SAT Preparation Tools

Solution: To solve this problem, we simply need to remember what it means when a number is an average (or mean) of a particular data set. The average or mean = Sum of the terms / Number of terms

Here, 8 numbers have an average of 8. Therefore, their sum is 8 x 8 = 64.

If we subtract 2 from 4 of the numbers, it removes 2(4), or 8 from the sum.
The new sum is therefore 64 - 8 = 56, which means that the new average is 56/8 =7. Choice D is correct.

Example 2: Problems with Variables

The average (mean) SAT score for a group of M students in Montana is 1400, while the mean SAT score for a group of V students in Virginia is 1650. When the scores of both groups are combined, the mean is 1600. What is the value of V/M?

a.	1/4
b.	1/2
c.	1
d.	2
e.	4

Solution: From the data in the problem, we can write an equation to identify the value of V/M:

Remember, the average (or mean) of the data set is simply the sum of the scores over the number of scores. Therefore, our equation becomes:

(Montana Students + Virginia Students)/(Total Students) = 1600

Montana Students = 1400 M
Virginia Students = 1650V
Total Students = M + V
Overall Mean = 1600

Mathermatically, this reduces to:

{1400M + 1650V} / (M + V) = 1600
1400M + 1650V = 1600M + 1600V
50V = 200M
V = 4M
V/M = 4. Choice E is correct.

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