{"status": "success", "data": {"description_md": "A rectangle with positive integer side lengths in $\\text{cm}$ has area $A$ $\\text{cm}^2$ and perimeter $P$ $\\text{cm}$. Which of the following numbers cannot equal $A+P$?\n\n$\\textbf{(A) }100\\qquad\\textbf{(B) }102\\qquad\\textbf{(C) }104\\qquad\\textbf{(D) }106\\qquad\\textbf{(E) }108$\n===Note:=== \nAs it originally appeared in the AMC 10, this problem was stated incorrectly and had no answer; it has been modified here to be solvable. This is the original question:\nA rectangle with side lengths in $\\text{cm}$ has an area of integer $A$ $\\text{cm}^2$ and a perimeter of integer $P$ $\\text{cm}$. Which of the following numbers cannot equal $A+P$?\n$\\textbf{(A) }100\\qquad\\textbf{(B) }102\\qquad\\textbf{(C) }104\\qquad\\textbf{(D) }106\\qquad\\textbf{(E) }108$", "description_html": "<p>A rectangle with positive integer side lengths in  <span class=\"katex--inline\">\\text{cm}</span>  has area  <span class=\"katex--inline\">A</span>   <span class=\"katex--inline\">\\text{cm}^2</span>  and perimeter  <span class=\"katex--inline\">P</span>   <span class=\"katex--inline\">\\text{cm}</span> . Which of the following numbers cannot equal  <span class=\"katex--inline\">A+P</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }100\\qquad\\textbf{(B) }102\\qquad\\textbf{(C) }104\\qquad\\textbf{(D) }106\\qquad\\textbf{(E) }108</span> <br/>\n=<mark>Note:</mark>=<br/>\nAs it originally appeared in the AMC 10, this problem was stated incorrectly and had no answer; it has been modified here to be solvable. This is the original question:<br/>\nA rectangle with side lengths in  <span class=\"katex--inline\">\\text{cm}</span>  has an area of integer  <span class=\"katex--inline\">A</span>   <span class=\"katex--inline\">\\text{cm}^2</span>  and a perimeter of integer  <span class=\"katex--inline\">P</span>   <span class=\"katex--inline\">\\text{cm}</span> . Which of the following numbers cannot equal  <span class=\"katex--inline\">A+P</span> ?<br/>\n <span class=\"katex--inline\">\\textbf{(A) }100\\qquad\\textbf{(B) }102\\qquad\\textbf{(C) }104\\qquad\\textbf{(D) }106\\qquad\\textbf{(E) }108</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2015 AMC 10A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/15_amc10A_p21", "prev": "/problem/15_amc10A_p19"}}