Hi swerve,

We're told that the number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively and that the sixth car through the production line has either 3, 7, or 12 defects. We're asked which of the following three values does the MEAN number of defects per car for the first six cars equal the MEDIAN. This question comes down to organizing the data (to find the Median) and using the Average Formula.

I. 3 defects

IF... the 6th car has 3 defects, then the six numbers would be: 3, 4, 6, 7, 9 and 10
The Median would be (6+7)/2 = 6.5
The Average would be (3+4+6+7+9+10)/6 = 39/6 = 6.5
The Average and the Median ARE equal.
Eliminate Answers B and C.

II. 7 defects

IF... the 6th car has 7 defects, then the six numbers would be: 4, 6, 7, 7, 9 and 10
The Median would be (7+7)/2 = 7
The Average would be (4+6+7+7+9+10)/6 = 43/6 = 7 1/6
The Average and the Median are NOT equal.
Eliminate Answer E

III. 12 defects

IF... the 6th car has 12 defects, then the six numbers would be: 4, 6, 7, 9, 10 and 12
The Median would be (7+9)/2 = 8
The Average would be (4+6+7+9+10+12)/6 = 48/6 = 8
The Average and the Median ARE equal.
Eliminate Answer A.

Final Answer: D

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

swerve wrote: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 these 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

Let's check each number in the given Roman numerals.

I. 3

The average is (3 + 4 + 6 + 7 + 9 + 10)/6 = 6.5.

The median is (6 + 7)/2 = 13/2 = 6.5.

We see that I is correct.

II. 7

The average is (4 + 6 + 7 + 7 + 9 + 10)/6 ≈ 7.17.

The median is (7 + 7)/2 = 14/2 = 7.

We see that II is not correct.

III. 12

The average is (4 + 6 + 7 + 9 + 10 + 12)/6 = 8.

The median is (7 + 9)/2 = 16/2 = 8.

We see that III is correct.

Answer: D