Bunuel wrote:
Tough and Tricky questions: Statistics.
x is an integer greater than 7. What is the median of the set of integers from 1 to x inclusive?
(1) The average of the set of integers from 1 to x inclusive is 11.
(2) The range of the set of integers from 1 to x inclusive is 20.
X>7 and the set (let it be S) contains 1 to X inclusive.
I normally read both the statements and start with the easier one. In this case, it is statement 2.
Statement 2: If the range is 20. Then X must be 21. Since X is the last term. In this case, we can easily find the median. So Sufficient.
Statement 1: If we know the average of the set, we can find the sum and number of elements in the set. But this is a tedious process to jot down all the numbers and find the sum.
But we can use statement 2 as a clue to solve this easily without crushing our brain. Since two statements never contradicts each other. If we plugin X as 21. We get the sum as 231(using the sum of n numbers formula) and average as 11.
Bingo!!
We can find the median from this statement as well. So Sufficient.
Answer : D: Both statement Individually sufficient to solve.
since number are consecutive integers. therefore there sum from 1 to x can be given as (x(1+x))/2; where x is the last term