GMAT Prep Data Suffeciency problem

[krishna239455]

Pls help to solve this problem.

[Anurag@Gurome]

Pls help to solve this problem.

(1) 4 is the integer closets to X + Y implies 3.5 < (X + Y) < 4.5; NOT sufficient.
(2) 1 is the integer closest to X - Y implies 0.5 < (X - Y) < 1.5; NOT sufficient.

Combining (1) and (2), we add the two inequalities in statements 1 and 2,
(3.5 + 0.5) < (X + Y) + (X - Y) < (4.5 + 1.5)
4 < 2X < 6
2 < X < 3, which implies X can be closer to 2 as well as 3, as if X = 2.2, then it is closer to 2 and if X = 2.9 then X is closer to 3; NOT sufficient.

The correct answer is E.

[krishna239455]

Dear Anurag
One doubt:
I have seen your style that when you deal with inequalities and when you combine two statements, you directly add them up.
Is this the correct way?

[Anurag@Gurome]

Dear Anurag
One doubt:
I have seen your style that when you deal with inequalities and when you combine two statements, you directly add them up.
Is this the correct way?

If inequalities face the same way, we can add them directly. Example: If z - 3m > 0 and 4m - z > 0, you can add those in their current state (since both of the inequality signs are "greater than") to yield m > 0. 

If the inequalities are of the form, a < b and c > d, and we want to combine them, then simply turn one of them around by multiplying by a negative quantity, usually -1: -a > -b, c > d 
Adding we get, c - a > d - b