The daily high temperatures were recorded at an Antarctic weather stat

Question

The daily high temperatures were recorded at an Antarctic weather station. If a temperature of -38.2 degrees Celsius is 2 units of standard deviation below the mean temperature, and a temperature of -22.6 degrees Celsius is 4 units of standard deviation above the mean, which of the following temperatures is 1 unit of standard deviation above the mean?

A) -35.6 degrees Celsius
B) -33.0 degrees Celsius
C) -30.4 degrees Celsius
D) -27.8 degrees Celsius
E) -25.2 degrees Celsius
 
NOTE: I can think of at least 3 different ways to solve this question. 
Kudos for every correct solution.

BrentGMATPrepNow · Accepted Answer

Here's an approach that starts the same as abhimahna's solution and then takes a shortcut:

Let M = mean
Let d = standard deviation

So, we get: M - 2d = -38.2
and: M + 4d = -22.6

At this point, we COULD solve for the individual values, but we can save some time by simply ADDING the two equations to get: 
2M + 2d = -60.8
Divide both sides by 2 to get: M + d = -30.4
Since M + d represents 1 unit of standard deviation above the mean, the correct answer is -30.4

Answer:  C

abhimahna · Answer

Let us suppose mean = M and SD = d.

So, we are given M - 2d = -38.2

and M + 4d = -22.6

solving both the equations, we will get M = -33 an d = 2.6

So, we need to find out M + d = -33 + 2.6 = -30.4. Hence, C

BrentGMATPrepNow · Answer

Here's another approach:
 https://i1168.photobucket.com/albums/r500/GMATPrepNow/SD_zpsqspez3m3.png 
Notice that  1 unit of standard deviation above the mean  is an  equal distance  from  2 units of standard deviation below the mean  and  4 units of standard deviation above the mean .

So,  1 unit of standard deviation  will be the average of the  two outer values 
That is,  1 unit of standard deviation above the mean  = ( -38.2  +  -22.6 )/2
= 60.8/2
= 30.4

Answer: C

Abhigmat2019 · Answer

For moving 6 units Std Deviation above mean, temperature difference equals -22.6-(-38.2)= 15.6 units
Therefore, temperature difference for single unit SD above mean= 15.6/6= 2.6
Hence, for mean + 1 unit SD = -38.2+(2.6*3)= -30.4

Optn C

Kinshook · Answer

Given: The daily high temperatures were recorded at an Antarctic weather station.

Asked: If a temperature of -38.2 degrees Celsius is 2 units of standard deviation below the mean temperature, and a temperature of -22.6 degrees Celsius is 4 units of standard deviation above the mean, which of the following temperatures is 1 unit of standard deviation above the mean?

Let m be the mean and s be standard deviation.

-38.2 = m - 2d
-22.6 = m + 4d

6d = -22.6 - (-38.2) = 38.2 - 22.6 = 15.6
d = 15.6/6 = 2.6

m = -22.6 - 4*2.6 = -22.6 - 10.4 = - 33

The temperature 1 unit of standard deviation above the mean = m +d = -33 + 2.6 = - 30.4

IMO C

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The daily high temperatures were recorded at an Antarctic weather stat

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