Data Sufficiency

Is n > 6 ?
1) square_root(n)>2.5
2) n>square_root(37)

My answer was A . I was about to choose D (Both independently sufficient) but I chose A because square_root(37) could be positive or negative and there is no additional information about n like n> 0 or n represent distance/children.

Why is D right answer.

Brent,
Thanks for replying but it still does not answer my question .

How can you say with 100% assurance

'We know that √37 > √36'

What if √37 = -6.08

The problem should read as follows:

Is n > 6 ?
1) √n > 2.5
2) n > √37

√ means the POSITIVE ROOT ONLY.

Statement 1:
Squaring both sides, we get:
(√n) > (5/2)²
n > 25/4
n > 6.25.
Thus, n > 6.
SUFFICIENT.

Statement 2: n > √37
Since √37 > √36, √36 = 6, √37 > 6.
Thus:
n > √37 > 6.
n > 6.
SUFFICIENT.

The correct answer is D.

To clarify:
n² = 25 implies that n = ±5.
But since √ means the positive root only:
n = √25 implies that n = 5.

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.

Is n > 6 ?
1) square_root(n)>2.5
2) n>square_root(37)

For inequality questions, if the range of the question includes that of the condition, the condition is sufficient.
There is one variable (n) and 2 equations are given by the 2 conditions, giving a high chance (D) will be the answer.
For condition 1, if we square both sides of sqrt (n)>2.5, n>2.5^2=6.25. This is sufficient.
For condition 2, n> sqrt(37)>sqrt(36)=6. This is sufficient. Therefore the answer is (D)

For cases where we need 1 more equation, such as original conditions with "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations", we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.