1957 AHSME Problems/Problem 43

Problem

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:

$\textbf{(A)}\ 24 \qquad \textbf{(B)}\ 35\qquad \textbf{(C)}\ 34\qquad \textbf{(D)}\ 30\qquad \textbf{(E)}\ \infty$

Solution

$[asy] path p = (0,0){right}..(1,1)..(2,4)..(3,9)..(4,16); // Shaded Region fill(p--(4,0)--cycle,lightred); // x-Axis draw((-4,0)--(16,0), arrow=Arrows); label("$x$",(18,0)); // y-Axis draw((0,-4)--(0,16), arrow=Arrows); label("$y$",(0,18)); // y=x^2 draw(p); // x=4 draw((4,-5)--(4,20), arrow=Arrows(TeXHead)); [/asy]$

$\boxed{\textbf{(B) }35}$ .

1957 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 42	Followed by Problem 44
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1957 AHSME Problems/Problem 43

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