Data Sufficiency

BTGmoderatorDC wrote: ↑

Wed May 03, 2023 1:27 am

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.


OA B

Source: GMAT Prep

Key concept: The standard deviation of a set of values is zero if and only if all of the values in the set are equal

Given: A store received 7 crates of oranges.

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 many different scenarios that satisfy statement 1. Here are two:
Case a: The number of oranges in each of the seven crates is {9,9,9,9,9,9,9}. In this case, the answer to the target question is the standard deviation of the numbers of oranges in the 7 crates is 0
Case b: The number of oranges in each of the seven crates is {2,2,2,9,9,9,9}. In this case, the answer to the target question is the standard deviation of the numbers of oranges in the 7 crates is NOT 0
Since we can’t 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 equals 0, then (biggest number in the set) - (smallest number in the set) = 0, which means all of the numbers in the set must be equal.
If all of the numbers in the set are the same, then the standard deviation of the set must be zero
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B