MathRevolution wrote:
[Math Revolution GMAT math practice question]
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
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 questionSince we COULD answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: m = 2There 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 1Case 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 1Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
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