[問題]GWD 7 - Math 36

[puresillylily]

Dear People:

Can someone please kindly explain this math question for me:
GWD7-Math 36:
If a and b are positive integers such that a-b and a/b are both even integers, which of the following must be an odd integer?
a) a/2
b) b/2
c) (a+b)/2
d) (a+2)/2
e) (b+2)/2

The answer is D.
However, I am having a tough time figuring out this question. Your help will be genuinely appreciated!

Puresillylily

[Ace]

我當初做這題沒用什麼特殊的方法
因為看到must be
所以我盡量找岀無法滿足的選項
以(8,4)(4,2)兩組數去try
a b c e 都被排除
所以D OK

FYI

[StanleyHuang]

我的"實在有夠慢"解法如下：
(1) a-b is even ==> 不是 odd - odd 就是 even - even
(2) a/b is even ==> 一定是even - even，而且 a 是 2*(2*s) = 4*s ，而 b 是 2*t 。s, t 是任意integer。
接下來就一個一個來看選項了
(a) a/2 ==> 4s/2 = 2s ==> even
(b) b/2 ==> 2t/2 = t ==> not sure, depends on t
(c) (a+b)/2 ==> (4s+2t)/2 = 2s+t ==> not sure, depends on t
(d) (a+2)/2 ==> (4s+2)/2 = 2s+1 ==> odd
(e) (b+2)/2 ==> (2t+2)/2 = t+1 ==> not sure, depends on t

所以選(D)
結論是，Ace大大的方法比較好

[Ace]

謝謝 小史哥的讚美

不過還是勸大家多了解小史哥的解題邏輯
扎實的學習才是必勝的把握唷 :D