canbtg wrote:Let S be a finite set of consecutive multiples of 7. How many terms are there in S?

(1) The sum of the terms in set S is 105.
(2) The standard deviation of set S is equal to 3.5

Statement 1: The sum of the terms in Set S is 105
For any EVENLY SPACED SET, the number of terms = sum/median.

Case 1: median = 35.
Number of terms = sum/median = 105/35 = 3.
Since the median of the 3 consecutive multiples of 7 is 35, we get:
Set S = {28, 35, 42}, with the result that the sum = 28+35+42 = 105.

Case 2: median = 21
Number of terms = sum/median = 105/21 = 5.
Since the median of the 5 consecutive multiples of 7 is 21, we get:
Set S = {7, 14, 21, 28, 35}, with the result that the sum = 7+14+21+28+35 = 105.

Since there are 3 terms in Case 1 but 5 terms in Case 2, INSUFFICIENT.

Statement 2: The standard deviation of set S is equal to 3.5
For any EVENLY SPACED SET, average = median.
Let m = the average and median of Set S.
Since Set S is composed of consecutive multiples of 7, Set S is composed of values drawn from the following:
...m-21, m-14, m-7, m, m+7, m+14, m+21...

Standard deviation is determined by DISTANCES FROM THE MEAN.
If Set S has 3 terms {m-7, m, m+7}, the combination of distances will be different than if Set S has 5 terms {m-14, m-7, m, m+7, m+14}.
As a result, each case will yield a DIFFERENT STANDARD DEVIATION.
Implication:
Only ONE combinations of distances will yield a standard deviation of 3.5.
Thus, the number of terms required to yield the right combination of distances can be determined.
SUFFICIENT.

The correct answer is B.