1957 AMC 12 Problem 43

Question

We define a lattice point as a point whose coordinates are integers, zero admitted. Then the number of lattice points on the boundary and inside the region bounded by the

x

-axis, the line

x=4,

and the parabola

y=x^2

is:

24

35

34

30

not finite

Answer: B

Concepts:lattice point parabola counting integers in a range

Difficulty rating: 1550

Small hint:

Only the integer

x

-coordinates

0,

1,

2,

3,

and

4

occur

Big hint:

For a fixed integer

x,

count the integer

y

-values from

0

through

x^2

Solution:

For each

x

among

0,

1,

2,

3,

and

4,

there are

x^2+1

integer values from

y=0