Question

满足|x|+|y|≤4的整点(横、纵坐标为整数)的个数是(    )

A.16             B.17                  C.40                   D.41

Answer 1

D

解析：当x=0时，y∈{±4,±3,±2,±1,0};

当x=±1时，y∈{±3,±2,±1,0};

当x=±2时，y∈{±2,±1,0};

当x=±3时，y∈{±1,0};

当x=±4时，y∈{0}.

∴整点个数为9+2×7+2×5+2×3+2=9+14+10+6+2=41.