GMAT Prep Question

[kriti87]

Hi, Please help.

For a certain examination, a score of 58 was 2 standard deviations below the mean and a score of 98 was 3 standard deviations above the mean. What was the mean score for the exam?

The answer is supposed to be 74.

Please provide a solution for this.

thanks,

kriti87

[vineeshp]

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

Subtracting 2nd from 1st.

5SD = 40
SD = 8

M = 58 + 2SD
= 58 + 16 = 74.

[Anurag@Gurome]

Hi, Please help.

For a certain examination, a score of 58 was 2 standard deviations below the mean and a score of 98 was 3 standard deviations above the mean. What was the mean score for the exam?

The answer is supposed to be 74.

Please provide a solution for this.

thanks,

kriti87

Let us assume that the mean = x and 1 standard deviation = y. We want to find the value of x.
Then, x - 2y = 58 and x + 3y = 98
Multiply eqn 1 by 3 and eqn 2 by 2, 3x - 6y = 174 and 2x + 6y = 196
Next add the equations: 5x = 370 or x = 74

[blaster]

distance between 58 and 98 is 5 standard deviation,so

58+5x=98
x=8

58 is 2 standard deviation apart from mean,so

58+8*2=74