Max@Math Revolution wrote:
What is the range of 10 numbers?
1) The average (arithmetic mean) of the 10 numbers is 10
2) The greatest of the 10 numbers is 15
Target question: What is the range of 10 numbers?
Statement 1: The average (arithmetic mean) of the 10 numbers is 10
Let's TEST some values.
There are several sets of numbers that satisfy statement 1. Here are two:
Case a: the numbers are {10, 10, 10, 10, 10, 10, 10, 10, 10, 10}. In this case, the answer to the target question is
the range is 0
Case b: the numbers are {0, 10, 10, 10, 10, 10, 10, 10, 10, 20}. In this case, the answer to the target question is
the range is 20
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The greatest of the 10 numbers is 15
There are several sets of numbers that satisfy statement 2. Here are two:
Case a: the numbers are {10, 10, 10, 10, 10, 10, 10, 10, 10, 15}. In this case, the answer to the target question is
the range is 5
Case b: the numbers are {0, 10, 10, 10, 10, 10, 10, 10, 10, 15}. In this case, the answer to the target question is
the range is 15
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
There are still several sets of numbers that satisfy BOTH statements. Here are two:
Case a: the numbers are {5, 10, 10, 10, 10, 10, 10, 10, 10, 15}. In this case, the answer to the target question is
the range is 10
Case b: the numbers are {0, 10, 10, 10, 10, 10, 10, 10, 15, 15}. In this case, the answer to the target question is
the range is 15
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
