{"status": "success", "data": {"description_md": "Consider the set of all fractions $\\tfrac{x}{y},$ where $x$ and $y$ are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by $1$, the value of the fraction is increased by $10\\%$?\n\n$\\textbf{(A) }0\\qquad\\textbf{(B) }1\\qquad\\textbf{(C) }2\\qquad\\textbf{(D) }3\\qquad\\textbf{(E) }\\text{infinitely many}$", "description_html": "<p>Consider the set of all fractions  <span class=\"katex--inline\">\\tfrac{x}{y},</span>  where  <span class=\"katex--inline\">x</span>  and  <span class=\"katex--inline\">y</span>  are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by  <span class=\"katex--inline\">1</span> , the value of the fraction is increased by  <span class=\"katex--inline\">10\\%</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }0\\qquad\\textbf{(B) }1\\qquad\\textbf{(C) }2\\qquad\\textbf{(D) }3\\qquad\\textbf{(E) }\\text{infinitely many}</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 15", "can_next": true, "can_prev": true, "nxt": "/problem/15_amc10A_p16", "prev": "/problem/15_amc10A_p14"}}