小女数学不好，求高人解答数学题！

margaretfang23

a-b is even integer ->a-b=2m,m=1,2,3...
a/b is even integer->a/b=2n->a=2nb, n=1,2,3...
plug a=2nb into a-b=2k we get b(2n-1)=2m->b must be even integer denotes b=2k,k=1,2,3...
plug b=2k into a=2nb ->a=4kn, k,n=1,2,3...
(1) a/2=2kn, must be even integer
(2) b/2=k, k=1,2,3... can be odd or even integer
(3) (a+b)/2=(4kn+2k)/2=k(2n+1), k,n=1,2,3... can be odd or even integer
(4) (a+2)/2=(4kn+2)/2=2kn+1, k,n=1,2,3... must be odd integer
(5) (b+2)/2=(2k+2)/2=k+1, k=1,2,3... can be odd or even integer

therefore, the answer is D.

-- by 会员 wyw1018 (2011/8/17 5:07:35)

另外还想请教一道数学题：Q21:
If x and y are positive integers, what is the value of (x+y)²?
(1)   x = y - 3
(2) x and y are prime numbers.
                 
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.
为什么答案是C啊？

wyw1018

关于Q21：
很显然条件（1），（2）单独都不能确定x及y值。
条件（1）可得出y-x=3 --》x与y必定一奇一偶
条件（2）得出是偶数的质数只有2，因此--》x=2，y=5
所以选C。

sonic217

Since x and Y are both prime, the only possibilities are 5 and 2 because for any prime number above 2 it must be an odd number, then, an odd number minus 3 must be an even number which will not be a prime number. Therefore, when conditions A and B combined, they will have to be 5 and 2.

margaretfang23

关于Q21：
很显然条件（1），（2）单独都不能确定x及y值。
条件（1）可得出y-x=3 --》x与y必定一奇一偶
条件（2）得出是偶数的质数只有2，因此--》x=2，y=5
所以选C。

-- by 会员 wyw1018 (2011/8/17 14:23:48)

原来如此，我一遇到奇偶问题就晕菜啦~ 嘿嘿，非常感谢

gx911

你可以看看陈向东那本数学的前面总结部分，有一些关于奇偶的性质总结，可能会有帮助。网上可以找到，或者买本也没多少钱，个人认为时间充足的话好好看看。