Standard Dev again!!

[zagcollins]

For a certain examination, a score of 58 was 2 SD's below the mean, and a score of 98 was 3 SD's above the mean. What was the mean score for the examination?

A.74
B.76
C.78
D.80
E.82

OA is 74....solved it correctly but not sure whats the best method to do this...m counting on the math experts....

[pepeprepa]

Mean=M
S=Standard Deviation


A score of 58 was 2 SD's below the mean, we can write it like this:
58=M-2S

And a score of 98 was 3 SD's above the mean.
98=M+3S

2 equations and 2 unknowns, it's ok:
58+2S=M
so we reimplace in the second one, it gives
98=58+2S+3S
40=5S
S=8

Now,
58+2S=M
58+2*8=M
M=74

[zagcollins]

pepeprepa, you are going to absolutely tear apart the demon called GMAT!

[dbart06]

Here is how i solved it :

98-58 = 5sd's this means each sd =8

2sd +58=74
98-3sd=74