[{"data":1,"prerenderedAt":154},["ShallowReactive",2],{"\u002Fpublic\u002Ftopics\u002Frazonamiento-matematico\u002Fcertezas?{}":3,"topics-with-content:razonamiento-matematico":112},{"course":4,"topic":12,"counts":17,"universities":22,"channels":35,"sampleQuestions":67,"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},1705,"certezas","Certezas",4,{"topicId":13,"courseId":5,"questions":18,"classes":19,"videos":20,"minutes":21},27,144,117,1890,[23,32],{"universityId":24,"questions":25,"years":26},1,25,[27,28,29,30,31],2026,2025,2024,2023,2022,{"universityId":33,"questions":33,"years":34},2,[28],[36,39,42,45,48,51,54,57,59,61,63,65],{"name":37,"classes":38},"Alberto Cruz",39,{"name":40,"classes":41},"Academia Grupo Ciencias",28,{"name":43,"classes":44},"Ciclo Uni-San Marcos",23,{"name":46,"classes":47},"Academia ipluton",14,{"name":49,"classes":50},"Academias Aduni y César Vallejo",12,{"name":52,"classes":53},"Salón Sapiens",7,{"name":55,"classes":56},"Academia_Pitagoras",5,{"name":58,"classes":56},"CEPRE UNMSM",{"name":60,"classes":16},"META VILLARREAL",{"name":62,"classes":16},"Trilce Multimedia",{"name":64,"classes":33},"Academia Internet",{"name":66,"classes":24},"Pamer Corporación Educativa",[68,94],{"id":69,"courseId":5,"topicId":13,"pastExamId":70,"stem":71,"options":72,"correctKey":86,"explanation":88,"difficulty":89,"status":90,"source":91,"stats":92},5115,249,"Sobre una mesa hay tres cajas de madera: dos contienen sólidos geométricos de colores y una está vacía. La primera contiene 6 esferas blancas y 5 negras; la segunda, 3 cubos blancos y 4 negros. Si el contenido de las dos cajas mencionadas se coloca en la tercera caja, ¿cuántos objetos se deben extraer, como mínimo, de uno en uno y sin ver para tener la seguridad de haber extraído una esfera y un cubo del mismo color?",[73,76,79,82,85],{"key":74,"text":75},"A","9",{"key":77,"text":78},"B","5",{"key":80,"text":81},"C","7",{"key":83,"text":84},"D","8",{"key":86,"text":87},"E","6","",3,"published","UNMSM 2026-II · Área A · Ciencias de la Salud",{"attempts":93,"accuracy":93},0,{"id":95,"courseId":5,"topicId":13,"pastExamId":96,"stem":97,"options":98,"correctKey":74,"explanation":88,"difficulty":16,"status":90,"source":109,"stats":110},5303,252,"En una caja no transparente, Miguel tiene 50 bolos numerados con números enteros, del 10 al 59, sin repetir. ¿Cuántos debe extraer al azar, de uno en uno, como mínimo, para tener la certeza de haber extraído dos bolos cuyas numeraciones sean números primos y que sumen más de 25?",[99,101,103,105,107],{"key":74,"text":100},"40",{"key":77,"text":102},"41",{"key":80,"text":104},"43",{"key":83,"text":106},"42",{"key":86,"text":108},"39","UNMSM 2026-II · Área D · Ciencias Económicas y de la Gestión",{"attempts":93,"accuracy":93},[],[113,114,115,116,13,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153],1701,1702,1703,1704,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1791501535366]