Fifty people are standing in a line to buy tickets for a movie, with Vicky positioned 22nd from the beginning of the line. After 10 minutes, one-third of the people ahead of Vicky leave the line, while the number of people behind her increases by one-fourth. Based on this information, select for Change the change in the total number of people in the line after 10 minutes, and select for Position Vicky's position from the end of the line after 10 minutes.

Official Solution: Initially, the positioning is as follows: {21 people} {Vicky} {28 people} When one-third of the people ahead of Vicky leave the line, and the number of people behind her increases by one-fourth, the positioning becomes: {14 people} {Vicky} {35 people} Thus, there are 14 + 1 + 35 = 50 people in the line, and Vicky is in the 36th position from the end of the line. Correct answer: Change "0" Position "36" GMAT-Club-Forum-xiavor8a.png

1. We can draw out the situation before and after through a table: # of people ahead of Vicky Vicky's position # from the beginning of the line # of people behind Vicky Before ? ? ? After ? ? ? 2. Vicky is positioned 22nd originally and there are 50 people in the line. So, 22 - 1 = 21 are ahead of her and 50 - 22 = 28 people are behind her. # of people ahead of Vicky Vicky's position # from the beginning of the line # of people behind Vicky Before 21 22 28 After ? ? ? 3. Then, the number of people ahead decrease by one-third, which is 21 - \frac{1}{3} * 21 = 21 - 7 = 14 and the number of people behind increase by one-fourth, which is 28 + \frac{1}{4} * 28 = 28 + 7 = 35 . # of people ahead of Vicky Vicky's position # from the beginning of the line # of people behind Vicky Before 21 22 28 After 14 ? 35 4. Vicky's position from the end of the line after 10 minutes will be 35 + 1 = 36 and the total number of people in the line after 10 minutes will be 14 + 1 + 35 = 50, so the change is 50 - 50 = 0. 5. Our answer will be: Change - 0 and Position - 36 .