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What is the value of x among 25, 26, 30, 35, 36, 40, and x?

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by Max@Math Revolution » Fri May 13, 2016 4:11 am
What is the value of x among 25, 26, 30, 35, 36, 40, and x?
1) The range of them is 25
2) The median of them is 30

* A solution will be posted in two days.
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by 800_or_bust » Fri May 13, 2016 5:16 am
Max@Math Revolution wrote:What is the value of x among 25, 26, 30, 35, 36, 40, and x?
1) The range of them is 25
2) The median of them is 30

* A solution will be posted in two days.
(1) Insufficient. X could be 50, or it could be 15. Either of these values would result in a range of 25.

(2) Insufficient. This simply tells us that x must be less than or equal to 30. There are an infinite number of possibilities.

(1) & (2) combined are SUFFICIENT. X must be less than or equal to 30 AND x must be either 50 or 15. Therefore, x must be 15.
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by Max@Math Revolution » Sun May 15, 2016 8:11 pm
There is 1 variable (x) in the original condition. In order to match the number of variables and the number of equations, we need 1 equation. Hence, there is high chance that D is the correct answer choice.
In the case of the condition 1), x=15 and 50. So, it is not sufficient.
In the case of the condition 2), x≤30. So it is also not sufficient.
Using the condition 1) and the condition 2) at the same time, we get x=15. Hence, the answer is unique and the conditions are sufficient. The correct answer choice is C.

- 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.
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