Problem Solving

willshu wrote:Here is a question from a Kaplan CAT and the solution. I disagree with their answer for the reasons below. Please read the question and solution and see if you agree with me.

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?
2 greater than equal to x less than or equal to 11
3 x 12
4 x 13
5 x 14
6 x 15

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Correct Choice: (D)

First let's assume that each group has the maximum number of people (6). The number of complete groups made up of people who arrived before Samantha must be 4, because the highest multiple of 6 that is less than or equal to 27 is 24, which is 4(6). So Samantha is in the next group - the 5th group.

Now let's assume that each group has the minimum number of people (2). Since the highest multiple of 2 that is less than or equal to 27 is 26, there must be groups before Samantha, putting her in the 14th group.

So x must be at least 5, but no more than 14. This is expressed by answer choice (D).

I agree with the second part of the answer, that there must be at least 5 groups, but not the part about no more than 14 groups. If Samantha is the last person in the line, then she will be part of the 13th group, not the 14th, as you cannot have a group consisting of one person. Therefore, she would be part of a group of 3, that is the 13th group and all the other 12 groups will consist of 2. If there is a 28th person, then yes, there would be a 14th group, but this is not clear from the question.

Any comments?