When there are consecutive integers and if their range is eq

[Max@Math Revolution]

When there are consecutive integers and if their range is equal to their median, what is the number of them?

1) The smallest number of them is 5
2) The largest number of them is 15


* A solution will be posted in two days.

[Dario@VinciaPrep]

We can represent this set in two different ways.

If we say that n is the first number in the set, and that 2a is the range, then:
- the range is 2a
- the median is n+a
And if 2a=n+a, it means that n=a.

If we say that m is the last number in the set, and that 2a is the range, then:
- the range is 2b
- the median is m-b
And if 2b=m-b, it means that m=3b.

Statement 1 alone states that n=5. This means that a=5, so the median will be 10, the last number will be 15, and the set will have 11 elements. STATEMENT 1 ALONE IS SUFFICIENT.

Statement 2 alone states that m=15. This means that b=5, so the median will be 10, the first number will be 5, and the set will (again) have 11 elements. STATEMENT 2 ALONE IS SUFFICIENT.

Thus the answer is (D).

[Max@Math Revolution]

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

When consecutive integers are there and if their range is equal to their median, what is the number of them?

1) The smallest number of them is 5
2) The largest number of them is 15


In the original condition, there are 2 variables(you need to figure out the starting number and the number of them) and 1 equation(range=median), which should match with the number of equations. So you need 1 variable. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), only 5,6,7,8,9,10,11,12,13,14,15 are possible and so as 2).
Therefore, the answer is D.