{"status": "success", "data": {"description_md": "Let $(a,b,c,d)$ be an ordered quadruple of not necessarily distinct integers, each one of them in the set $\\{0,1,2,3\\}.$ For how many such quadruples is it true that $a\\cdot d-b\\cdot c$ is odd? (For example, $(0,3,1,1)$ is one such quadruple, because $0\\cdot 1-3\\cdot 1 = -3$ is odd.)\n\n$\\textbf{(A) } 48 \\qquad \\textbf{(B) } 64 \\qquad \\textbf{(C) } 96 \\qquad \\textbf{(D) } 128 \\qquad \\textbf{(E) } 192$", "description_html": "<p>Let  <span class=\"katex--inline\">(a,b,c,d)</span>  be an ordered quadruple of not necessarily distinct integers, each one of them in the set  <span class=\"katex--inline\">\\{0,1,2,3\\}.</span>  For how many such quadruples is it true that  <span class=\"katex--inline\">a\\cdot d-b\\cdot c</span>  is odd? (For example,  <span class=\"katex--inline\">(0,3,1,1)</span>  is one such quadruple, because  <span class=\"katex--inline\">0\\cdot 1-3\\cdot 1 = -3</span>  is odd.)</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 48 \\qquad \\textbf{(B) } 64 \\qquad \\textbf{(C) } 96 \\qquad \\textbf{(D) } 128 \\qquad \\textbf{(E) } 192</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": "2020 AMC 10A Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc10A_p19", "prev": "/problem/20_amc10A_p17"}}