kumadil2011 wrote:S is a set of positive integers. The average of the terms in S is equal to the range of the terms in S. What is the sum of all the integers in S?
(1) The range of S is a prime number that is less than 11 and is not a factor of 10.
(2) S is composed of 5 different integers
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We are given that S is a set of positive integers and the average of the terms in S is equal to the range of the terms in S. We need to determine the sum of all the integers in S.
Statement One Alone:
The range of S is a prime number that is less than 11 and is not a factor of 10.
Using information in statement one, we know that the range of S is 3 or 7. Thus, the average of S is also 3 or 7. However, since we don't know whether it is 3 or 7, nor do we know the number of integers in S, statement one alone is not sufficient to answer the question.
Statement Two Alone:
S is composed of 5 different integers.
Since we don't know any of the 5 integers, statement two alone is not sufficient to answer the question.
Statements One and Two Together:
From statement one, we know that the range and average are either both 3 or both 7. From statement two, we know S is composed of 5 different positive integers. Thus, the sum of these 5 integers is either 15 (if the average is 3) or 35 (if the average is 7). Therefore, we have two cases to consider: range = average = 3 (case 1) and range = average = 7 (case 2).
Case 1: range = average = 3
We can let x = the smallest number, so the largest number = x + 3. We can "squeeze" 2 more integers between x and x + 3, namely x + 1 and x + 2. So, there could be only 4 different total integers. However, remember that there should be 5 different integers in S; thus, case 1 is not possible.
So, it must be case 2: range = average = 7. If that is the case, the sum of the 5 integers is 35.
For example, the 5 integers could be 4, 5, 7, 8, and 11. We see that the range is 11 - 4 = 7 and the sum is 4 + 5 + 7 + 8 + 11 = 35 with an average of 7.
Answer:
C
