kiran120680 wrote:
A set S={10,1,5,a,b,6,c} where a,b&c are different positive integers, represents the different score of 7 teams in a match. What is the mean score of the 7 teams in the match?
I. a, b, c are 3 distinct prime numbers less than 9.
II. a=b+c, where b&c are consecutive integers less than 5.
Information from the question stem1. a, b, and c are different positive integers.
2. I am interpreting "represents different score of 7 teams in a match" to mean that the elements of set S are distinct.
What is to be found? Mean score of the 7 teams.
When is the data sufficient?If we can find a unique value for a + b + c or for a, b, and c independently the data is sufficient.
Evaluate statement 1 alonea, b, c are 3 distinct prime numbers less than 9.
Prime numbers less than 9 are 2, 3, 5, and 7.
Set S already includes 5 in it. Therefore, the values that a, b, and c can take are 2, 3, and 7 - not necessarily in that order.
Even though we do not know which of a, b, and c corresponds to the 3 values, we can find the sum, a + b + c and hence the mean of set S with this information.
Statement 1 alone is sufficient. Answer options narrow down to A or D.
Evaluate statement 2 alonea=b+c, where b&c are consecutive integers less than 5
Possible values for b and c
1. (1, 2)
2. (2, 3)
3. (3, 4)
Set S already includes 1. So, possibility 1 can be eliminated.
Set S already includes 5. So, possibility 2 can be eliminated. If b and c take values 2 and 3, the value of 'a' will be 5. That is not possible.
So, possibility 3 is the only one that is valid.
From statement 2, we can find a + b + c and hence the average of set S.
Statement 2 alone is also sufficient.
Choice D is the answer