Problem Solving

A little extra background on standard deviations above and below the mean

If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc

So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean = 17 [since 9 + 2(4) = 17]
1.5 standard deviations BELOW the mean = 3 [since 9 - 1.5(4) = 3]
3 standard deviations ABOVE the mean = 21 [since 9 + 3(4) = 21]
etc.
-----------------------------

Okay, now onto your question:

src_saurav wrote:If two deviations down the mean is 58 and three up is 98. What is the mean?

Let M = the mean
Let d = 1 standard deviation

two [standard] deviations down [below] the mean is 58
So, M - 2d = 58

three deviations above the mean is 98
So, M + 3d = 98

We now have the following system that we can solve for M:
M - 2d = 58
M + 3d = 98

Subtract the top equation from the bottom equation to get: 5d = 40
Solve to get d = 8

Now that we know d = 8, plug d = 8 into one of the equations we created.
M - 2d = 58 becomes M - (2)(8) = 58
Simplify: M - 16 = 58
Solve: M = 74

ASIDE: We have 2 free videos on standard deviation:
Part I: https://www.gmatprepnow.com/module/gmat- ... ics?id=806
Part II: https://www.gmatprepnow.com/module/gmat- ... ics?id=809