{"status": "success", "data": {"description_md": "Twenty-four identical $1 \\times 1$ squares form a $4 \\times 6$ rectangle, as shown. A *lattice point* is a point where a horizontal grid line intersects a vertical grid line. A diagonal of this rectangle passes through the three lattice points $P$, $Q$ and $R$. When a $30 \\times 45$ rectangle is constructed using identical $1 \\times 1$ squares, how many lattice points will a diagonal of this rectangle pass through?\n\n<center><img class=\"problem-image\" src=\"/static/pascal/2014/crops/14_pascal_p21_fig.png\" alt=\"figure\" width=\"321\"></center>\n\n$\\text{(A)}\\ 19\\qquad\\text{(B)}\\ 16\\qquad\\text{(C)}\\ 15\\qquad\\text{(D)}\\ 18\\qquad\\text{(E)}\\ 12$\n\n___\n\n**[Pascal](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "<p>Twenty-four identical <span class=\"katex--inline\">1 \\times 1</span> squares form a <span class=\"katex--inline\">4 \\times 6</span> rectangle, as shown. A *lattice point* is a point where a horizontal grid line intersects a vertical grid line. A diagonal of this rectangle passes through the three lattice points <span class=\"katex--inline\">P</span>, <span class=\"katex--inline\">Q</span> and <span class=\"katex--inline\">R</span>. When a <span class=\"katex--inline\">30 \\times 45</span> rectangle is constructed using identical <span class=\"katex--inline\">1 \\times 1</span> squares, how many lattice points will a diagonal of this rectangle pass through?</p>\n<center><img class=\"problem-image\" src=\"/static/pascal/2014/crops/14_pascal_p21_fig.png\" alt=\"figure\" width=\"321\"></center>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 19\\qquad\\text{(B)}\\ 16\\qquad\\text{(C)}\\ 15\\qquad\\text{(D)}\\ 18\\qquad\\text{(E)}\\ 12</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Pascal</a>, by <a href=\"https://cemc.uwaterloo.ca/\">CEMC</a>, is licensed under the <a href=\"https://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0 DEED</a>. They are not affiliated with or endorse TopsOJ in any way.</strong></p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2014 Pascal Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/14_pascal_p22", "prev": "/problem/14_pascal_p20"}}