please explain gmat prep question

[yvonne12]

for certain examination , a score of 58 was 2 standard eviation below the mean and a score of 98 was 3 standard deviation above the mean. what was the score for the exam?

ans 74

[800GMAT]

You mean, what was the mean score for the exam.

Let M be Mean
and D be standard deviation

M-2D=58
M+3D=98

Solving the above equations, You get mean score = 74

[yvonne12]

Am I subtracting these equations, am I solving them separately?

can you expand this solution for me?

thank you

[aim-wsc]

Am I subtracting these equations, am I solving them separately?

can you expand this solution for me?

thank you

you need M so you should not subtract.
multiply eqn1 by 1.5 and add both eqns.
it'll be

2.5 M= 185

[yvonne12]

multiply eqn 1 by 1.5, which is half of 3, is this the way to solve this type statistic problem?

so, if the second eqn was + 4 , for instance, I multiply the first eqn by 2?

Please clear this up for me, why am I multiplying the first eqn by 1.5??

On your first recponse, you said solve for both eqns, yet in the GMAT responses this is equivalent to adding or subtracting equations such as this one.

I simply would like to know, for future refrence, how would I be able to solve questions or problems like this one in a standard setting.

Your explanation is unclear to me.

[gabriel]

multiply eqn 1 by 1.5, which is half of 3, is this the way to solve this type statistic problem?

so, if the second eqn was + 4 , for instance, I multiply the first eqn by 2?

Please clear this up for me, why am I multiplying the first eqn by 1.5??

On your first recponse, you said solve for both eqns, yet in the GMAT responses this is equivalent to adding or subtracting equations such as this one.

I simply would like to know, for future refrence, how would I be able to solve questions or problems like this one in a standard setting.

Your explanation is unclear to me.

alright yvonne .. according to the given information in the q we get two eqns

M-2D=58 ....(1)
M+3D=98....(2)

this is what we call a simultaneous eqn ...

simultaneous eqn is a eqn that has two unknown variables (in this case M & D) .... and two linear eqn for these variables...

when we have a pair of simultaneous eqn bfor us our aim is to find out values of the two unknown variable ....

one way of solving this is subtracting the first eqn form the first one ... so we get M+3D -M +2D =98-58=40 ... 5D=40....D=8 ...substituting this value of D in either of the eqn we get M=74...

but since in the above problem only M is of importance to us we can proceed by eliminating D from the eqn ... if u look at the 2nd eqn u wuld see that the coefficient of D is 3 so if we multiply the 1st eqn by 3/2 ... D in the first eqn too wuld have 3 as a coefficient... once this is done we can add the two eqn which wuld eliminate the -3D in the 1st eqn and the +3D in the 2nd eqn...

alternatively ..as the D in the 1st eqn has a coefficient of 2 u culd multiply the 2nd eqn by 2/3 which will make the coefficient of D in the 2nd eqn =2 ... and then again adding the 2 eqns... wuld eliminate D and give a eqn only in M...

the basic aim is to eliminate D ...so that u get a eqn in M alone..... and yes if u had +4D in the 2nd eqn u wuld multiply the first eqn by 2 and then add the 2 eqns...

[yvonne12]

thank you, that was most helpful.

[Cybermusings]

Let the standard deviation be x.

58 + 2x = 98 - 3x

Therefore 5x = 40 and x = 8

Hence mean = 58 + 2*8 or 98 - 3*8 = 74