Data Sufficiency

I read the question as asking, "How many 5's are in the set of 11 numbers?"
It's the only way I could make sense of the "how many" part.

Max@Math Revolution wrote:How many 5's are in the set of 11 numbers?

1) The average (arithmetic mean) of the 11 numbers is 5
2) The median of the 11 numbers is 5

Target question: How many 5's are in the set of 11 numbers?

Statement 1: The average (arithmetic mean) of the 11 numbers is 5
This statement doesn't FEEL sufficient, so I'll TEST some cases.
There are several sets of numbers that satisfy statement 1. Here are two:
Case a: {5,5,5,5,5,5,5,5,5,5,5} in which case there are ELEVEN 5's in the set
Case b: {0,1,2,3,4,5,6,7,8,9,10} in which case there is ONE 5 in the set
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: The median of the 11 numbers is 5
There are several sets of numbers that satisfy statement 2. Here are two:
Case a: {5,5,5,5,5,5,5,5,5,5,5} in which case there are ELEVEN 5's in the set
Case b: {0,1,2,3,4,5,6,7,8,9,10} in which case there is ONE 5 in the set
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several sets of numbers that satisfy BOTH statements. Here are two:
Case a: {5,5,5,5,5,5,5,5,5,5,5} in which case there are ELEVEN 5's in the set
Case b: {0,1,2,3,4,5,6,7,8,9,10} in which case there is ONE 5 in the set
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

RELATED VIDEO:
Mean, Median & Mode: https://www.gmatprepnow.com/module/gmat ... /video/800