BTGModeratorVI wrote: ↑

Sun Apr 05, 2020 9:04 am

If the average (arithmetic mean) of a, b and c is m, is their standard deviation less than 1?

1) a, b and c are consecutive integers with a < b < c.
2) m = 2

Answer: A
Source: Math Revolution

Target question: Is the standard deviation of a, b and c less than 1?

Statement 1: a, b and c are consecutive integers with a < b < c.
It's important to know that standard deviation is a measure of dispersion (how spread apart the values are).
So, ANY 3 consecutive integers will have the same standard deviation.
For example, the standard deviation of {1,2,3} = the standard deviation of {6,7,8} = the standard deviation of {23,24,25} etc
So, IF we calculate the standard deviation of {1,2,3} then THAT value will provide sufficient info to the answer to the target question
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: m = 2
There are several values a, b and c that satisfy statement 2. Here are two:
Case a: a = 2, b = 2 and c = 2 (mean = 2 and standard deviation = 0). In this case, the answer to the target question is YES, the standard deviation IS less than 1
Case b: a = -100, b = 0 and c = 106 (mean = 2 and standard deviation = some number much greater than 1. In this case, the answer to the target question is NO, the standard deviation is NOT less than 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent