from statement (1),\(\frac{x+81+73+71+98+98+73+64}{7} = 80\), so with an equation of one variable, we can know the value of x --> sufficient

from statement (2), the range of 36 can be either (98-x) or (x-64), and the value of x can be either 32 or 100 respectively --> insufficient
A

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
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I think the only trap here was the range which could be seen two ways and not only one

Statement 1:

We now know the sum is 7*80, subtract the rest of the known numbers to find x. Sufficient.

Statement 2:

The current range without x is \(98 - 64 = 34\). So x will need to expand the range by 2, it can be \(x = 98 + 2\) or \(x = 64 - 2\) to expand the range. We don't know which one is x so this is insufficient.

Ans: A
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Given:
List of numbers: X, 81, 73, 71, 98, 73, 64

To find:
Value of X

Process above:
There is only missing number in above list.
Let's arrange the list in ascending order: 64, 71, 73, 73, 81, 98, X. Put X at the end of list for the time being.

1) Mean(m) = 80. From mean we can find the sum of all number of the list and as X is the only missing one, we can find X easily. Sufficient

2)Range R = 36. Without X in the list, range of list = 34. So we know for sure that X can't be anywhere in between the list, it has to be at one of the ends for the range to be 36.
But X can be at the left end(smallest element, X=62) or X can be at the right end(largest element X = 100). Not Sufficient

Hence answer is A

64,71,73,73,81,98,x

(1) When AM=80 Sum=560

64+71+73+73+81+98+x=560
x=100
Sufficient.

(2) When range =36
x could be 100 or 62.
Not sufficient.

A
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(1) Knowing the average, we can certainly find the average of x. SUFFICIENT.

(2) Be wary when they give the range of a set of numbers. x could be 98 - 36 = 62 or it could be 64 + 36 = 100; INSUFFICIENT.

Answer is A.
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