[{"data":1,"prerenderedAt":154},["ShallowReactive",2],{"\u002Fpublic\u002Ftopics\u002Frazonamiento-matematico\u002Fhabilidad-operativa?{}":3,"topics-with-content:razonamiento-matematico":112},{"course":4,"topic":12,"counts":17,"universities":22,"channels":35,"sampleQuestions":68,"sameName":111},{"id":5,"slug":6,"name":7,"shortName":8,"area":9,"icon":10,"sortOrder":11},17,"razonamiento-matematico","Razonamiento Matemático","R. Mat.","reasoning","i-lucide-puzzle",16,{"id":13,"courseId":5,"slug":14,"name":15,"sortOrder":16},1714,"habilidad-operativa","Habilidad operativa",13,{"topicId":13,"courseId":5,"questions":18,"classes":19,"videos":20,"minutes":21},10,159,116,1873,[23,30],{"universityId":24,"questions":25,"years":26},1,5,[27,28,29],2025,2024,2023,{"universityId":31,"questions":25,"years":32},2,[33,27,28,29,34],2026,2022,[36,39,42,45,48,51,53,56,59,62,64,66],{"name":37,"classes":38},"Alberto Cruz",41,{"name":40,"classes":41},"Academia Grupo Ciencias",26,{"name":43,"classes":44},"Academia ipluton",24,{"name":46,"classes":47},"Ciclo Uni-San Marcos",21,{"name":49,"classes":50},"Academias Aduni y César Vallejo",14,{"name":52,"classes":18},"Academia Internet",{"name":54,"classes":55},"Salón Sapiens",8,{"name":57,"classes":58},"META VILLARREAL",4,{"name":60,"classes":61},"Academia_Pitagoras",3,{"name":63,"classes":61},"CEPRE UNMSM",{"name":65,"classes":61},"Trilce Multimedia",{"name":67,"classes":31},"Pamer Corporación Educativa",[69,94],{"id":70,"courseId":5,"topicId":13,"pastExamId":71,"stem":72,"options":73,"correctKey":84,"explanation":89,"difficulty":58,"status":90,"source":91,"stats":92},1688,199,"Si $a$, $b$ y $c$ son reales positivos, distintos de la unidad, que satisfacen la condición\n$\\dfrac{a}{1-a}+\\dfrac{b}{1-b}+\\dfrac{c}{1-c}=1,$\ndetermine el valor de\n$\\dfrac{1}{1-a}+\\dfrac{1}{1-b}+\\dfrac{1}{1-c}.$",[74,77,80,83,86],{"key":75,"text":76},"A","1",{"key":78,"text":79},"B","2",{"key":81,"text":82},"C","3",{"key":84,"text":85},"D","4",{"key":87,"text":88},"E","5","","published","UNI 2026-2 · Aptitud Académica y Humanidades",{"attempts":93,"accuracy":93},0,{"id":95,"courseId":5,"topicId":13,"pastExamId":96,"stem":97,"options":98,"correctKey":87,"explanation":89,"difficulty":58,"status":90,"source":109,"stats":110},1146,190,"Se define: $a_{0}=1$;\n$-a_{1}=c_{1}+c_{2}+c_{3}$;\n$a_{2}=c_{1}c_{2}+c_{1}c_{3}+c_{2}c_{3}$;\n$-a_{3}=c_{1}c_{2}c_{3}$.\nSi $c_{j}=5-2^{j-1}$ para $j=1,\\,2,\\,3$; determine el valor de\n$K=\\dfrac{\\displaystyle\\prod_{i=0}^{3}a_{i}}{96+\\displaystyle\\sum_{i=0}^{3}a_{i}}$",[99,101,103,105,107],{"key":75,"text":100},"–19",{"key":78,"text":102},"–12",{"key":81,"text":104},"0",{"key":84,"text":106},"12",{"key":87,"text":108},"19","UNI 2025-1 · Aptitud Académica y Humanidades",{"attempts":93,"accuracy":93},[],[113,114,115,116,117,118,119,120,121,122,123,124,125,13,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153],1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1791501535437]