Number of defects

[crackgmat007]

The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?
I. 3
II. 7
III. 12
A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III

How is it D? Can anyone explain pls? Tx

[Pranay]

The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?
I. 3
II. 7
III. 12
A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III

How is it D? Can anyone explain pls? Tx

My answer is B - Please let me know of correct answer ..

[scoobydooby]

1) if the 6th number is 3, then mean=39/6=6.5
median of 3, 4, 6, 7, 9, 10 is (6+7)/2=6.5


2) if the 6th is 7, mean is (36+7)/6=43/6=7. something
but the median is 7 . mean not equal to median

3) if the 6th number is 12, mean is (36+12)/6=8
median of 4, 6, 7, 9, 10, 12 is (7+9)/2=8


1) and 3) have mean=median. hence, D