rohitgarg 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.
A - average
(1) Primes less than 11 are 2, 3, 5, and 7. Not factor of 10, we are left with 3 and 7.
If A = 3, we can have {2, 2, 3, 5} or {1, 2, 3, 4, 4, 4}.
Not sufficient.
(2) For 5 evenly spaced numbers, k - 2d, k - d, k, k + d, k + 2d the range is 4d and the average is k.
We can simply take k = 4d, and we have infinitely many sets fulfilling the condition of the form {2d, 3d, 4d, 5d, 6d}.
For example {2, 3, 4, 5, 6}, {20, 30, 40, 50, 60}...
Not sufficient.
(1) and (2) together:
We have seen above that the range can be either 3 or 7.
If the range is 3, we cannot have 5 distinct integers in the set, so only 7 is left.
We know that the sum of the 5 integers is 5 * 7 = 35, the smallest number is k and the largest number is k + 7, where k is some positive integer.
Necessarily 35 - 7 = 28 > 5k, so k must be not greater than 5.
If k = 5, the first and the last number are 5 and 12. The smallest 3 remaining integers are 6, 7, and 8 together with 5 and 12 will give a sum of 37.
If k = 4, we find sets which fulfill the condition: {4, 5, 7, 8, 11} and also (4, 5, 6, 9, 11}.
Obviously, not sufficient.
Answer E.
CORRECTION:
What a miss! We have to find the sum of the numbers and not the set of numbers. Although there is more than one possibility, the total sum is clearly 7*5 = 35.
Answer C.
And IanStewart is right about (1), in a set of numbers, each element is different.
_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.