I12-19

Question

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.

Bunuel · Answer

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"

ankitsethia96 · Answer

Whoever has marked 15 for the "position of Vicky" is conceptually correct.
However the question is  tricky , and it asks for "position of Vicky   from the end of the queue  ", thus we need to give the answer from the end or rear.

Thanks.

Bunuel · Answer

I have revised the question, solution, and formatting by adding more details to enhance clarity.

Rahul885 · Answer

Hi Bunuel,

I have a small doubt. Even the answer pair (change=7) and (position from back=1) works.
so basically saying vicky was already the last person in queue and no one was behind her.

In general in GMAT should we consider that at least some value exists when question says people increased by 25%,etc?  or can we assume that people initially were zero so even after increase zero.

Thanks in advance!

Bunuel · Answer

In general, on the GMAT, when a question mentions an increase by a percentage (e.g., 25%), it implies that there was at least some initial value to begin with. You cannot assume the initial value was zero, as a percentage increase of zero does not make logical sense in such contexts.

In this case, if the number of people behind Vicky increases by one-fourth, it logically follows that there were people behind her initially, even if the exact count is not specified upfront. Therefore, assuming Vicky was already the last person in the line would not align with the intended meaning of the question.

I hope this clears up the confusion!

Rahul885 · Answer

Just one more follow-up question, What happens in a similar situation in Data Sufficiency?
There also should we assume a variable not zero if same language exists? I might be getting unnecessarily specific but I get questions wrong because of such nuances.

Bunuel · Answer

It depends. If the variables are not linked to a real-life situation, you should consider the possibility of them being zero (unless other constraints explicitly restrict this). However, if it’s a real-life scenario, such as the example above in a Data Sufficiency question, it would be safe to assume that the number of people behind Vicky is not zero.

bumpbot · Answer

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I12-19

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