Problem 29: a system of equations with three variables and a parameter m . She started substituting, but her mind went blank. “Si el sistema tiene infinitas soluciones, halle m.” She remembered: the determinant of the coefficient matrix must be zero. She calculated quickly. m = 2 . She bubbled D.
1. The Weight of a Number Lima, February. The heat clung to everything—the cracked sidewalk on Avenida Universitaria, the plastic chairs in the pensión where Sofía rented a room, and the thin mattress where she’d slept only four hours. On her desk lay a worn-out copy of Aritmética Razonada by Baldeón, its spine held together with tape. Next to it, a stack of mock exams from the Academia César Vallejo . The top page read: Simulacro N° 12 – Puntaje: 482 . examen de admision pucp
Admission to PUCP required 1,200 points. Problem 29: a system of equations with three
Sofía opened the exam. Page one: “Complete la analogía: POEMA : ESTROFA :: NOVELA : ?” Easy. She answered capítulo . Then sinónimos —a breeze. Then came the first mathematical reasoning problem: a series of numbers with a missing term. She solved it in forty seconds. Good. She calculated quickly
Then problem 14: a logic puzzle about four friends seated around a table, with conditions like “Ana no está al lado de Carlos” and “Betty está frente a Diana.” She drew a grid. One minute. Two minutes. Her pencil trembled. Then—click—the configuration revealed itself. She bubbled in C. By the math section, her confidence was a thin wire. Problem 21: “Una empresa reparte 720 soles entre tres empleados. El segundo recibe el doble del primero. El tercero recibe 80 soles más que el segundo. ¿Cuánto recibe el primero?” She solved it: x + 2x + (2x+80) = 720 → 5x = 640 → x = 128 . Easy.
But problem 27 was a trap. A geometry problem: a triangle inscribed in a semicircle, with an altitude drawn, asking for a length. She knew the Thales theorem, but the numbers were ugly. She spent six minutes. Her pulse raced. She skipped it. Problem 28: probability with two dice— “suma mayor que 9” —she could do that. 10, 11, 12: 6 favorable cases out of 36. Simplify to 1/6. Good.