GWD20-36

meckychen

Q36:

If a and b are positive integers such that a
– b and a/bare 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

Answer is D

How to calculate?

Thank you.



Answer:

栖叶泠风

因为a/b是偶数，所以a一定是偶数，所以D
又因为a-b是偶数，a是偶数，所以B也是偶数，但是要排除B是2的情况，这样的话E就不能成立了~

jojo1213

(1)a/b  is even integer, so a = 2b, 4b,.... 2nb
(2)a-b is even integer, so a and b are at the same time either even or odd .
According to (1)+(2), a must be even, and b is even. So A, B, C are wrong.
Attention, if b = 2, then (b+2)/2=2, so E is wrong.  
But a is not 2 (a-b is even)
D right.

tjr

a-b偶：双奇或双偶
a/b偶：双偶且a是4的倍数（a不是2）

D

因不能排除b=2：E错

meckychen

thank you.