Is x > 4? (1) |x| > 5 (2) x > -5

How come it's C? Both statements guarantee that x=> 5, but what about the space between +4 and +5?

Thanks!

Hello iliavko

Please note that your theory of x=> 5 is completely wrong

IXI>5
it means
if X is positive then X>5
if X is negative -X>5------>X<-5(multiply by -1 both sides and flip the sign)
so x could be X>5 or X<-5
Which is not sufficient to answer

statement (2) confirms that X is only greater than -5 so it could be anything > or < 4
so insuff to ans the question.

Combining both
from (1) we know X>5 or X<-5 and from (2) as X>-5 leaving only option from (1) that X>5(we are in no need to see for space between +4 and +5)
if X>5 ,So X must be >4
sufficient
Ans C

Plz let me know if u have any doubt..??

rohit thanks for the reply, i will go through a couple more DSs to see if I can get this better, I mean I know what you mean by your explanation, but it's strange to me that the interval between +4 and +5 is irrelevant. For me it's E.
1) x can be anything except -5 -> +5; 2) x can be anything -5 and forward. But combining 1 and 2, we have intersection only from +5 onward, so x IS greater then 4 (obviously), yes, but the fact that the intersection only starts at +5 confuses me. Anyways, I need some more practice and it will fall into place.

Thank you for the reply!

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 x > 4?

(1) |x| > 5
(2) x > -5


When it comes to inequality question, if range of que includes range of con, it is crucial that con is sufficient.
In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), in x<-5, 5<x, the range of que doesn’t include the range of con, which is not sufficient.
For 2), in x>-5, the range of que doesn’t include the range of con, which is not sufficient.
When 1) & 2), in 5<x, the range of que includes the range of con, which is sufficient.
Thus, C is the answer.


 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.

I still don't fully understand this. Can someone explain why we disregard anything between -5 and 4?

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