Question 25
In triangle ABC, points $A_{1}$, $A_{2}$,…, $A_{2020}$ are chosen as follows: $A_{1}$ divides AB in ratio 1:4 ( $AA_1$: $A_{1}$ B=1:4); $A_{2}$ divides $A_{1}$ C in ratio 1:3 ($A_{1}$ $A_{2}$: $A_{2}$ C=1:3); $A_{3}$ divides $A_{2}$ B in ratio 1:4 ($A_{2}$ $A_{3}$: $A_{3}$ B=1:4); $A_{4}$ divides $A_{3}$ C in ratio 1:3 ($A_{3}$ $A_{4}$: $A_{4}$ C=1:3); and so on. What is the ratio of the area of ABC to that of $A_{2020}$ BC?
Original printed choices: A) (3/5)¹⁰¹⁰; B) (3/5)¹⁰⁰⁹ × 4/5; C) (3/5)¹⁰⁰⁹ × 3/4; D) (3/5)¹⁰¹⁰ × 4/5; E) (5/3)²⁰²⁰
Editorial note: Explain whether the printed question and choices are consistent. Give the literal mathematical result and distinguish any intended correction.
Original printed choices: A) (3/5)¹⁰¹⁰; B) (3/5)¹⁰⁰⁹ × 4/5; C) (3/5)¹⁰⁰⁹ × 3/4; D) (3/5)¹⁰¹⁰ × 4/5; E) (5/3)²⁰²⁰
Editorial note: Explain whether the printed question and choices are consistent. Give the literal mathematical result and distinguish any intended correction.