What is the value of X in the above list of 7 numbers?

Target question: What is the value of X?

Statement 1: The average (arithmetic mean) of these 7 numbers is 80.

We can write: \(\frac{X + 81+73+71+98+73+64}{7}=80\)

Multiplyvboth sides of the equation by \(7\) to get: \(X + 81+73+71+98+73+64 = 560\)

At this point, we can see that we COULD solve this equation for X, which means we could answer the target question (but we would never waste time doing so on test day)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The range of these 7 numbers is 36.
Let's arrange the 6 KNOWN values in ascending order: 64, 71, 73, 73, 81, 98
98 - 64 = 34
So the range of the 6 KNOWN values is 34.
To get a range of 36, X can be one of two different values. Consider these two cases:

Case a: x = 62, which means we get: 62, 64, 71, 73, 73, 81, 98. Range = 98 - 62 = 36 (Perfect!) In this case, the answer to the target question is x = 62
Case b: x = 100, which means we get: 64, 71, 73, 73, 81, 98, 100. Range = 100 - 64 = 36 (Perfect!) In this case, the answer to the target question is x = 100
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent