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A line of people is divided into groups. Each group consists

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A line of people is divided into groups. Each group consists [#permalink] New post 25 Feb 2012, 23:59
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A line of people is divided into groups. Each group consists of a continuous section of the line. Samantha was the 27th person in line. Each group has a minimum of 2 people, and a maximum of 6. If the groups are numbered from the front of the line to the back, and Samantha is in group x, which of the following must be true?

A. 2 <= x <= 11
B. 3 <= x <= 12
C. 4 <= x <= 13
D. 5 <= x <= 14
E. 6 <= x <= 15
[Reveal] Spoiler: OA

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Last edited by Bunuel on 26 Feb 2012, 04:12, edited 1 time in total.
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Re: A line of people is divided into groups. Each group consists [#permalink] New post 26 Feb 2012, 04:11
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Chembeti wrote:
A line of people is divided into groups. Each group consists of a continuous section of the line. Samantha was the 27th person in line. Each group has a minimum of 2 people, and a maximum of 6. If the groups are numbered from the front of the line to the back, and Samantha is in group x, which of the following must be true?

A. 2 <= x <= 11
B. 3 <= x <= 12
C. 4 <= x <= 13
D. 5 <= x <= 14
E. 6 <= x <= 15


In order to minimize x (the # of group Samantha is in) we should maximize # of people in groups before Samantha. Since maximum # of people in a group is 6 then Samantha can be minimum in 5th group: 4 groups of 6 make 24 people, which means that Samantha could be in the next group, so in 5th;

In order to maximize x (the # of group Samantha is in) we should minimize # of people in groups before Samantha. Now, minimum # of people in a group is 2. Two cases here:
1. Samantha is NOT last in the line. Then 13 groups of 2 make 26 people and Samantha will be in 14th group;
2. Samantha IS last in the line. Then 13 groups of 2 make 26 people but since Samantha is last in the line and each group has a minimum of 2 people then she could not be in 14th group alone, so she must be in 13th group.

But, in any case x must be less than or equal to 14.

So, we have that \(5\leq{x}\leq{14}\)

Answer: D.
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Re: A line of people is divided into groups. Each group consists [#permalink] New post 27 May 2013, 04:48
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Re: A line of people is divided into groups. Each group consists [#permalink] New post 22 Jan 2014, 02:31
Bunuel wrote:
Chembeti wrote:
A line of people is divided into groups. Each group consists of a continuous section of the line. Samantha was the 27th person in line. Each group has a minimum of 2 people, and a maximum of 6. If the groups are numbered from the front of the line to the back, and Samantha is in group x, which of the following must be true?

A. 2 <= x <= 11
B. 3 <= x <= 12
C. 4 <= x <= 13
D. 5 <= x <= 14
E. 6 <= x <= 15


In order to minimize x (the # of group Samantha is in) we should maximize # of people in groups before Samantha. Since maximum # of people in a group is 6 then Samantha can be minimum in 5th group: 4 groups of 6 make 24 people, which means that Samantha could be in the next group, so in 5th;

In order to maximize x (the # of group Samantha is in) we should minimize # of people in groups before Samantha. Now, minimum # of people in a group is 2. Two cases here:
1. Samantha is NOT last in the line. Then 13 groups of 2 make 26 people and Samantha will be in 14th group;
2. Samantha IS last in the line. Then 13 groups of 2 make 26 people but since Samantha is last in the line and each group has a minimum of 2 people then she could not be in 14th group alone, so she must be in 13th group.

But, in any case x must be less than or equal to 14.

So, we have that \(5\leq{x}\leq{14}\)

Answer: D.


Question doesn't state that "Samantha is last in the line" hence the statement "but since Samantha is last in the line and each group has a minimum of 2 people then she could not be in 14th group alone, so she must be in 13th group." shouldn't matter and Samantha will be in 14th group.
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Re: A line of people is divided into groups. Each group consists [#permalink] New post 06 Apr 2015, 07:46
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Re: A line of people is divided into groups. Each group consists [#permalink] New post 07 Apr 2015, 17:54
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Hi All,

Based on the wording of this prompt, there's a great way to 'visualize' the solution by drawing some pictures and doing a little arithmetic:

Since there are no individual people in line (everyone is part of a 'group' from 2 to 6 people), we can think about minimizing or maximizing the number of groups to find out where Samantha's group COULD be in line. We know that she's the 27th person, so we can use that to our advantage.

Let's start by figuring out the maximum number of groups that could be in line AHEAD of Samantha....

By making ALL of those groups as SMALL as possible, we can maximize the number of groups ahead of Samantha:

2 2 2 2 2 2 2 2 2 2 2 2 2 (then Samantha's group)

With thirteen groups of 2, we account for 26 people. Samantha would then be in the NEXT group (regardless of the size). So the LARGEST potential value is 14. Looking at the answer choices, we can eliminate Answers A, B and C (since none of them accounts for 14 groups).

Next we can figure out the minimum number of groups that would be in line AHEAD of Samantha....

By making ALL of those groups as LARGE as possible, we can minimize the number of groups ahead of Samanatha:

6 6 6 6 (then Samantha's group)

With four groups of 6, we account for 24 people. Samantha could then be in the NEXT group. So the SMALLEST potential value is 5. Eliminate Answer E.

Final Answer:
[Reveal] Spoiler:
D


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Re: A line of people is divided into groups. Each group consists   [#permalink] 07 Apr 2015, 17:54
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