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Click the link immediately below to view the SAT Verbal diagnostic test.

AVERAGES
Problems involving averages are very common on the SAT. They can be classified into four major categories as follows.

I. The average of N numbers is their sum divided by N, that is, average = sum/N.

Example: The average of x, 2x, and 6 is

II. Weighted average: The average between two sets of numbers is closer to the set with more numbers.

Example: If on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather

Here, 90 has a weight of 3--it occurs 3 times. Whereas 80 has a weight of 2--it occurs 2 times. So the average is closer to 90 than to 80 as we have just calculated.

III. Using an average to find a number.

Sometimes you will be asked to find a number by using a given average. An example will illustrate.

Example: If the average of five numbers is -10, and the sum of three of the numbers is 16, then what is the average of the other two numbers?
(A) -33 (B) -1 (C) 5 (D) 20 (E) 25

Let the five numbers be a, b, c, d, e. Then their average is

Now three of the numbers have a sum of 16, say, a + b + c = 16. So substitute 16 for a + b + c in the average above:

Solving this equation for d + e gives d + e = -66. Finally, dividing by 2 (to form the average) gives

Hence, the answer is (A).

IV. Average Speed = Total Distance/Total Time

Although the formula for average speed is simple, few people solve these problems correctly because most fail to find both the total distance and the total time.

Example: In traveling from city A to city B, John drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was his average speed for the whole trip?
(A) 50 (B) 53 1/2 (C) 55 (D) 56 (E) 57 1/2

The total distance is 1(50) + 3(60) = 230. And the total time is 4 hours. Hence,