gmattesttaker2 wrote:
A store received 7 crates of oranges. What was the standard deviation of the numbers of oranges in the 7 crates?

(1) For the 7 crates of oranges, the median of the numbers of oranges was equal to the greatest of the numbers of oranges.
(2) For the 7 crates of oranges, the range of the numbers of oranges was 0.

Aside: When solving questions involving standard deviation, always be on the lookout for scenarios where the standard deviation is zero. These are scenarios where all the values in a set are equal.


Target question: What was the standard deviation of the numbers of oranges in the 7 crates?

Statement 1: For the 7 crates of oranges, the median of the numbers of oranges was equal to the greatest of the numbers of oranges.
There are several sets of numbers that satisfy this condition. Here are two:
Case a: the 7 values are {2, 2, 2, 2, 2, 2, 2} in which case the standard deviation equals 0
Case b: the 7 values are {1, 1, 2, 2, 2, 2, 2} in which case the standard deviation does not equal 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: For the 7 crates of oranges, the range of the numbers of oranges was 0.
If the range = 0, then all 7 values are equal, which means the standard deviation equals 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent