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Change: 0
Position: 36
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
55% (02:04) correct
45%
(02:07)
wrong
based on 571
sessions
History
Date
Time
Result
Not Attempted Yet
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.
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.
| Change | Position | |
| 0 | ||
| 1 | ||
| 7 | ||
| 15 | ||
| 35 | ||
| 36 |
ShowHide Answer
Official Answer
Change: 0
Position: 36
11 Dec 2024, 01:06
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Bunuel
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"
Attachment:
GMAT-Club-Forum-xiavor8a.png [ 8.91 KiB | Viewed 1764 times ]
11 Dec 2024, 17:01
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1. We can draw out the situation before and after through a table:
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.
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 \(28 + \frac{1}{4} * 28 = 28 + 7 = 35\).
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.
| # 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.
