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# 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.

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# GMAT Question of the Day - Data Sufficiency - Weighted Average/Ratios

Each Doctor at a certain medical practice is either a specialist or a generalist. What is the ratio of generalists to specialists?

1) The average (arithmetic mean) number of procedures performed per year by specialists is 50 less than the average (arithmetic mean) number of procedures performed per year by generalists.

2) The average (arithmetic mean) number of procedures performed by generalists is 40 more than the average (arithmetic mean) number of procedures performed by all of the doctors at the practice.

## GMAT Question of the Day Solution:

The question is asking about ratios/proportions so think about picking numbers. It should be clear that each piece of information on it's own is insufficient. There are too many moving parts. Try a few different sets of numbers to prove this to yourself. Putting things together the results are locked into a ratio of 1:4. Again, pick numbers for this. You know that there must be more specialists than generalists so assume that there's only one generalist and that there are x specialists. Also from statement 1 you know that the average for generalists is 50 more than the average for specialists. So you can pick numbers to represent this. I chose 150 for the generalists and 100 for the specialists. Set up the equation and solve for x.

# GMAT Question of the Day - Data Sufficiency - Inequalities

If m and z are positive numbers is 30m/(m+z) + 50z/(m+z) greater than 39?

(1) z/m > 1

(2) m/(m+z) < 1/2

## GMAT Question of the Day Solution:

Look at this as a weighted average question. If m = z then the answer will end up in the middle of 30 and 50. In this case 40. So the real question here is: z > m?  If this is confusing then I would suggest trying some numbers to make this concept very clear. Make  z=m, z > m, and finally m > z. Hopefully that will shed some light on how this question works (I worked this out at the bottom).

(1) Simplify the algebra to z > m. If z is greater than m then the value of the expression must be closer to 50 than 30. So the expression must be greater than 39. Sufficient.

(2) If the first part of the expression has less than half of the weight than the total expression must be closer to 50 then 30. So the expression must be greater than 39. Sufficient.

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