Problem Solving

Hi swerve,

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: D

GMAT assassins aren't born, they're made,
Rich

swerve 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 the 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?

$$A.\ 2\le x\le11$$
$$B.\ 3\le x\le12$$
$$C.\ 4\le x\le13$$
$$D.\ 5\le x\le14$$
$$E.\ 6\le x\le15$$

Let's first determine the maximum number of groups, which can be obtained by assuming each group has 2 (the least number of) people. In that case, we have 27/2 = 13 R 1, so Samantha must be in the 14th group.

Similarly, let's now determine the minimum number of groups, which can be obtained by assuming each group has 6 (the greatest number of) people. In that case, we have 27/6 = 4 R 3, so Samantha must be in the 5th group.

Thus, we see that Samantha can be in the 5th group or the 14th group, or any group in between. Thus, x can be any integer from 5 to 14, inclusive.

Answer:D