value of x is largely dependent on n

2)  n ≠ 0  =>
   if n is even integer, x = +1 or -1
   if n is odd integer, x = +1 or -1
  thus, value of x is always +1 or -1, no matter what n is...

所以应该选 B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

大家帮忙看看我的分析对嘛？还是因为x有两个可能值，所以就认为是不充分的。。。没道理啊。。

yazhouwu

自顶！谢谢各位！

justgo

数一定要确定，有任何不同可能的值都不算解出来。

sirenfish

x只能有一个值，那条件才算是充分

tinyhuhu

'E' IMO
X^n - X ^(-n) = 0
=> X^n = X ^(-n) i.e. X^(2n)=1

A. X is an integer
n is unknown. If n=1, X^2=1 & X=+/-1

Insufficient

B. n ≠ 0
No info on X.

Insufficient

Taken together, X is integer & n ≠ 0
Whatever the value of n, X=+/-1

Insufficient.

Answer is E

refer to: http://www.beatthegmat.com/what-is-the-value-of-x-t28726.html

yazhouwu

okay,谢谢，那考试的时候要仔细点了。。。