goodyear2013 wrote:
A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among six colors produced enough color codes to identify all but 5 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in the codes does not matter.)
7
10
15
17
20
OE
If 6 colors have to be divided into groups of 2, the number of unique groupings 6C2 = 6! / (2!)(4!) = 15.
Number of combinations was sufficient to account for all but 5 of the subjects
Number of subjects = 15 + 5 = 20.
Hi, I found this question stem not clear. Can anyone explain this for me, please.
Dear
goodyear2013,
I'm happy to help.
I'm not entirely sure I understand what you found unclear. I will try telling the story in my own words.
A scientist was conducting a study, and he had to test individual subjects. As a way to identify the subjects, the scientist gave each subject something, say a badge, with two colors on it, and the scientist wanted the color combination to be different for each subject. Say there were N subjects in total. The scientist used six different individual colors, and different pairs formed from these six colors formed enough combinations to make unique color combinations for (N - 5) of the subject, so the scientist probably had to "double up" or do something different for those last 5 subjects.
This question is about counting techniques. See:
http://magoosh.com/gmat/2012/gmat-quant-how-to-count/http://magoosh.com/gmat/2012/gmat-permu ... binations/If we have six colors, the number of unique pairs of color we can create is
6C2 = 15
Each of the first 15 subjects got her or his unique pair of colors, leaving the last 5 with some other arrangement. Total = 15 + 5 = 20
Does all this make sense?
Mike
I thought that since it is a code the order matters. let say we have Red/Green two color, Color code RG is different from GR and So 2! *6C2 + 5 = 35 .
that the question stem is ambiguous.