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.