问题 选择题
已知整数X,Y满足
X
+2
Y
=
72
,那么整数对(X,Y)的个数是(  )
A.2B.3C.4D.5
答案

当y=0时,

x
=
72
,x=72,整数对为(72,0);

当y=1时,

x
=
72
-1,x不是整数;

当y=2时,

x
=
72
-2
2
=4
2
=
32
,x=32,整数对为(32,2);

当y=3时,

x
=
72
-2
3
=6
2
-2
3

当y=4时,

x
=
72
-2
4
=6
2
-4;

当y=5时,

x
=
72
-2
5
=6
2
-2
5

当y=6时,

x
=
72
-2
6
=6
2
-2
6

当y=7时,

x
=
72
-2
7
=6
2
-2
7

当y=8时,

x
=
72
-2
8
=6
2
-4
2
=2
2
,x=8,整数对为(8,8);

当y=9时,

x
=
72
-2
9
=6
2
-6;

当y=10时,

x
=
72
-2
10
=6
2
-2
10

当y=11时,

x
=
72
-2
11
=6
2
-2
11

当y=12时,

x
=
72
-2
12
=6
2
-4
3

当y=13时,

x
=
72
-2
13
=6
2
-2
13

当y=14时,

x
=
72
-2
14
=6
2
-2
14

当y=15时,

x
=
72
-2
15
=6
2
-2
15

当y=16时,

x
=
72
-2
16
=6
2
-8;

当y=17时,

x
=
72
-2
17
=6
2
-2
17

当y=18时,

x
=
72
-2
18
=6
2
-6
2
=0,x=0,整数对为(0,18).

故整数对(X,Y)是(72,0),(32,2),(8,8),(0,18)共四个.

故选C.

不定项选择
填空题