E?

E is correct, pls explain how?

Just pick some crazy numbers.

For example, statement 1 says 4 is closest integer to x+y. So let's make x=2.5 and y=1.5, for a perfect 4. Of course, we could debate that the question is garbage since 2.5 can't be said to be closer to 2 or 3, but let's ignore that for a moment. Now we could also say that x = -2.5 and y = 6.5 for a perfect 4 again. (it says nothing about negatives) Mulitple values are possible.

We can do the exact same thing for statement 2.

Now, putting them together we can again use our x=2.5 and y=1.5, but we could fiddle slightly. x=2.25 and y=1.5 to get 3.75 when we add and .75 when we subtract. Going the other way x=2.75 and y=1.5 we'd get 4.25 when we add and 1.25 when we subtract. Both sets fit the statements, but we bounce from closer to 2 to closer to 3.

Cheers,
Steve

I did it this way.

Obviously we can rule out A, B and D.

1) x + y is closest to 4.
2) x - y is closest to 1. That means x > y.

From 1) 3.5 < x+y < 4.5
From 2) 0.5 < x - y < 1.5

Adding both we get
4 < 2x < 6 which means 2 < x < 3. Well x could be nearer to 2 or 3 we don't know. Hence E.

Calista.