What is the mean of the exams taken by a group of students?

VERITAS PREP OFFICIAL SOLUTION:

The correct response is (C).

While this data sufficiency employs statistical terms, it is an algebra question that can be solved using the technique of simultaneous equations.

Statement (1) can be expressed as: Mean + 3 Standard Deviations = 95. Since this one equation has two unknowns it is insufficient to determine the mean.
Statement (2) can be expressed as: Mean – 2 Standard Deviations = 60. Since this one equation has two unknowns it is insufficient to determine the mean.
If you combine the two, you have two equations with two unknowns:

Mean + 3 Standard Deviations = 95
Mean – 2 Standard Deviations = 60 By subtracting the second equation from the first one, you get:

5 Standard Deviations = 35

By dividing both sides by 5, you get:

1 Standard Deviation = 7

By substituting this value into either equation you get the mean.

The mean is 74, making (C) the correct response.

What is the mean of the exams taken by a group of students?

(1) The score 3 standard deviations above the mean is 95
(2) The score 2 standard deviations below the mean is 64

First, notice this is a data sufficiency question asking about a specific value. So, I'm evaluating whether the statements give me one value.

Statement 1 - Insufficient.

Standard deviation is the average distance of each number from the mean. Let's call standard deviation x. We also don't know the mean, so let's call this A (for average). Statement one tells me that 95 is 3 standard deviations above the mean. Another way of saying this is 95=3x+A. I have two variables, so I can't solve for the average. This statement is insufficient.

Statement 2 - Insufficient.

Like statement 1, statement 2 gives me another equation, 64=A-2x. Once again, I have two variables, so I can't solve for the average. This statement is insufficient.

Finally, my only task left is to see whether I could combine these two statements to find a specific value for the mean, or if they still wouldn't be sufficient when taken together. I have two equations, and they're different.

Looking at them together, like the below, I see I could combine them-specifically, subtract "A" from "A"--to isolate one variable, "x".

95=3x+A
64=A-2x
_____________

This is enough for me to say that combining statements 1 and 2 would enable me to solve for x--the mean--making C the correct answer.

I don’t understand the info in the statement.

What does the score 3 or the score 2 mean?

In my opinion it is not written in proper english.

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