GMAT Question of the Day - Data Sufficiency - Ratio/Weighted Average
The ratio of the number of students in the math department, history department, and science department is 3 to 7 to 10 respectively. Is the average height of students from all of the departments less than 60 inches?
(1) The sum of the heights of all the students is less than 100 feet.
(2) This math department has 7 fewer students than the science department.
GMAT Question of the Day Solution
This GMAT question of the day presents another threshold question. In this case we want to know whether we are above or below 60 inches. From the given information we know that the minimum number of students is 20 (3 + 7 + 10).
Statement (1) If we divide max height (100 feet or 1,200 inches) by min students (20) we get 60. That's right at the threshold. Because we have an inequality we must be below this threshold. Sufficient.
Statement (2) From this we can infer the number of students but have no information on their heights. Insufficient.